*Article* **Comparison of the Nucleation Parameters of Aqueous L-glycine Solutions in the Presence of L-arginine from Induction Time and Metastable-Zone-Width Data**

**Lie-Ding Shiau 1,2**


**Abstract:** Induction time and metastable-zone-width (MSZW) data for aqueous L-glycine solutions in the presence of L-arginine impurity were experimentally measured using a turbidity probe in this study. The nucleation parameters, including the interfacial free energy and pre-exponential nucleation factor, obtained from induction time data, were compared with those obtained from MSZW data. The influences of lag time on the nucleation parameters were examined for the induction time data. The effects of L-arginine impurity concentration on the nucleation parameters based on both the induction time and MSZW data were investigated in detail.

**Keywords:** crystallites; impurities; induction time; metastable zone width; nucleation parameters

#### **1. Introduction**

In crystal growth, the induction time is defined as the time interval between the establishment of the supersaturated state and the formation of detectable nuclei. The metastable-zone-width (MSZW) limit is defined as the time taken at a given cooling rate between the establishment of the supersaturated state and the formation of detectable nuclei. Nucleation is the initial process for the formation of crystals in liquid solutions. Thus, both the induction time and MSZW data are related to the nucleation rate of the crystallized substance in solutions. In classical nucleation theory (CNT) [1–3], the nucleation rate is expressed in the Arrhenius form, governed by two nucleation parameters, including the interfacial free energy and pre-exponential nucleation factor. The interfacial free energy is the energy required to create a new solid/liquid interface for the formation of crystals in liquid solutions, while the pre-exponential factor is related to the attachment rate of solute molecules to a cluster in the formation of crystals. The influences of impurities on the nucleation parameters have long been investigated using induction time or MSZW data with the addition of different impurities in solutions for a variety of compounds [4–14].

The nucleation parameters of a crystallized substance have been traditionally determined from induction time data by assuming *ti* <sup>−</sup><sup>1</sup> ∝ *J*, where *J* is nucleation rate [1]. Recently, various methods have been proposed to calculate the nucleation parameters from MSZW data [15–21]. Although the induction time and MSZW processes are two different temperature-controlling methods for determination of the nucleation parameters in a crystallization system, a model should be available to relate the induction time and MSZW data with the nucleation parameters. Furthermore, as a cooling process is applied first to reach the desired operating temperature and then a constant temperature is adopted in the induction time measurements, there always exists a lag time between the prepared supersaturated solution being at a higher temperature and it being cooled to the desired lower constant temperature. For simplicity, the lag time is usually neglected in determining the nucleation parameters from the induction time data.

The nucleation process can behave differently. For certain systems, induction time cannot even be considered due to sharp phase transition, while for some cases there is

**Citation:** Shiau, L.-D. Comparison of the Nucleation Parameters of Aqueous L-glycine Solutions in the Presence of L-arginine from Induction Time and Metastable-Zone-Width Data. *Crystals* **2021**, *11*, 1226. https:// doi.org/10.3390/cryst11101226

Academic Editors: Heike Lorenz, Alison Emslie Lewis, Erik Temmel and Jens-Petter Andreassen

Received: 14 September 2021 Accepted: 11 October 2021 Published: 12 October 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

induction time governed by different material properties. For example, by evaporating a cellulose nanocrystal-based cholesteric drop, the drop edges are pinned to the substrate, which leads to nonequilibrium sliding of the individual cholesteric fragment with active ordering [22]; following the induction period of cholesteric collagen tactoids, phase separation goes through the nucleation process during which multiple chiral nuclei spontaneously emerge and grow throughout the continuous isotropic phase [23]. In the present work, a model was proposed based on CNT to relate the induction time and MSZW data with the nucleation parameters for the systems with an experimentally measurable nucleation point. The proposed model was then applied to determine the nucleation parameters for the aqueous L-glycine solutions in the presence of L-arginine impurity from the induction time and MSZW data. The effects of lag time on the nucleation parameters within the induction time data were investigated. L-glycine was adopted in this work as it is the simplest amino acid and is often used as a model compound in the study of solution nucleation [24–30]. L-arginine is another amino acid which was randomly chosen as impurity in the aqueous L-glycine solutions.

#### **2. Theory**

The nucleation rate according to CNT is expressed as [1–3]

$$J = A \exp\left[-\frac{16\pi v^2 \gamma^3}{3k\_B T^3 \ln^2 S}\right] \tag{1}$$

where *A* is the nucleation pre-exponential factor, *γ* is the interfacial free energy, *kB* is the Boltzmann constant, *v* = *Mw*/*ρcNA* is the molecular volume, *T* is the temperature, and *S* is the supersaturation.

A model is derived based on CNT to determine *γ* and *A* by relating the induction time and MSZW data with *J* as follows. If a solution saturated at *T*<sup>0</sup> is cooled to *Tm* at a constant cooling rate *b* within the time period *t* = 0 to *tm* and then the temperature is kept at *Tm* within the time period *tm* to *tm* + *ti*, the nucleation event for this combined process is assumed to be detected at *t* = *tm* + *ti*. If *tm* is small compared to *ti*, this combined process can be regard as the induction time process with consideration of the lag time *tm*, which is the time required for the solution saturated at *T*<sup>0</sup> to cool to *Tm* at cooling rate *b*. Thus, Δ*Tm* = *T*<sup>0</sup> − *Tm* and the lag time is given by *tm* = Δ*Tm*/*b*. This combined process for *tm* = 0 corresponds to the induction time process without consideration of the lag time. On the other hand, this combined process for *ti* = 0 corresponds to the MSZW process.

Figure 1 depicts the MSZW process for a saturated solution of *C*<sup>0</sup> cooled at a constant cooling rate *b*, where *T*<sup>0</sup> is the initial saturated temperature at *t* = 0, *Tm* is the nucleation temperature at *tm*, *C*<sup>0</sup> is the saturated concentration at *T*0, *Cm* is the saturated concentration at *Tm*, *Ceq*(*T*) is the solubility, and *S*(*T*) = *C*0/*Ceq*(*T*) is the supersaturation. As *Ceq*(*T*) generally decreases with decreasing temperature, *S*(*T*) increases and subsequently *J* increases with time. For the nucleation point at *tm*, *Sm* is the supersaturation at *Tm* defined as *Sm* = *C*0/*Ceq*(*Tm*) = *C*0/*Cm*. The nucleation rate at *Tm* is given by

$$J\_m = A \exp\left[-\frac{16\pi v^2 \gamma^3}{3k\_B ^3 T\_m ^3 \ln^2 S\_m}\right]. \tag{2}$$

**Figure 1.** A schematic diagram showing the increasing of supersaturation during the cooling process reproduced from Shiau [31], where *Ceq*(*T*) is the temperature-dependent solubility ( represents the starting point and • represents the nucleation point).

Note that both *Sm* and Δ*Tm* are measures of the MSZW.

As the first appearance of nuclei can be regarded as a random process, the stochastic process of nucleation can be described by the Poisson's law [32–34]. For the combined process described above, as the temperature is cooled from *T*<sup>0</sup> to *Tm* within the time period *t* = 0 to *tm*, *S*(*T*) increases and *J* increases with time; and as the temperature is kept at *Tm* within the time period *tm* to *tm* + *ti*, the supersaturation remains the same at *Sm* and *J* remains the same at *Jm*. Based on the given reasoning, the average number of expected nuclei *N* in a solution volume *V* within the time period *t* = 0 to *tm* + *ti* is proposed in this study as

$$N = \left(\int\_0^{t\_m} fVdt\right) + f\_m Vt\_i\,.\tag{3}$$

where the first term on the right-hand side represents the average number of expected nuclei generated within the time period *t* = 0 to *tm* and the second term on the right-hand side represents the average number of expected nuclei generated within the time period *tm* to *tm* + *ti*.

Based on the two-point trapezoidal rule for computing the value of a definite integral, one can derive [35]

$$\int\_{0}^{t\_m} fVdt = \frac{1}{2}(J\_0 + J\_m)Vt\_m = \frac{J\_mV\Delta T\_m}{2b} \,\, , \tag{4}$$

where *J*<sup>0</sup> and *Jm* represent the nucleation rate at *t* = 0 and *t* = *tm*, respectively. Note that *J*<sup>0</sup> = 0 at *t* = 0 when *S*(*T*0) = 1 and *tm* = Δ*Tm*/*b*.

According to the single nucleus mechanism (SNM) proposed by some researchers through experimental validation [32–34], a single primary nucleus is formed in a supersaturated solution, which grows out to a particular size and undergoes secondary nucleation by

crystal-stirring-impeller or crystal-wall collision. Based on the assumptions that the growth time between the formation of nucleus and growth to the minimum size for secondary nucleation is negligible, and one secondary nucleation is enough to generate detectable crystal volume increase in a negligible amount of time, the nucleation event is detected after the secondary nucleation of the single primary nucleus. Thus, the nucleation event for the combined process occurs at *t* = *tm* + *ti* when the first nucleus is formed. By substituting *N* = 1 in Equation (3), combining Equations (2)–(4) leads to

$$\ln\left(\frac{\Delta T\_m}{2b} + t\_i\right) = -\ln(AV) + \frac{16\pi v^2 \gamma^3}{3k\_B ^3 T\_m ^3 \ln^2 S\_m} \,\mathrm{}.\tag{5}$$

Thus, Equation (5) can be applied to determine the nucleation parameters from the induction time data, *ti*, with consideration of the lag time, Δ*Tm*/*b*. A plot of ln(Δ*Tm*/2*b* + *ti*) versus ln2 *Sm* should give a straight line, the slope and intercept of which permit determination of *γ* and *A*, respectively.

Equation (5) for Δ*Tm*/*b* = 0 reduces to

$$\ln t\_i = -\ln(AV) + \frac{16\pi v^2 \gamma^3}{3k\_B^3 T\_m^3 \ln^2 S\_m} \,\mathrm{}\,\mathrm{}\tag{6}$$

Which corresponds to the conventional method adopted in determination of *γ* and *A* from the induction time data without consideration of the lag time. Equation (5) for *ti* = 0 reduces to

$$\ln\left(\frac{\Delta T\_m}{2b}\right) = -\ln(AV) + \frac{16\pi v^2 \gamma^3}{3k\_B^3 T\_m^3 \ln^2 S\_m} \,\text{.}\tag{7}$$

Which can be applied to determine *γ* and *A* from the MSZW measurements, where a solution saturated at *T*<sup>0</sup> is cooled at a constant rate *b* from *t* = 0 to *tm* and the nucleation event is detected at *Tm*.

If the temperature-dependent solubility is described in terms of the van't Hoff Equation (1), one obtains

$$\ln S\_{\rm H} = \ln \left( \frac{C\_0}{C\_m} \right) = \frac{-\Delta H\_d}{R\_G} \left( \frac{1}{T\_0} - \frac{1}{T\_m} \right) = \left( \frac{\Delta H\_d}{R\_G T\_0} \right) \left( \frac{\Delta T\_m}{T\_m} \right) \,, \tag{8}$$

where Δ*Hd* is the heat of dissolution and *RG* is the gas constant. Substituting ln *Sm* in Equation (8) into Equation (7) yields

$$\left(\frac{T\_0}{\Delta T\_m}\right)^2 = \frac{3}{16\pi} \left(\frac{k\_B T\_0}{\upsilon^{2/3} \gamma}\right)^3 \left(\frac{\Delta H\_d}{R\_G T\_0}\right)^2 \left[\ln\left(\frac{\Delta T\_m}{b}\right) + \ln\left(\frac{AV}{2}\right)\right].\tag{9}$$

A plot of (*T*0/Δ*Tm*) <sup>2</sup> versus ln(Δ*Tm*/*b*) based on the MSZW data should give a straight line, the slope and intercept of which permit determination of *γ* and *A*, respectively. Equation (9) is consistent with the result developed by Shiau and Wu [21] in determination of *γ* and *A* from the MSZW data.

#### **3. Experimental Methods**

Deionized water, L-glycine (>99%, Alfa Aesar) and L-arginine (>98%, ACROS) were used to prepare the desired supersaturated solution for the specified impurity concentration. The experimental apparatus adopted by Shiau and Lu [18] was used in the study of nucleation, which consists of a 250 mL crystallizer equipped with a magnetic stirrer at a constant stirring rate of 350 rpm, immersed in programmable thermostatic water. A turbidity probe with a near-infrared source (Crystal Eyes manufactured by HEL limited, Hertford, UK) was used to detect the nucleation event.

The solubility of L-glycine in water from 303 K to 318 K was measured in this work. The solubility measurements indicated that the solubility of L-glycine in water was nearly not influenced by the presence of L-arginine ranging from *Cim* = 0–10 kg arginine/m3 solution, which corresponds to 0–0.02 mol arginine/mol glycine. The measured solubility of Lglycine in water was consistent with the solubility data reported by Park et al. [36]. In terms of the van't Hoff equation for the measured solubility, one obtains Δ*Hd* = 10.2 kJ/mol with *Ceq*(303 K) = 215 kg/m3 and *Ceq*(318 K) = 261 kg/m3 in this work.

For the induction time and MSZW experiments, a 200 mL aqueous L-glycine solution *<sup>V</sup>* = <sup>2</sup> × <sup>10</sup>−<sup>4</sup> <sup>m</sup><sup>3</sup> at the desired concentration was held at 5 K above the saturated temperature for 20 min to ensure a complete dissolution at the beginning of the experiments, which was also confirmed by the turbidity measurement. In the induction time experiments, the induction time and lag time data were measured by rapidly cooling the supersaturated solution at various supersaturations to 303 K. In the MSZW experiments, MSZW data were measured by cooling the solution saturated at 318 K with different constant cooling rates. Each run was carried out at least three times at each condition for the solubility, the induction time, and the MSZW measurements.

Although L-glycine can be crystallized in different polymorphs, including α-form, βform and γ-form, α-form is usually obtained from pure aqueous L-glycine solutions [24–30]. In this work, the final dried crystals at the end of the experiments were analyzed using Raman spectroscopy (P/N LSI-DP2-785 Dimension-P2 System, 785 nm, manufactured by Lambda Solutions, INC., Seattle, WA, USA) to validate the polymorph of the L-glycine crystals. By comparing with the Raman spectra of α-form crystals reported by Murli et al. [37], it was found that α-form L-glycine crystals were formed from aqueous L-glycine solutions in this work for various supersaturations without and with the presence of L-arginine impurity. Figure 2 shows some Raman spectra of the L-glycine crystals obtained in this work at *S* = 1.07 and *S* = 1.12 for *Cim* = 0 and *Cim* = 10 kg/m3, respectively.

**Figure 2.** *Cont*.

**Figure 2.** The Raman spectra of the produced L-glycine crystals at *S* = 1.07 and *S* = 1.12 for (**a**) *Cim* = 0 and (**b**) *Cim* = 10 kg/m3, respectively.

#### **4. Results and Discussion**

The induction time data of aqueous L-glycine solutions were measured for various supersaturations at 303 K in the presence of L-arginine for various impurity concentrations, *Cim*. The average induction times are listed in Table 1. The average lag times for the induction time data are listed in Table 2, which were measured based on *b* ∼= 0.038 K/s adopted for cooling the heated supersaturated solution to the desired constant temperature. The lag time corresponds to the time required for the heated solution to be lowered to 303 K. Thus, as the temperature range Δ*Tm* increases, the lag time increases. The MSZW data of aqueous L-glycine solutions saturated at *T*<sup>0</sup> = 318 K were measured for various *b* in the presence of L-arginine for *Cim* = 0–10 kg/m3. The average MSZWs are listed in Table 3. Note that *Mw* = 0.075 kg/mol, *<sup>ρ</sup><sup>c</sup>* = 1607 kg/m3, and *<sup>v</sup>* = 7.757 × <sup>10</sup>−<sup>29</sup> <sup>m</sup><sup>3</sup> for L-glycine.

**Table 1.** The average induction times, *ti*, in the induction time measurements for various impurity concentrations, *Cim*, and supersaturations, *S*, at 303 K. The standard deviations in the least significant digits are given in parentheses.


**Table 2.** The average lag time, Δ*Tm*/*b*, based on *b* ∼= 0.038 K/s in the induction time measurements for various impurity concentrations, *Cim*, and supersaturations, *S*, at 303 K, where Δ*Tm* corresponds to the temperature range for a solution with concentration *C*<sup>0</sup> saturated at *T*<sup>0</sup> and cooled to 303 K. Note that Δ*Tm* = *T*<sup>0</sup> − 303 K and *S* = *C*0/*Ceq*(303 K). The standard deviations in the least significant digits are given in parentheses.


**Table 3.** The average MSZWs, Δ*Tm*, in the MSZW measurements for a solution saturated at *T*<sup>0</sup> = 318 K cooled at various impurity concentrations, *Cim*, and cooling rates. The standard deviations in the least significant digits are given in parentheses.


Table 1 indicates that *ti* increases significantly with increasing *Cim* for each *S* and decreases with increasing *S* for each *Cim*. Thus, L-arginine exerts a nucleation inhibition effect in aqueous L-glycine solutions, which increases with increasing *Cim*. Table 2 indicates that Δ*Tm*/*b*, increases slightly with increasing *S* for each *Cim* and remains nearly independent of *Cim*. Note that Δ*Tm* corresponds to the temperature range for a solution saturated at *T*<sup>0</sup> cooled to 303 K, where *T*<sup>0</sup> increases with increasing *S* and remains nearly independent of *Cim*. For example, Δ*Tm*/*b* = 236 s is quite significant compared with *ti* = 442 s at *S* = 1.12 (Δ*Tm* = 8.7 K) for *Cim* = 0. On the other hand, Δ*Tm*/*b* = 135 s is negligible compared with *ti* = 2672 s at *S* = 1.07 (Δ*Tm* = 5.1 K) for *Cim* = 0.

Figure 3 shows plots of ln *ti* against ln2 *Sm* for each *Cim* according to Equation (6) based on the induction time data without consideration of the lag time. Figure 4 shows plots of ln(Δ*Tm*/2*b* + *ti*) against ln2 *Sm* for each *Cim* according to Equation (5) based on the induction time data with consideration of the lag time. Calculated values of *γ* and *A* from the slope and intercept of the best-fit plots for each *Cim* are listed in Table 4. Note that the regression coefficient, *R*2, with the lag time is generally greater than that without the lag time for each *Cim*, which indicates that Equation (5) with the lag time fits the induction time data better than Equation (6) without the lag time.

**Figure 3.** Plots of ln *ti* against ln2 *Sm* for various impurity concentrations, *Cim*, according to Equation (6) based on the induction time data without consideration of the lag time.

**Figure 4.** Plots of ln(Δ*Tm*/2*b* + *ti*) against ln2 *Sm* for various impurity concentrations, *Cim*, according to Equation (5) based on the induction time data with consideration of the lag time.

**Table 4.** Calculated values of *γ* and *A* with the regression coefficients, *R*2, based on the induction time data. The number before the slash represents the value without consideration of the lag time and the number after the slash represents the value with consideration of the lag time.


As indicated in Table 4, one can note that the value of *γ* with the lag time, *γlag*, is lower by about 2% than that without the lag time, *γ*, while the value of *A* with the lag time,

*Alag*, is lower by about 15% than that without the lag time, *A*. These findings are consistent with *γlag* < *γ* and *Alag* < *A* derived in Supplementary Materials.

Table 3 indicates that Δ*Tm* increases with increasing *Cim* for each *b* and increases with increasing *b* for each *Cim*. Thus, as similar to the results from the induction time data, L-arginine exerts a nucleation inhibition effect in aqueous L-glycine solutions, which increases with increasing *Cim*. Figure 5 shows plots of (*T*0/Δ*Tm*) <sup>2</sup> against ln(Δ*Tm*/*b*) for various *Cim* according to Equation (9) based on the MSZW data. Calculated values of *γ* and *A* from the slope and intercept of the best-fit plots for each *Cim* are listed in Table 5.

**Figure 5.** Plots of (*T*0/Δ*Tm*) <sup>2</sup> against ln(Δ*Tm*/*b*) for various impurity concentrations, *Cim*, according to Equation (9) based on the MSZW data.

**Table 5.** Calculated values of *γ* and *A* with the regression coefficients, *R*2, based on the MSZW data.


The values of *γ* and *A* obtained from the MSZW data in Table 5 are consistent with those obtained from the induction time data in Table 4. They all indicate that, as *Cim* increases, *γ* increases slightly while *A* decreases quite significantly. For example, as *Cim* increases from 0 to 10 kg/m3, *γ* only increases slightly in the range of 10% to 30%, while *A* decreases significantly in the range of 50% to 60%. It is speculated that the presence of L-arginine in the aqueous L-glycine solution leads to some L-arginine molecules adsorbed on the nucleus surface of L-glycine, which suppresses nucleation and results in a higher *γ* compared to that without L-arginine adsorbed on the nucleus surface of L-glycine. On the other hand, the presence of L-arginine in the aqueous L-glycine solution suppresses nucleation and results in a lower *A* compared to that without L-arginine in the aqueous L-glycine solution. As the effects of L-arginine impurity on *γ* and *A* become more profound at a greater concentration of L-arginine impurity, a greater *Cim* results in a higher *γ* and a lower *A*. This trend is consistent with the finding reported by Heffernan et al. [8] for the nucleation of curcumin in propan-2-ol due to the presence of demethoxycurcumin and bisdemethoxycurcumin.

#### **5. Conclusions**

A model was proposed based on CNT to determine the nucleation parameters from both the induction and MSZW data. The unique feature is that the derivation of this model for both the induction and MSZW data is based on the same assumption that the nucleation point corresponds to the formation of a single primary nucleus in a supersaturated solution. This model results in two different equations. One is derived for the induction data while the other is derived for the MESZW data. The proposed model was applied to calculate the interfacial free energy and pre-exponential nucleation factor from both the induction time data and the MSZW data for the aqueous L-glycine solutions in the presence of L-arginine impurity. The results indicated that the values of interfacial free energy and pre-exponential nucleation factor obtained from the MSZW data are consistent with those obtained from the induction time data. The induction time data with consideration of the lag time lead to a lower interfacial free energy and a lower pre-exponential nucleation factor than those for the induction time data without consideration of the lag time. As the impurity concentration increases, the interfacial free energy increases slightly while the pre-exponential nucleation factor decreases quite significantly based on both the induction time and MSZW data.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/10 .3390/cryst11101226/s1, The derivation of *γlag* < *γ* and *Alag* < *A*.

**Funding:** This research was funded by Chang Gung Memorial Hospital (CMRPD2K0012) and Ministry of Science and Technology of Taiwan (MOST108-2221-E-182-034-MY2).

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The author would like to thank Chang Gung Memorial Hospital (CMRPD2K0012) and Ministry of Science and Technology of Taiwan (MOST108-2221-E-182-034-MY2) for financial support of this research. The author also expresses his gratitude to Pin-Jhu Li and Dai-Rong Wu for their experimental work.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Notation**

*<sup>A</sup>* <sup>=</sup> pre <sup>−</sup> exponential nucleation factor (m<sup>−</sup>3s−1) *b* = cooling rate (K/s) *C*<sup>0</sup> = initial saturated concentration at *T*<sup>0</sup> kg/m3 *Ceq*(*T*) = saturated concentration at *T* kg/m3 *Cm* = saturated concentration at *Tm* kg/m3 *Cim* = concentration of impurity kg/m3 *J* = nucleation rate (m<sup>−</sup>3s−1) *J*<sup>0</sup> = nucleation rate at *t* = 0 (m<sup>−</sup>3s−1) *Jm* = nucleation rate at *tm* (m<sup>−</sup>3s−1) *kB* = Boltzmann constant <sup>=</sup> 1.38 <sup>×</sup> <sup>10</sup>−<sup>23</sup> J/K *MW* = molar mass (kg/mol) *N* = average number of expected nuclei (−) *NA* <sup>=</sup> Avogadro number <sup>=</sup> 6.02 <sup>×</sup> <sup>10</sup><sup>23</sup> mol−<sup>1</sup> *RG* <sup>=</sup> gas constant = 8.314 J mol<sup>−</sup>1K−<sup>1</sup> *S* = supersaturation (−) *Sm* = supersaturation at *tm* (−) *T* = temperature (K) *T*<sup>0</sup> = initial saturated temperature (K) *Tm* = temperature at *tm* (K) *t* = time (s)

*ti* = induction time (s) *tm* = time at the MSZW limit (s) *V* = solution volume (m3) **Greek Letters** *ρ<sup>c</sup>* = crystal density kg/m3 *v* = volume of the solute molecule m3 *γ* = interfacial free energy J/m2 Δ*Hd* = heat of dissolution (J/mole) Δ*Tm* = MSZW (K)

#### **References**


**Gina Kaysan 1, Alexander Rica 1, Gisela Guthausen 2,3 and Matthias Kind 1,\***


**Abstract:** The production of melt emulsions is mainly influenced by the crystallization step, as every single droplet needs to crystallize to obtain a stable product with a long shelf life. However, the crystallization of dispersed droplets requires high subcooling, resulting in a time, energy and cost intensive production processes. Contact-mediated nucleation (CMN) may be used to intensify the nucleation process, enabling crystallization at higher temperatures. It describes the successful inoculation of a subcooled liquid droplet by a crystalline particle. Surfactants are added to emulsions/suspensions for their stabilization against coalescence or aggregation. They cover the interface, lower the specific interfacial energy and form micelles in the continuous phase. It may be assumed that micelles and high concentrations of surfactant monomers in the continuous phase delay or even hinder CMN as the two reaction partners cannot get in touch. Experiments were carried out in a microfluidic chip, allowing for the controlled contact between a single subcooled liquid droplet and a single crystallized droplet. We were able to demonstrate the impact of the surfactant concentration on the CMN. Following an increase in the aqueous micelle concentrations, the time needed to inoculate the liquid droplet increased or CMN was prevented entirely.

**Keywords:** crystallization; microfluidic; contact-mediated nucleation; melt emulsion

#### **1. Introduction**

Emulsions are dispersions in which two mutually insoluble liquid substances are present. The dispersed droplet phase for oil-in-water emulsions is represented by oil and the continuous phase by water. According to Bancroft's rule [1], the type of emulsion is determined by the solubility of surface-active substances (e.g., emulsifiers). The phase in which the emulsifier is more soluble forms the continuous phase.

A thermodynamic description of emulsions is provided by Sharma et al. [2]. The stability of emulsions is influenced by different physical effects, such as Ostwald ripening, flocculation, aggregation, sedimentation (creaming), phase inversion and coalescence. The time scales in which these effects influence the stability of emulsions may vary profoundly [3].

One potential method of stabilizing emulsions for a longer time is the addition of emulsifiers. Emulsifiers are excipients with a characteristic molecular structure. According to the chemical structure of the surfactant, they accumulate at the interface of the two phases and decrease the specific interfacial energy [4].

Emulsifiers are amphiphilic molecules with a hydrophilic (head group) and a hydrophobic part (tail). The head is polar, while the tail usually consists of long, nonpolar hydrocarbon chains. The emulsifiers at the oil-water interface arrange themselves according to their affinity to the solvent, i.e., the head groups are on the aqueous side, whereas

**Citation:** Kaysan, G.; Rica, A.; Guthausen, G.; Kind, M. Contact-Mediated Nucleation of Subcooled Droplets in Melt Emulsions: A Microfluidic Approach. *Crystals* **2021**, *11*, 1471. https:// doi.org/10.3390/cryst11121471

Academic Editors: Béatrice Biscans, Heike Lorenz, Alison Emslie Lewis, Erik Temmel and Jens-Petter Andreassen

Received: 29 October 2021 Accepted: 22 November 2021 Published: 26 November 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the tails reach into the oil phase [5]. The hydrophilic part of an emulsifier can be charged and classified as ionic (anionic, cationic), zwitterionic or nonionic [4].

The phase distribution of the emulsifier in thermodynamic equilibrium occurs at the equivalence of temperature, pressure and chemical potentials of the surfactant in both phases, at the interface and in the micelles [6]. A quantitative description of thermodynamic equilibrium between the oil and the water phase is possible using the Nernst partition coefficient [7]. Accordingly, the distribution coefficient at phase equilibrium can be calculated using the concentrations of the component of these two phases.

#### *1.1. Contact-Mediated Nucleation*

Contact-mediated nucleation (CMN) describes a mechanism of crystallization, triggered by means of contact between a liquid, subcooled droplet and an already crystallized droplet (= particle).

McClements et al. [8] found that the fraction of solidified droplets increased during the experimental time when an equivalent initial distribution of solidified particles and liquid droplets was provided for a quiescent subcooled n-hexadecane-water emulsion with emulsifier Tween®20 (diffusional motion only). This occurred despite the fact that subcooling should have prevented spontaneous nucleation. Measurements by nuclear magnetic resonance (NMR) showed that no crystallization occurred after 175 h within an emulsion with only liquid n-hexadecane droplets. McClements et al. [9] found that the higher the available surfactant concentration in the emulsion, the higher the final solids fraction of the droplets. Additionally, Dickinson et al. [10] determined an increase in the solid content relative to an increase in the emulsifier concentration in the continuous phase for the same material system. They estimated that one in 10<sup>7</sup> collisions between crystallized and liquid droplets resulted in CMN. Hindle et al. [11] found a steady increase in the fraction of solidified droplets of a subcooled n-hexadecane-water emulsion with emulsifier Tween®20. The increase occurred after crystallized n-hexadecane droplets were added. Complete crystallization of the dispersed phase occurred during the 15 days after the addition of crystallized droplets. They concluded that, according to their results, micelles could not mediate nucleation and any increases in the solid fraction were due to the contact between a liquid droplet and a solid particle. They also state that micelles may affect CMN.

Regarding experiments performed in the field of coalescence, Dudek et al. [12] determined longer coalescence times with increasing surfactant concentrations. This is contrary to the results described above, because increasing micellular numbers should improve the coalescence process as more dispersed phase can be transported from one droplet to another. Additionally, with increasing aqueous surfactant concentrations, higher energy barriers must be overcome to achieve direct contact between the two collision partners [13]. The latter is discussed in further detail later in this paper.

In order to enhance the contact between crystallized particles and liquid droplets, achieving a relative motion between each particle and droplet is advantageous. According to Vanapalli et al. [14], the relative motion between droplets and particles can be classified into orthokinetic (externally imposed velocity fields) or perikinetic (Brownian motion). In this work, the relative motion is governed by the orthokinetic mechanism due to the microfluidic setup and droplet sizes used.

In analogy to the coalescence theory, three external flow factors can influence CMN: contact time, contact force and collision frequency [15]. The contact time and contact force depend on further flow phenomena, such as the flattening of the film radius, film drainage and film rupture [16]. The surfactant may play an important role for CMN because it influences the specific interfacial energy and forms micelles in the continuous phase which may inhibit the contact of colliding partners.

#### *1.2. Microfluidics*

Microfluidic systems have become an important tool in emulsion research [17]. The application of microfluidics offers many advantages, for example, laminar flow conditions, high surface-to-volume ratios, small fluid volumes, the possibility of droplet manipulation, easy access for microscopical analysis, and excellent control over mass and heat transport. Microfluidics in crystallization research appears as a supporting platform for fundamental research into crystallization processes and crystal formation [18,19]. Hence, new possibilities have been made available to investigate processes within relevant time scales [20,21], for example, the investigation of CMN. Single droplet experiments are also used to investigate coalescence and to correlate specific interfacial energy to droplet stability [22–25].

#### *1.3. Theoretical Description of Contact-Mediated Nucleation—An Approach*

Similarities can be found between the modelling of coalescence processes and CMN [15]. So far, there are no established, specific theoretical descriptions of CMN in the literature. The process of coalescence takes places between liquid droplets or between gaseous bubbles. No phase change takes place upon coalescence. There is an asymmetry in the aggregate state in CMN, since one of the two contact partners is already crystallized and the other is a liquid, subcooled droplet. This results in the following general assumption of contactmediated nucleation: the interface of the liquid droplet can take several states, from mobile to rigid, depending on the interfacial surfactant concentration, whereas the interface of the crystallized particle is only rigid.

According to [26], the interstitial film needs to fall below a critical thickness for coalescence to take place. Below that specific thickness, the Van der Waals attraction between two droplets approaching each other is stronger than any possible repulsive forces. Different mechanisms are detailed in the following passage, which could counteract the film thinning in the material system of an n-hexadecane–water emulsion used, stabilized with Tween®20.

The Derjaguin-Landau-Verwey-Overbeek (DLVO) theory [27,28] is a theoretical description of the stability of colloidal systems, such as emulsions, that account for attractive and repulsive forces. Regarding stability factors [29] larger than 1, repulsion dominates the interaction of two suspended particles. Electrostatic repulsion between colloids requires equally charged surfaces. Therefore, an increased charge of equal polarity between colloids could counteract film thinning. Dimitrova et al. [30] measured the forces between ferrofluidic suspension droplets in an aqueous solution stabilized with Tween®20. When the concentration of the emulsifier increased, the electrostatic repulsion also increased. The authors only found agreement with the DLVO theory for low concentrations of the emulsifier. The repulsive force measured at higher surfactant concentrations showed higher values at shorter distances than the predicted values calculated via the DLVO theory. In order to explain this discrepancy, the authors suspected a steric component of the repulsive force. This was thought to be caused by the presence of Tween®20 micelles between the droplets.

The influence of micelles in the continuous phase on the contact between colloids could be explained by the oscillating structural and depletion forces (OSF) [31]. These forces occur in the interstitial film when the film thickness decreases in the presence of small, dissolved entities in the film liquid, for example, micelles.

Taking OSF into account, Basheva et al. [13] derived a nonlinear relationship between the diameter of spherical micelles, the volume fraction of these micelles, the distance of the two colliding droplets and the interaction energy between the two droplets. This approach is used to estimate emulsion stability as a function of the number of micelles present in the solution. We calculated the interaction energy *Utotal* analogously with the literature presented regarding the occurrence of OSF (Figure 1). The corresponding material system parameters are listed in Table 1. *Utotal* was estimated by the sum of the oscillatory component (*Uosc*) and the Van der Waals interaction (*UvdW*). A full description of the equations can be found in [13].

**Figure 1.** Simulated interaction energy of two spherical droplets with the distance *H* according to Trokhymchuk et al. [32] and Basheva et al. [13]. It is assumed that the film between the droplets contains hard, spherical micelles. Parameters used for calculation are summarized in Table 1. The volume fraction of the micelles in the continuous phase *ϕm* for a given aqueous surfactant concentration *<sup>c</sup>H*2*<sup>O</sup> TW*<sup>20</sup> was approximated with a linear expression according to data obtained by Basheva et al. [13]: *<sup>ϕ</sup><sup>m</sup>* <sup>=</sup> 1.7 <sup>×</sup> <sup>10</sup>−<sup>3</sup> *<sup>m</sup>*3*mol*−<sup>1</sup> · *<sup>c</sup>H*2*<sup>O</sup> TW*20.

**Table 1.** Parameters used for calculation of the total interaction energy *U*.


Figure 1 indicates the possible influence of micelles in the aqueous phase because they are able to hinder or delay CMN by increasing the repulsive forces. As indicated, a particular volume density of micelles is necessary to achieve stability factors larger than 1.

We used a microfluidic setup for our studies to investigate the efficiency of CMN depending on the specific interfacial energy and micellular concentration in the continuous phase. We suggest increasing induction times and decreasing wetting by increasing aqueous micellular concentrations. Moreover, we assume that a link can be made between the coalescence theory and CMN to characterize the latter regarding its crystallization efficiency.

#### **2. Materials and Methods**

#### *2.1. Materials Used*

Microfluidic experiments were performed with n-hexadecane (C16H34, Hexadecane ReagentPlus®, Sigma-Aldrich, Schnelldorf, Germany, purity: 99%) as the dispersed phase and ultrapure water (OmniTap®, stakpure GmbH, Niederahr, Germany; electrical conductivity 0.057 μS cm−1) as the continuous phase. The surfactant used in this study was Polyoxyethylen(20)-sorbitan-monolaurat (Tween®20, Merck KGaA, Darmstadt, Germany) in different concentrations.

#### *2.2. Microfluidic Measurement Setup*

A microfluidic system based on the type of continuous-flow emulsion-based droplet microfluidics was applied [34]. The multiple phase flow appeared as the so-called Taylor flow [35]. A characteristic sequence of liquid droplets was formed, separated by slugs of the continuous phase. These slugs were sections of the aqueous phase [36]. The droplets had an average droplet volume of around 25 nL and mean equivalent diameters of approximately 525 μm. The droplet volume was calculated according to [37].

The microfluidic chip acted as the central element of the setup (Figure 2). It consisted of a transparent polycarbonate plate (thickness 2 mm) into which several microchannels have been milled. The channels were 300 μm wide and 200 μm deep. Additionally, a channel for a temperature sensor was milled into the side of the chip. The channels received their characteristic rectangular cross-sectional area by bonding a thin 250 μm polycarbonate foil on top. In order to guarantee that wetting of n-hexadecane did not occur on the channel walls, the latter were hydrophilized according to [38]. The microfluidic chip was fixed on a water-tempered aluminum cooling block with two independently controlled temperature zones. The temperature of the microfluidic chip was measured with a temperature sensor (Pt 100, ES Electronic Sensor GmbH, Heilbronn, Germany) close to the location of the contact experiment. Crystallization processes were tracked with a high-speed camera (sCMOS pco.edge 5.5®, Excelitas PCO GmbH, Kelheim, Germany) connected to a stereo microscope (SZ61, OLYMPUS EUROPA® Se & Co. KG, Hamburg, Germany) with an integrated polarization filter. Two silicon wafers were installed directly beyond the microfluidic chip to support the polarization filter in highlighting crystalline structures. Volume flow rates of the continuous and dispersed phases were adjusted by a low-pressure injection pump system (Nemesys, CETONI GmbH, Korbußen, Germany). This syringe pump system was connected to the computer via a BASE120 base module.

**Figure 2.** (**a**) Schematic view of the microfluidic chip with rectangular channels and sectional temperature regulation with scale (mm). The temperature sensor was inserted sideways into the chip through a fitting channel (yellow). The n-hexadecane droplets were formed at the T-junction (green frame) at a temperature above the melting point of n-hexadecane *Tm*. The produced droplets flowed along the channel in the direction indicated (*uflow*). (**b**) Half of the chip was cooled (blue area) to a subcooling of around Δ*T*<sup>1</sup> = *Tm* − *T*<sup>1</sup> = 7.6 K for spontaneous nucleation (initialization). The other half was kept below the melting point at Δ*T*<sup>2</sup> = 1.1 K (red area); the droplets on this side retained liquid. The whole microfluidic chip was kept at Δ*T*<sup>2</sup> (red area) for the contact-mediated nucleation (CMN) measurement. The purple frame exemplarily displays a time-resolved CMN.

The microfluidic T-junction allowed for the formation of reproducible droplet sizes (Figure 2). At the beginning of the droplet formation process, the dispersed phase began to fill the channel cross-section almost completely, and when a critical proportion between droplet size and channel cross-sectional area was reached, droplets of the dispersed phase were formed.

The aim of the experiments was to investigate the CMN as a function of surfactant concentration. The temperature profile of the microfluidic chip during one collision followed a predefined protocol, as shown in Figure 3.

**Figure 3.** Temperature profile of the microfluidic chip *Texp* over time measured by the incorporated temperature sensor. After initiating spontaneous, primary nucleation at a subcooling of Δ*T*<sup>1</sup> = *Tm*,*μ<sup>F</sup>* − *Tprimary* = 7.6 K, the temperature was set to a subcooling of Δ*T*<sup>2</sup> = *Tm*,*μ<sup>F</sup>* − *Tcontact* = 1.1 K for the observation of CMN. The melting point of n-hexadecane *Tm*,*μ<sup>F</sup>* was defined as 18.6 ◦C.

In order to initialize the experiment, droplets were formed at the T-junction and, as soon as both plates were covered with droplets, one side of the chip was cooled to around *Tprimary* = 11 ◦C (Δ*T*<sup>1</sup> = 7.6 K) to enforce spontaneous droplet crystallization. To avoid spontaneous crystallization during the experiments, both plates were thermostated at *Tcontact* = 17.5 ◦C (Δ*T*<sup>2</sup> = 1.1 K), which is below the melting point of n-hexadecane, and, as a result, the frozen particles did not thaw. Following this, the continuous phase was initiated, and the liquid droplet moved towards the solid particle. Volume flow rates ranging from 15 to 400 μL h−<sup>1</sup> were applied. The solid particle was fixed on the channel walls as a result of crystallization. Due to the rectangular cross-sectional area of the channel and the round particle, the aqueous phase was still able to flow around the solid particle. This experimental design allowed for the controlled contact of two collision partners. A detailed experimental protocol is shown in Figure 4.

**Figure 4.** Experimental protocol for microfluidic experiments designed to investigate CMN.

A high-speed camera allowed time-resolved detection of the contact progress (for example, relative velocity of the droplet and the particle Δ*u* and wetting evolution) and of the nucleation events. All collisions were tracked with the camera at a frame rate of 100 frames per second. The relative velocity Δ*u* was determined by the distance travelled by the subcooled liquid droplet within a specific timeframe, while the solid particle had a fixed position (compare Figure 2).

#### *2.3. Melting Point Measurements*

In order to quantify the possible impact of the microfluidic system on the melting point of n-hexadecane, the presence of water or emulsifier was determined in the microchannel to *Tm*,*μ<sup>F</sup>* = 18.6 ± 0.2 ◦C. A broad range of melting points can be found in the literature, varying between 16.7 and 20.0 ◦C [39–44]. Our results are in good agreement with the available literature and, therefore, no impact of the setup or the presence of the water phase and surfactant was identified. In the following, *Tm*,*μ<sup>F</sup>* was used to calculate subcooling.

#### *2.4. Specific Interfacial Energy Measurements*

Droplet formation within the microfluidic device was possible with and without the usage of an additional surfactant. Therefore, it was not possible to estimate the specific interfacial energy and, consequently, the droplet surface coverage achieved by the emulsifier directly during the microfluidic experiment. However, surface coverage may play an important role for CMN as interfacial energy is known to greatly influence coalescence [45].

Measurements of the specific interfacial energy were obtained via the pendant drop method (OCA 25, DataPhysics Instruments GmbH, Filderstadt, Germany) to quantify the time needed by the surfactants to cover the liquid-liquid interface completely. A syringe with an outer diameter of 0.91 mm was used for the generation of the droplet, and the temperature was set to 20 ± 0.2 ◦C. Measurements without surfactant resulted in specific interfacial energies of 48.6 ± 0.5 mN·m−1, which is in good agreement with the specific interfacial energies described in the literature ([46]: 43.16 mN·m−1, [47]: 47.0 mN·m−1). Time-resolved specific interfacial energies were considered to characterize the adsorption process of the surfactant to the liquid-liquid interface and to outline any dependencies of the surfactant concentration in the aqueous or oil phase (Tables 2 and 3, Figure 4).

*cH*<sup>2</sup>*<sup>O</sup> TW*20(*<sup>t</sup>* <sup>=</sup> <sup>0</sup>)/**mol m**−<sup>3</sup> *<sup>γ</sup>LL*/**mN m**−<sup>1</sup> 8.2 3.5 ± 0.3 16.6 2.9 ± 0.2

**Table 2.** Specific interfacial energies approximately 4 h after interface formation for different surfactant concentrations dissolved in the continuous phase (*cH*2*<sup>O</sup> TW*20(*<sup>t</sup>* <sup>=</sup> <sup>0</sup>)).

**Table 3.** Specific interfacial energies about 4 h after interface formation for different surfactant concentrations added at the beginning to the dispersed phase (*chex TW*20(*t* = 0)).


As Figure 5 and Tables 2 and 3 indicate, the phase in which the surfactant is dissolved at the beginning of the experiment (*t* = 0) plays a major role. The convolution of the surfactant distribution between the aqueous and oil phases will be discussed in Section 3. The measurements were obtained in a time frame of approximately 4 h (data not shown), without reaching a constant specific interfacial energy. The microfluidic experiments were performed within around 0.2 h. For *t* < 0.2 h, the final distribution of the surfactant between the continuous phase, dispersed phase and liquid-liquid interface was not reached according to the specific interfacial energy measurements. It should also be mentioned

that the specific interfacial energy tension reduced from around 48 mN·m−<sup>1</sup> to values between approximately 1 and4Nm−<sup>1</sup> within the first seconds after droplet formation. This suggests that most surfactants adsorbed to the interface shortly after droplet formation and any further changes were only due to the ad- and desorption of a smaller number of molecules.

**Figure 5.** Two exemplary time-resolved specific interfacial energy (*γLL*) measurements with surfactant supported in either the aqueous, continuous (*cH*2*<sup>O</sup> TW*20(*<sup>t</sup>* <sup>=</sup> <sup>0</sup>) = 16.6 mol·m−3) or dispersed oil phase (*chex TW*20(*<sup>t</sup>* <sup>=</sup> <sup>0</sup>) <sup>=</sup> 6.4 mol·m<sup>−</sup>3).

The increasing specific interfacial energy for systems in which the emulsifier was previously dissolved in the dispersed phase, shows the convective transport of the emulsifier from the interface to the surrounding continuous phase. As soon as thermodynamic equilibrium would be reached, the specific interfacial energies should be the same, without any differences regarding initial surfactant concentration gradients between the aqueous and oil phase, providing there is enough surfactant to completely cover the interface.

When transferring these findings to an idealistic model, we assumed different, instationary surfactant distributions between the dispersed and continuous phase, depending on the initial surfactant concentration (Figure 6). We assumed that the depicted surfactant distribution represented the situation during our microfluidic experiments.

**Figure 6.** (**a**) Schematic system description when the surfactant was initially dissolved in the continuous phase (water). The subcooled droplet is presented in a light color, the solid particle is shown as a brown sphere. (**b**) Schematic system description when the surfactant was initially dissolved in the dispersed phase (n-hexadecane). Both systems had not yet reached the thermodynamic equilibrium.

Within the experimental time range, a higher emulsifier concentration at the interface can be assumed for systems where the surfactant is dissolved in the oil phase at *t* = 0 due to lower specific interfacial energies (Figures 5 and 6b). In addition, the concentration of the surfactant affects the specific interfacial energy and, thus, the emulsifier concentration at the interface across relevant time scales. Decreasing specific interfacial energies with increasing surfactant concentration (even above the critical micellular concentration: CMC) are also described in the literature [12,48]. During the microfluidic experiments, we assumed that, when the surfactant was initially supported in the water phase, more micelles were present in the aqueous phase compared to the number of micelles when the surfactant was initially dissolved in the oil phase.

#### *2.5. Wetting*

Different types of wetting between the liquid droplet and the solid particle were observed (Figure 7). The efficiency of CMN can be obtained by taking the wetting angle ϕ of the two collision partners into account.

**Figure 7.** Definition of the wetting angle ϕ between a liquid, subcooled droplet and a solid particle. Both contact partners are stabilized with surfactant.

In this work, four different forms of contact are identified by their corresponding wetting angle and their efficiency in initiating nucleation. A brief overview is provided in Table 4.

**Table 4.** Classification of CMN based on the wetting angle ϕ. The differentiation is made based on whether nucleation occurs or not. Additionally, a schematic abstraction and the experimental observation are shown. In the abstraction, solid structures are light brown (left particle), and liquid droplets (right) are visualized in white. For the experimental illustration, solid structures are either light white, in cases where crystallization had just taken place, or dark gray. The liquid droplet volume is represented by the transparent parts. We assumed that solid–liquid interfaces are partially composed of surfactant. In the case of ϕ = 0◦, hug, the red circle highlights the part of the liquid droplet that has already crossed the solid particle and appears directly behind the latter. The first two rows illustrate that contact occurred when the surfactant was supported in the continuous phase; the last two rows show wetting angles for the initial surfactant support in the dispersed phase.



**Table 4.** *Cont.*

Crystallization did not occur when the wetting angle was 180◦, and we assume that no wetting occurred either. When the surfactant was dissolved in the aqueous phase, crystallization was visible with increasing relative velocities and a decreasing aqueous surfactant concentration, but not immediately after the first contact. The liquid droplet even surrounded the solid particle at certain points (Table 4, ϕ = 0◦, hug, red circle).

#### **3. Results**

#### *3.1. Surfactant Distribution between the Water and Oil Phase and the Liquid-Liquid Interface*

The CMN may be influenced by the surface coverage of the droplet and particle with emulsifier. The influence of the specific interfacial energy on coalescence has already been discussed in the literature (e.g., [45]). In addition, the appearance of micelles may play an important role for the successful inoculation of the subcooled droplet. Due to the above-mentioned reasons, it is of great importance to estimate the surfactant distribution between the aqueous continuous and the dispersed oil phase.

In order to determine whether a diffusion process of surfactant from the water to the oil phase occurs, that is driven by concentration gradients due to different chemical potentials, NMR measurements were performed using a 400 MHz spectrometer (Avance Neo, Bruker BioSpin GmbH). Samples were prepared with surfactant concentrations up to *<sup>c</sup>H*2*<sup>O</sup> TW*<sup>20</sup> <sup>=</sup> 180 mol·m<sup>−</sup>3. N-hexadecane was added at two different mass ratios to the continuous phase: [50:50] and [80:20] (water:n-hexadecane). After the addition of nhexadecane, the samples were mixed with a stirring fish at 700 rpm for 2 min. Droplets between 10 and 500 μm were produced. The samples were left untouched for one week. During this time, a phase separation occurred, and three different phases became visible. Large n-hexadecane droplets were found at the top. The intermediate phase consisted of smaller n-hexadecane droplets and the bottom phase was aqueous. The aqueous phase was carefully separated with a syringe to determine the surfactant distribution after one week. This sample was analyzed by 1H NMR spectroscopy (Figure 8).

The measured samples are in good agreement with the calibration curve up to a concentration of *<sup>c</sup>H*2*<sup>O</sup> TW*<sup>20</sup> (*<sup>t</sup>* <sup>=</sup> <sup>0</sup>) = 90 mol·m<sup>−</sup>3. Therefore, up to the specified concentration, no measurable number of surfactants dissolved in the n-hexadecane phase. This supports our hypothesis that surfactant diffusion due to concentration gradients and, thus, chemical potential differences between the continuous and dispersed phase did not play a major role within our experimental time frame (*cH*2*<sup>O</sup> TW*20(*<sup>t</sup>* <sup>=</sup> <sup>0</sup>) < 50 mol·m−3). Moreover, we did not notice an influence of the volume ratios of water and oil on the distribution of the surfactant. The concentration of surfactant at the interface was too small to be measurable with NMR. Pendant drop measurements must be considered to obtain information about the interfacial surfactant concentration (Figure 5, Tables 2 and 3).

**Figure 8.** The concentration of Tween®20 in the water phase determined via NMR spectra *<sup>c</sup>H*2*<sup>O</sup> TW*20,*NMR* as a function of the concentration of the weighed-in components *<sup>c</sup>H*2*<sup>O</sup> TW*<sup>20</sup> (*<sup>t</sup>* <sup>=</sup> <sup>0</sup>) of samples with a 50:50 or 80:20 mass ratio of the continuous phase to the dispersed phase (n-hexadecane). In addition, reference samples of Tween®20 in ultrapure water with defined concentrations are displayed (red). The samples were measured at 20 ◦C. Inset: Zoom-in to concentrations up to *<sup>c</sup>H*2*<sup>O</sup> TW*20(*<sup>t</sup>* <sup>=</sup> <sup>0</sup>) = 50 mol·m<sup>−</sup>3. The relative measurement error of the spectrometer was 2%.

The measured surfactant concentrations, for initial concentrations higher than *<sup>c</sup>H*2*<sup>O</sup> TW*<sup>20</sup> (*<sup>t</sup>* <sup>=</sup> <sup>0</sup>) = 90 mol·m−3, differ from the reference calibration line. This may indicate that the molecular solubility limit of Tween®20 in the continuous phase had been exceeded. The information on the solubility of Tween®20 in water in the literature spans a certain range although a concrete solubility limit could not be found. Data sheets [49,50] mention the solubility limit at emulsifier concentrations of *<sup>c</sup>H*2*<sup>O</sup> TW*<sup>20</sup> <sup>=</sup> <sup>2</sup> <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>g</sup>·L−<sup>1</sup> and <sup>100</sup> <sup>g</sup>·L<sup>−</sup>1. These correspond to the following values: *<sup>c</sup>H*2*<sup>O</sup> TW*<sup>20</sup> <sup>=</sup> <sup>2</sup> <sup>×</sup> <sup>10</sup>−<sup>9</sup> mol·m−<sup>3</sup> and <sup>1</sup>·10−<sup>4</sup> mol·m−3, respectively, with *<sup>ρ</sup>H*2*O*(20 C) = 998.2 kg·m<sup>−</sup>3. These values are much lower than the emulsifier concentrations investigated and used in the present series of experiments. Pollard et al. [51] found Tween®20 to be 'extremely soluble' in water and other solvents. In their experiments, Tween®20 was completely solvable in water up to <sup>671</sup> <sup>g</sup>·L−<sup>1</sup> at 20 ◦C (*cH*2*<sup>O</sup> TW*<sup>20</sup> <sup>=</sup> 546 mol·m−3), and the authors did not investigate further additions of emulsifier. The maximum solubility was not reached at this concentration. No phase separation of Tween®20 in water, that was measurable by eye, could be identified in any of our experiments. Nonetheless, a nonvisible phase separation could have taken place. Another possible explanation may be the diffusion of surfactant from the aqueous to the oil phase. With an increasing aqueous surfactant concentration, the difference of the chemical potential between Tween®20 in water and n-hexadecane increased, leading to a faster rate of surfactant diffusion into the oil phase.

Long-term experiments were performed over a period of 43 days to support the findings of the slow equilibrium adjustment of the surfactant between the continuous and the dispersed phase (Figure 9) and to estimate the distribution coefficient *KTW*<sup>20</sup> of Tween®20 between water and n-hexadecane. *KTW*<sup>20</sup> is defined as

$$K\_{TW20} = \frac{\tilde{\mathcal{C}}\_{TW20}^{\text{hxc}}}{\tilde{\mathcal{C}}\_{TW20}^{H20}},\tag{1}$$

where *<sup>c</sup>hex TW*<sup>20</sup> represents the molar concentration of Tween®20 in the n-hexadecane phase and *<sup>c</sup>H*2*<sup>O</sup> TW*<sup>20</sup> represents the molar concentration in the water phase.

**Figure 9.** (**a**) 1H spectra of the aqueous phase, where the surfactant Tween®20 was dissolved at the beginning of the experiment. The water peak appears at about 4.8 ppm; all other visible peaks are related to Tween®20. Inset: time-resolved evolution of the CH2 peak of Tween®20. (**b**) Time-resolved measurements of Tween®20 concentration in the continuous phase over a period of 43 days, determined by NMR spectroscopy. The volume ratio of water and n-hexadecane was 50:50 and the interface had an area of 13.2 mm2. Additionally, the fitted exponential decay curve is visible as a dashed line.

A 300 MHz spectrometer (nanobay, Bruker BioSpin GmbH) was used to determine the distribution coefficient. The measured sample consisted of two separated phases, namely of pure n-hexadecane, and water with an initial total surfactant concentration of 16.6 mol·m−3. The phase volumes were both 300 <sup>μ</sup>L. The sample was positioned in the sensitive measuring range so that only the water phase was measured. The CH2 peak was used for evaluation to avoid overlapping and the influence of the water peak on the peak of the ethoxylate group of the emulsifier at 3.7 ppm. Modelling of the experimental data with an exponential decay of the first order (Figure 9b) led to an equilibrium concentration of *<sup>c</sup>H*2*<sup>O</sup> TW*20(*<sup>t</sup>* <sup>→</sup> <sup>∞</sup>) = 13.6 mol·m<sup>−</sup>3. The value of *<sup>c</sup>hex TW*20(*t* → ∞) for the extrapolated equilibrium state was calculated as *<sup>c</sup>hex TW*20(*<sup>t</sup>* → <sup>∞</sup>) = 3.0 mol·m−<sup>3</sup> by mass balance calculations of the two-phase system observed. The distribution coefficient (Equation (1)) was found to be *KTW*<sup>20</sup> = 0.22 for an initial aqueous surfactant concentration of *<sup>c</sup>H*2*<sup>O</sup> TW*20(*<sup>t</sup>* <sup>=</sup> <sup>0</sup>) = 16.6 mol·m<sup>−</sup>3, similar volumes of water and n-hexadecane, and an interfacial area of approximately 13.2 mm2.

#### *3.2. Effect of Tween®20 Distribution on Contact-Mediated Nucleation*

As has been mentioned previously, the contact time and contact force required for nucleation may be influenced by the surfactant concentrations present in the water and oil phases and at the separating interface. This may be due to potentially prolonged film drainage times or the rearrangement of the surfactant at the interface when the two collision partners approach one another. Regarding industrial processes, wetting effects should be minimized to exclude partial coalescence and achieve comparable droplet/particle size distributions before and after the crystallization step. Partial coalescence describes when two particles are connected by a small bridge, but they do not form a single, spherical particle.

Within the experimental microfluidic time frame of around 10 min, the specific interfacial energy depended on the distribution of the surfactant between the continuous and dispersed phase (Figure 5). Different concentrations of Tween®20 in the dispersed and continuous phase were used for the collision experiments to outline the effect of the specific interfacial energy and the influence of micelles on the CMN. The number of micelles or single molecules per unit volume in the continuous phase and the specific interfacial energy may influence the contact force needed for crystallization. Here, we used the relative

velocity between the subcooled droplet and the crystalline particle as an indirect indicator of contact force because the latter cannot be measured directly. This velocity difference will be transformed into a contact force per contact area and thus into, for example, a contact pressure. The contact time is not limited in the microfluidic chip because the continuous phase constantly pushes the liquid droplet towards the solid particle. The induction time needed for crystallization is presented in Section 3.4.

The distribution of the surfactant cannot be determined within the microfluidic setup itself. An empirical approach was used to estimate the distribution. A diffusion-controlled model was applied for the adsorption of Tween®20 at the water–n-hexadecane interface. According to [52], this assumption is valid because the droplets had an average size larger than 10 μm. Tween®20 was assumed to be a highly surface-active molecule. Our calculations showed that a complete coverage of the interface was reached after at least 6 min for *<sup>c</sup>H*2*<sup>O</sup> TW*<sup>20</sup> = 8 <sup>×</sup> <sup>10</sup>−<sup>3</sup> mol·m−<sup>3</sup> and 1.2 <sup>×</sup> <sup>10</sup>−<sup>5</sup> s for *<sup>c</sup>H*2*<sup>O</sup> TW*<sup>20</sup> = 42.8 mol·m−3. The maximum surface loading was reached within less than 1 s (*tmax* 1 s) for all initial surfactant concentrations higher than the CMC. For the calculations according to [53], a maximal surface loading <sup>Γ</sup>*max* of 1.79 × <sup>10</sup>−<sup>6</sup> mol·m−<sup>2</sup> (calculated according to [54], assuming a surfactant monolayer at the liquid-liquid interface and a surface pressure equal to zero; 100% of interface covered with surfactant) and a diffusion coefficient of the single surfactant molecules in water of *<sup>D</sup>H*2*<sup>O</sup> TW*<sup>20</sup> = 2.6 × <sup>10</sup>−<sup>10</sup> <sup>m</sup>2·s−<sup>1</sup> (own measurements via NMR diffusion measurements [400 MHz spectrometer, Avance Neo, Bruker BioSpin GmbH]) was used. Assuming a fully loaded interface before starting the collision experiments, the continuous surfactant concentration still represents more than 99% of the initial bulk concentration of TW20 ( *<sup>c</sup>H*2*<sup>O</sup> TW*20(*<sup>t</sup>* <sup>=</sup> <sup>0</sup>) <sup>∼</sup> *<sup>c</sup>H*2*<sup>O</sup> TW*20(*t*), *<sup>c</sup>H*2*<sup>O</sup> TW*<sup>20</sup> <sup>&</sup>gt; *CMC*). Ad- and desorption processes from the interface into the n-hexadecane droplet phase can also be neglected within the experimental time range, as is shown in Figure 8.

When Tween®20 was initially dissolved in n-hexadecane, measurements of the specific interfacial energy suggested fast adsorption to the interface followed by a desorption to the continuous phase. The diffusion coefficient of Tween®20 in n-hexadecane was measured as *Dhex TW*<sup>20</sup> ∼ 2.0 × <sup>10</sup>−<sup>10</sup> m2·s−<sup>1</sup> for surfactant concentrations between 0.2 and 360 mol·m<sup>−</sup>3, which is comparable to *<sup>D</sup>H*2*<sup>O</sup> TW*20. We therefore assume that only single molecules are present in the n-hexadecane droplet and no inverse micelles are formed. Calculations of the maximum time needed for complete interfacial coverage, according to [53], revealed that a complete coverage can be assumed in periods significantly shorter than 10 min. We, furthermore, assume that no or only a few micelles are formed within the continuous phase until contact crystallization occurs when Tween®20 was initially dissolved in the oil phase. This hypothesis will be verified later, because micelles and single molecules in the continuous phase hinder contact crystallization tremendously. Nucleation occurred for all experiments where the surfactant was initially dissolved in the dispersed phase.

The wetting angle *ϕ* (Figure 10a,b) and crystallization probability *Pc* (Figure 10c) depended on the surfactant's concentration and the distribution of the surfactant throughout the system. The crystallization probability *Pc* represents the ratio between the crystallized droplets and the total number of droplets.

There was no initial nucleation visible by eye at first contact for any experiments in which the surfactant was added to the continuous phase alone at the beginning of the experiment. Higher relative velocities and, thus, higher shear rates and higher contact forces were necessary (e.g., Figure 10a, 7 · CMC) to trigger nucleation. The liquid droplet often surrounded the particle before nucleation occurred. We assume that the new liquid– liquid droplet surface can be refilled faster with an increasing surfactant concentration in the continuous phase. This, consequently, prevents the direct contact of crystalline structures with subcooled liquids and, therefore, hinders crystallization. Less free surfactant is available at a lower surfactant concentration and the new interface cannot be completely covered quickly enough. Consequently, crystallization occurs.

(**c**)

**Figure 10.** (**a**) Wetting angle as a function of the relative velocity (difference of velocities between droplets and particles) for different surfactant concentrations. Tween®20 was added to the continuous phase. (**b**) Wetting angle as a function of relative velocities for different surfactant concentrations as Tween®20 was dissolved in the dispersed phase. All experiments led to crystallization, but differences in the contact form were found according to the surfactant concentration. (**c**) Crystallization probability *Pc* as Tween®20 was added to the continuous phase for relative velocities ranging from 10−<sup>5</sup> up to 2 <sup>×</sup> <sup>10</sup>−<sup>3</sup> m s<sup>−</sup>1.

Only the two lower surfactant concentrations (*cH*2*<sup>O</sup> TW*<sup>20</sup> = 8 <sup>×</sup> <sup>10</sup>−<sup>3</sup> and 0.4 mol·m<sup>−</sup>3) led to nucleation within the experimental observation period of around 60 s. The crystallization probability *P*(*c*) (Figure 10c) decays exponentially as a function of the initial aqueous surfactant concentration. We, thus, assume that micelles in the continuous phase hinder nucleation, as the highest crystallization probability was reached at *<sup>c</sup>H*2*<sup>O</sup> TW*<sup>20</sup> = 8 <sup>×</sup> <sup>10</sup>−<sup>3</sup> mol·m<sup>−</sup>3, which is below the CMC of Tween®20 in water (*CMCTW*<sup>20</sup> = 0.059 mol·m−<sup>3</sup> [55]). Experiments without the surfactant were performed to prove this hypothesis. Crystallization occurred in all the experiments without the emulsifier. This confirms our assumption that micelles and increasing monomer concentrations in the continuous phase can weaken or even prevent CMN.

When the surfactant was initially added to the dispersed phase alone, all contacts resulted in nucleation, independent of the surfactant concentration and relative velocity. A differentiation can be made according to the presented wetting angles (Figure 10b).

The surfactant's equilibrium distribution between the two phases was investigated to determine the dominant factor in CMN. The phase composition is provided by *KTW*20, which was acquired from the long-term spectroscopic measurements (Figure 9). If the influence of the micelles is dominant, no crystallization should take place, whereas if the emulsifier in the dispersed phase and at the interface has a stronger influence, crystallization should take place in all collisions (Figure 11).

Successful nucleation was not observed for relative velocities up to 1.7 × <sup>10</sup>−<sup>3</sup> m s<sup>−</sup>1. This is a clear indication of the prevention of CMN by the presence of micelles in the continuous phase. Bera et al. [56] did not identify the occurrence of coalescence when the surfactant concentration was above the CMC, which is in good agreement with our results as we did not detect any CMN when the surfactant concentration was above 7 · CMC in the continuous phase.

#### *3.3. Formation of Liquid Bridges before Contact-Mediated Nucleation*

A formation of liquid bridges between the liquid droplet and the solid particle was detected during some experiments, when the surfactant was initially dissolved in the oil phase. Regarding the desirable separation of the two reaction partners after the collision in industrial processes, small or no liquid bridges are required. Otherwise, the shelf life of the product would be reduced, or the product properties may change due to partial coalescence. Separation after collision could not be achieved for the experiment setup used due to the limitations presented by the experimental execution.

The size of the liquid bridge, which was formed between droplet and particle, changed as a function of the surfactant concentration in the dispersed phase (Figure 12).

A very clear decrease in the mean size of the liquid bridge is visible. A significant difference between the population means and the population variances (Levene's test) was observed at a level of 0.05 by means of an analysis of variance of the experimental data. Nonetheless, the Tukey's post hoc test showed no significant difference between the two data sets of *<sup>c</sup>hex TW*<sup>20</sup> = 12.9 and 33.2 mol·m−<sup>3</sup> at a level of 0.05.

A decrease in the diameter of the liquid bridge with an increasing emulsifier concentration is also described by Nowak et al. [57] for two coalescing droplets. Since the addition of surfactant causes decreasing specific interfacial energies, smaller driving forces are needed for coalescence and, hence, for CMN in the experiments presented here. The specific interfacial energy has a gradient on the droplet surface during the CMN due to the movement of surfactants at the interface. Consequently, Marangoni flow [58] develops. This allows for a homogeneous surfactant distribution at the interface. Thus, there are two effects promoting small liquid bridges at higher surfactant concentrations. Firstly, since there is more emulsifier in the dispersed phase, diffusion-limited transport to the interface

is faster. Secondly, the gradient on the surface is greater because more emulsifier is present at the interface and, thus, the Marangoni flow is stronger. Higher surfactant concentrations also allow for a faster refilling of the interface when there is a concentration gradient between the continuous and dispersed phase, resulting in the desorption of surfactant molecules from the interface to the continuous phase. Chesters [16] hypothesizes that coalescence is favored for low viscosities of the dispersed phase. This may also promote the formation of larger liquid bridges at smaller surfactant concentrations and, thus, lower dispersed phase viscosities. Regarding industrial processes, smaller liquid bridges or even no bridges are favorable to avoid partial coalescence, coalescence or agglomeration so as to maintain the product quality.

**Figure 12.** (**a**) Dimensionless diameter of the liquid bridge between the solid particle and the liquid droplet shortly after formation for all relative velocities tested. The emulsifier was dissolved in the dispersed phase at different concentrations at the beginning of the experiment. (**b**) Determination of the diameter of the liquid bridge formed during CMN between a solid and liquid n-hexadecane droplet in a microfluidic channel. The images used for the determination of the diameter of the bridge were taken directly after contact of the droplets, with the maximum error between the moment of contact and the picture shot being *t* = 0.01 s.

#### *3.4. Induction Time*

Stirred vessels are used with wide shear rate distributions for industrial melt emulsion production and storage. Melt emulsification is a top-down approach that can produce suspensions with μm-sized particles, while overcoming the disadvantages of the energyand time-consuming wet-milling process [59,60]. The contact time is inversely proportional to the shear rate [16], therefore, it is important to know the required induction time *tind* to trigger crystallization. Once *tind* is obtained, it can be used to optimize process flows. For the collision experiments, *tind* was determined as a function of the surfactant concentration in either the continuous or dispersed phase (Figure 13). Furthermore, *tind* is defined as the time between the first visible contact and the detection of the first crystal.

When the experimental aqueous concentration of the surfactant was found to be above the CMC micelles were detected in the continuous phase with a volume fraction >0.1% (Figure 13, i: water) and the induction time was up to ten times higher than without or with very few micelles and aqueous single molecules (Figure 13, i: n-hexadecane). Without any surfactant, the induction time ranged from 0.1 to 0.4 s (data not shown), which highlights the crystallization-impeding effect of the aqueous emulsifier micelles or single molecules. A wide range of induction times measured is apparent. Aqueous surfactant concentrations of 16.6 mol·m−<sup>3</sup> (*ϕ<sup>m</sup>* ~2.8%) and 42.8 mol·m−<sup>3</sup> (*ϕ<sup>m</sup>* ~7.1%) are not shown because crystallization did not occur within 60 s.

**Figure 13.** Induction time *tind*, defined as the delay between nucleation and the first visible contact between the droplet and particle, as a function of surfactant concentration in either dispersed or continuous phase for relative velocities ranging from 6 <sup>×</sup> <sup>10</sup>−<sup>6</sup> up to 4 <sup>×</sup> <sup>10</sup>−<sup>3</sup> m s<sup>−</sup>1.

According to [61–63], we calculated the theoretical coalescence times for two nhexadecane droplets with a radius *r* in water without any surfactant. The theoretical coalescence times ranged from 0.3 s to 1.1 s at room temperature *η* = 30.3 mPa s, *ρhex* = 773 kg m−<sup>3</sup> , *ρwater* = 998 kg m<sup>−</sup>3, *γLL* = 47 mN m<sup>−</sup>1, *r* = 184 *μ*m Adding surfactant to the system increased the theoretical coalescence times by up to 43 s (*γLL* <sup>∼</sup> <sup>4</sup> mN m<sup>−</sup>1). Taboada et al. [25] measured coalescence times ranging from 10 s up to more than 30 min for different emulsifiers in single droplet experiments with water as the continuous phase. Regarding nonionic surfactants, Leister et al. [64] obtained coalescence times between 5 and around 100 s. The measurements from Taboada et al. [25] and Leister et al. [64] are within the same range as our calculated theoretical coalescence times. We expect induction times to be within the mentioned range, providing that the surfactant is dissolved in water, which is in good agreement with our experimental data (Figure 13). Moreover, the theoretical coalescence time without any surfactant and the determined experimental induction time are in the same range. Dudek et al. [12] described increasing mean coalescence times and the increasing distributional width of the coalescence times with increasing surfactant concentrations. We, therefore, assume that mechanisms that prevent coalescence also hinder crystallization, for example, an increasing surfactant concentration in the continuous phase.

.

When Tween®20 was dissolved in the dispersed phase during our experiments, induction times were comparable to the theoretical coalescence times without any surfactant. This highlights the influence of surfactant within the continuous phase. With increasing surfactant concentration in the oil phase (and, thus, decreasing specific interfacial energies), slightly shorter induction times were measured, and the span of the induction times decreased.

#### **4. Discussion**

The results presented show that higher relative velocities and, thus, higher contact forces are needed to ensure crystallization if the surfactant concentration in the continuous aqueous phase increases. Regarding aqueous surfactant concentrations of Tween®20 higher than *<sup>c</sup>H*2*<sup>O</sup> TW*<sup>20</sup> = 23 mol·m−<sup>3</sup> (aqueous micellular volume fraction *<sup>ϕ</sup>m*~3.8%), an oscillatory, repulsive force by micelles is considered likely, which is shown by calculations according to [13], where OSF are considered (Figure 1). Connecting this repulsive force with the Van der Waals forces, an aqueous surfactant concentration higher than around 90 mol·m−<sup>3</sup> (*ϕ<sup>m</sup>* ~15%) would show an energy barrier that must be overcome by contact force. Crystallization should take place for all aqueous surfactant concentrations presented

here because the stability factor is smaller than 1 and attractive forces should dominate. This hypothesis cannot be verified by the experimental results. From all the continuous surfactant concentrations tested above the CMC, only 7 · CMC shows CMN at relative velocities higher than 8 × <sup>10</sup>−<sup>4</sup> m s<sup>−</sup>1. Oscillatory forces are not expected at this surfactant concentration in the aqueous phase, and crystallization should take place even for low contact forces (=low relative velocities).

Consequently, in addition to the volume fraction of micelles, their stability also plays a major role. Christov et al. [65] concluded from atomic force microscopy measurements that Tween®20 micelles are significantly more unstable when exposed to hydrodynamic shear than, for example, micelles from Brij 35. The micelles dissolve into single molecules even in cases where only a small force is applied, therefore, a considerably larger number of single molecules are displaced from the gap between the droplet and the particle, which results in a greater time requirement for nucleation.

The single aqueous surfactant molecules can also occupy newly formed interfaces. The droplet spread around the particle and increased its interface for relative velocities higher than 7.5 <sup>×</sup> <sup>10</sup>−<sup>5</sup> m s−<sup>1</sup> and *<sup>c</sup>H*2*<sup>O</sup> TW*<sup>20</sup> > 8 <sup>×</sup> <sup>10</sup>−<sup>3</sup> mol·m<sup>−</sup>3. This effect was only observed when Tween®20 was dissolved in the continuous, aqueous phase and became more dominant with increasing relative velocities. Depending on the freely available, single molecule concentration, this newly formed interface is unlikely to be occupied fast enough and, thus, nucleation took place. Higher relative velocities then triggered crystallization. One possible reason is the increasing contact force relative to increasing relative velocities. Moreover, emulsifier could be detached from the droplet/particle surfaces due to the increased shear forces, resulting in an unoccupied interface.

Furthermore, pH and conductivity measurements (data not shown) revealed an electrical loading for the surfactants' head groups. Although nonionic emulsifiers were used by Dudek et al. [12] amongst others, a negative surface charge occurred in their experiments due to the deprotonated hydroxide groups of the emulsifiers' head groups. They attribute their observation of longer mean coalescence times to a stronger rejection of the head groups at an increased emulsifier concentration. An increase in the negative charge of oil-in-water emulsions with an increasing Tween®20 concentration has also been reported by Hsu et al. [66]. The electrostatic repulsion could explain the smaller bridge diameters (Figure 12), increased surfactant concentration in the oil phase and longer induction times (Figure 13) with an increasing continuous surfactant concentration because a higher number of surfactant molecules leads to increasing repulsion. Accordingly, the specific interfacial energy plays less of a role compared to the micelles. This hypothesis is further supported by the fact that the induction times for the experiments with surfactant dissolved in the dispersed phase are very similar to those determined without any surfactant.

It is well-known that, for biological systems, nonpolar substances attract each other in water due to hydrophobic interactions, although the mechanism behind this is not yet fully understood (e.g., [67]). In the literature, attraction was evidenced within distances ranging from 100 to 6500 Å [68,69] and even up to around 3.5 mm for rough (super)hydrophobic surfaces [70]. Nonetheless, any hydrophobic interactions between n-hexadecane particles and droplets are attenuated by the micelles to a greater degree in the continuous phase than by emulsifiers at the interface. The micelles seem to shield the two reaction partners from each other. When no micelles or only very few single molecules are present in the continuous phase, the hydrophobic interactions can be detected by the liquid bridge formation.

Krawczyk et al. [71] state that the rupture of the liquid film between two colliding partners is greatly affected by the phase in which the surfactant is dissolved. This is due to different surfactant transportation mechanisms to the interface. Surfactants dissolved in the continuous phase can delay film rupture, because the surfactant must travel from the film perimeter into the film center, where the lowest interfacial surfactant concentration occurs. This additional flux can influence the film rupture. Emulsifiers that are dissolved in the oil phase are required to travel shorter distances and are, therefore, more efficient in equalizing local specific interfacial energy gradients (as long as the film radius << the droplet radius). The authors describe similar behavior of systems with surfactant in the dispersed phase and systems without any surfactant. This can also be seen in our measured induction times, which are similar for systems without emulsifier and with surfactants dissolved in the dispersed oil phase. Comparable behavior may be explained by Bancroft's rule [1], which describes a stable emulsion as a system in which the emulsifier is preferentially dissolved in the continuous phase.

Another possible reason for limited nucleation could be the absence of a monolayer at the liquid–liquid interface and the presence of a multilayer or even micelles that attach to the interface (e.g., [72]). This additional shield could prevent or decrease the inoculation efficiency of the CMN.

#### **5. Conclusions**

Considering all our experimental results, we found that the variation of the locus of the initial dissolution and the concentration of the emulsifier had a significant influence on the contact form observed and on the efficiency of the CMN. Importantly, the aqueous surfactant concentration and the relative velocity between the droplet and the particle significantly impacted the CMN in the microfluidic system.

We were able to show that increasing surfactant concentration in the dispersed oil phase can trigger nucleation. In applying these results to industrial melt emulsion production, the processes after collision and crystallization must be considered as pivotal for influencing the particle size distribution and, thus, product properties. The higher the contact area is, the higher the probability that partial coalescence occurs, and, in the case of temperature fluctuations during, for example, transportation, coalescence may occur. Therefore, based on the observations of this study, dissolution of the water-soluble emulsifier in the hydrophobic dispersed phase prior to the experiment can be useful to trigger CMN. Partial coalescence could also be decreased with high micellular concentrations in the continuous phase, but, at the same time, CMN also becomes hindered.

Further experiments will test the newly stated hypothesis that the coalescence theory can be transferred to CMN. The emulsifier, for example, will be varied, and ionic emulsifiers will be used to investigate a possible ionic repulsion of the head groups. Furthermore, a differential pressure sensor will be connected to the microfluidic setup to calculate the contact force needed for crystallization and to determine the dependency of the contact force on the relative velocity and surfactant concentration. Moreover, experiments that take place in a new microfluidic device containing a larger liquid reservoir, where droplets and particle can freely collide without the geometric restrictions of a single channel, are planned. Similar experimental setups are described in the literature for coalescence-time experiments [56,73].

**Author Contributions:** Conceptualization, G.K., M.K.; methodology, G.K.; software, G.K., A.R., G.G.; validation, G.K., A.R., G.G., M.K.; formal analysis, G.K., A.R.; investigation, G.K., A.R.; data curation, G.K., G.G., M.K.; writing—original draft preparation, G.K.; writing—review and editing, G.G., M.K.; visualization, G.K., A.R.; supervision, M.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data and methods used in the research are presented in sufficient detail in the document for other researchers to replicate the work.

**Acknowledgments:** We acknowledge support from the KIT-Publication Fund of the Karlsruhe Institute of Technology. We thank the Deutsche Forschungsgesellschaft for the substantial financial contribution in the form of NMR instrumentation and access to the instrumental facility Pro2NMR. Special thanks to Nico Leister and Jasmin Reiner from the Institute of Process Engineering in Life Sciences, Chair I: Food Process Engineering, who permitted the surface tension measurements and engaged in helpful discussions. Additionally, this work would not have been possible without the support of the workshop employees at the Institute of Thermal Process Engineering, especially Max Renaud. Anisa Schütze, who is a student, also performed valuable experiments for this article.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Abad Albis 1,2,\*, Yecid P. Jiménez 2,3, Teófilo A. Graber <sup>2</sup> and Heike Lorenz <sup>4</sup>**

	- teofilo.graber@uantof.cl (T.A.G.)

**Abstract:** In this work, the kinetic parameters, the degrees of initial supersaturation (S0) and the profiles of supersaturation (S) were determined for the reactive crystallization of K2SO4 from picromerite (K2SO4 . MgSO4 . 6H2O) and KCl. Different reaction temperatures between 5 and 45 ◦C were considered, and several process analytical techniques were applied. Along with the solution temperature, the crystal chord length distribution (CLD) was continuously followed by an FBRM probe, images of nucleation and growth events as well as the crystal morphology were captured, and the absorbance of the solution was measured via ATR-FTIR spectroscopy. In addition, the ion concentrations were analyzed. It was found that S0 is inversely proportional to the reactive crystallization temperature in the K+, Mg2+/Cl<sup>−</sup>, SO4 <sup>2</sup>−//H2O system at 25 ◦C, where S0 promotes nucleation and crystal growth of K2SO4 leading to a bimodal CLD. The CLD was converted to square-weighted chord lengths for each S0 to determine the secondary nucleation rate (B), crystal growth rate (G), and suspension density (MT). By correlation, from primary nucleation rate (Bb) and G with S0, the empirical parameters b = 3.61 and g = 4.61 were obtained as the order of primary nucleation and growth, respectively. B versus G and MT were correlated to the reaction temperature providing the rate constants of B and respective activation energy, E = 69.83 kJ·mol<sup>−</sup>1. Finally, a general Equation was derived that describes B with parameters KR = 13,810.8, i = 0.75 and j = 0.71. The K2SO4 crystals produced were of high purity, containing maximal 0.51 wt% Mg impurity, and were received with ~73% yield at 5 ◦C.

**Keywords:** potassium sulfate; picromerite; nucleation; crystal growth; supersaturation

#### **1. Introduction**

Potassium is one of the three types of macronutrients [1]. Its natural sources are mineral salt deposits containing KCl in sylvinite or K2SO4 in kainite or picromerite and natural brines from salt flats such as Atacama-Chile [2,3] and Uyuni-Bolivia [4]. There are several known and traditional methods to produce K2SO4 as, for example, the reaction of KCl with sulphate containing compounds such as H2SO4 [5], Phosphogypsum in an NH4OH and isopropanol medium [6], Na2SO4 [7,8], and (NH4)2SO4 [9], or from seawater [10] and leonite or langbeinite minerals to produce intermediate picromerite by hydration and final transformation to K2SO4 [11].

Producing K2SO4 from MgSO4 and KCl by reactive crystallization in an aqueous solution involves the formation of picromerite and K2SO4, using the Jänecke projection that describes the reactions via the phase diagram of the reciprocal quaternary system K+, Mg2+/Cl−, SO4 <sup>2</sup>−//H2O at 25 ◦C [12]. The latter also allows estimating the proportions of reactants and products. Jannet et al. [12], Voigt [13], Fezei et al. [14], and

**Citation:** Albis, A.; Jiménez, Y.P.; Graber, T.A.; Lorenz, H. Reactive Crystallization Kinetics of K2SO4 from Picromerite-Based MgSO4 and KCl. *Crystals* **2021**, *11*, 1558. https:// doi.org/10.3390/cryst11121558

Academic Editor: Shujun Zhang

Received: 31 October 2021 Accepted: 8 December 2021 Published: 14 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Goncharik et al. [15] depict the reactive crystallization process based on the underlying phase equilibria in two stages: first, the formation of picromerite and second, the generation of K2SO4. The work mentioned above on the conversion processes and the K2SO4 yield improvement in a batch crystallizer do not explicitly consider the reactive crystallization kinetics of K2SO4.

Crystallization is the first and most crucial step to produce, purify, and isolate high purity products in batch and continuous processes, and batch crystallization is one of the unit operations widely used in the chemical, pharmaceutical, and food industries [16,17]. However, batch crystallization has disadvantages associated with its control and, in particular batch-to-batch variability, expressed in terms of product purity, crystal morphology, mean particle size, crystal size distribution (CSD), bulk density, filterability, and flow properties of the dry solids that depend on the profile of supersaturation achieved during the crystallization, drying, packaging, and transport process [18–20].

Therefore, to design the operating conditions with optimal control of a crystallizer, the crystallization kinetics must first experimentally be determined based on the population density [17]. This requires the collection of CSD data that directly relate the nucleation and crystal growth events occurring simultaneously. Furthermore, new crystals can result from two different nucleation mechanisms, classified as primary and secondary nucleation or a combination of both [18].

Nemdili et al. [21], Bari et al. [22], and Luo et al. [23] measured the metastable zone width (MSZW) of a K2SO4-water solution by means of a turbidimeter and an ultrasonic probe and used an ultrasonic and Focused Beam Reflectance Measurement (FBRM) probe, respectively, to determine mainly the primary nucleation parameters. Bari and Pandit [24] simulated the order and the primary and secondary nucleation constants of K2SO4 using the gPROMS program and data from MSZW. Luo et al. [23] concluded that the MSZW of the potassium sulfate solution increases with the increasing concentration of aluminium and silicon ions as impurities because they suppress nucleation and block the active sites of K2SO4 crystals. They reported a nucleation activation energy of 33.99 kJ·mol<sup>−</sup>1.

In relation to the K2SO4 growth kinetics, Nemdili et al. [21] determined the desupersaturation curve of a K2SO4-H2O solution when cooling from 40 to 27 ◦C and using a seed size of 250–355 μm. They derived the order of growth and concluded that growth occurs via the spiral growth mechanism. Gougazeh et al. [25] investigated the growth kinetics of a K2SO4 single crystal under a microscope analyzing the obtained images. They concluded that the order of growth is not affected by temperature, and the single crystal growth is governed by the spiral growth mechanism. They specified the activation energy of growth as 39.4 kJ·mol−<sup>1</sup> and claimed that the presence of 5 ppm Cr3+ blocks the active growth sites of K2SO4. Kubota et al. [26] confirmed this mechanism leading to suppressed growth. Mullin and Gaska [27] determined the growth kinetics of a K2SO4 single crystal in two selected directions, width (001) and length (100), finding that the linear growth rate is greater for axis 001 and minor for axis 100, due to flow effects of the supersaturated aqueous solution circulating through the cell. Furthermore, they reported that crystal growth of K2SO4 under the conditions used is diffusion-controlled.

Secondary nucleation occurs in the presence of "father" crystals and their interaction with themselves, the crystallizer walls, and the agitator. It results from seeding, presence of dendrites, breakage, and fluid shear forces according to mechanical, hydrodynamic, and supersaturation forces. In industry, secondary nucleation is the mechanism that governs the crystallization of soluble substances from a singular solute solution (e.g., salt-water) [28].

Chianese et al. [29] studied the effect of secondary nucleation on CSD for the K2SO4- H2O system in a seeded batch crystallizer. They found that the generation of fragments depends on suspension density and supersaturation. They incorporated the effects of secondary nucleation due to attrition in their model and established that the model does not predict the experimental behaviour at all. Mohamed et al. [30] simultaneously determined the kinetic parameters of secondary nucleation and growth of K2SO4 in its aqueous solution with seeding based on the population density data. They performed the population balance

and solved the population equilibrium Equation using the "s" plane analysis method. They correlated the magma density (MT), growth rate (G), solution circulation rate (Q), and absolute temperature (T). They reported the relative parameters of secondary nucleation rate (B) according to the model B = KRGi MT j Qkexp(-E⁄RT) with values of relative kinetic order, *i* = 0.90, exponent of magma density, *j* = 0.57, exponent of solution circulation rate, *<sup>k</sup>* = 1.49, and apparent secondary nucleation activation energy, *<sup>E</sup>* <sup>=</sup> −3.36 kJ·mol<sup>−</sup>1.

The effect of secondary nucleation on CSD is generally determined in binary systems because supersaturation and seeding can be adequately controlled. However, both primary and secondary nucleation mechanisms occur in the reactive crystallization process via the generation of supersaturation by reaction [31]. There, the reaction rate, the narrow variation in agitation, and the limited transfer of mass to the crystal interface make the study of secondary nucleation and growth complex. Despite these limitations, it is important to study secondary nucleation for soluble salts in reciprocal salt pair systems because many reactions produce intermediate compounds such as double salt hydrates as picromerite to which another reagent can be added to obtain the desired anhydrous product. Furthermore, these products can be redissolved to further improve the CSD by controlled cooling. There are a few related reports in the literature on reactive crystallization for sparingly soluble salts, such as the works of Taguchi et al. [31], Lu et al. [32] and Mignon et al. [33], but to the knowledge of the authors not on soluble salts in a reciprocal salt pair system.

Thus, the purpose of this work is to study the reactive crystallization kinetics between aqueous solutions (aq) of KCl(aq) and MgSO4(aq) (the latter from picromerite) to produce K2SO4. Reaction temperatures of 5, 15, 25, 35, and 45 ◦C were applied, and initial local supersaturations and the supersaturation profiles as a function of time were determined. Population density data in terms of crystal count, length, area, and volume were collected using an FBRM probe to simultaneously estimate primary (Bb) and secondary (B) nucleation kinetics, growth (G), and suspension density (MT) over time. Since the CLD measured by FBRM is related but not similar to the CSD [34], the CLD data was converted to CSD data based on the works of Heath et al. [35]; Togkalidou et al. [17]; Trifkovic et al. [36]; Óciardhá et al. [37], and, Ajinkya et al. [34]. During reactive crystallization, the absorbance and temperature of the solution were followed in situ and in real time using ATR-FTIR and Pt-100, respectively. In addition, the change in ion concentrations was measured, and images of nucleation and growth events, as well as crystal morphology were captured.

This work contributes to determining the kinetic parameters of nucleation and growth for the reciprocal salt system under study and the degree of supersaturation based on the Pitzer ionic interaction parameters for the reactive crystallization process of K2SO4(s). In addition, this research constitutes a potential tool for producing K2SO4 from picromerite.

#### *1.1. Reaction, Thermodynamic and Crystallization Kinetics Framework*

#### 1.1.1. Dissolution and Reaction of Picromerite

The dissolution of picromerite is an incongruent process; it decomposes in the presence of water according to the following Equation:

$$\mathrm{K}\_{2}\mathrm{SO}\_{4}\cdot\mathrm{MgSO}\_{4}\cdot6\mathrm{H}\_{2}\mathrm{O}\_{(s)} / \mathrm{H}\_{2}\mathrm{O} \leftrightarrow \mathrm{nK}\_{2}\mathrm{SO}\_{4(s)} + (1-n)\mathrm{K}\_{2}\mathrm{SO}\_{4(aq)} + \mathrm{MgSO}\_{4(aq)} + 6\mathrm{H}\_{2}\mathrm{O}\_{(l)} / \mathrm{H}\_{2}\mathrm{O} \tag{1}$$

In a second step, a KCl(aq) solution reacting with MgSO4(aq) from picromerite leads to the formation of K2SO4(s) product crystals according to Equation (2) which forms the basis of the crystallization kinetics study in this work.

$$\text{(1 -- n)}\text{K}\_2\text{SO}\_{4\text{(aq)}} + \text{MgSO}\_{4\text{(aq)}} + 2\text{KCl}\_{\text{(aq)}} \leftrightarrow \text{K}\_2\text{SO}\_{4\text{(s)}} + (1 - n)\text{K}\_2\text{SO}\_{4\text{(aq)}} + \text{MgCl}\_{2\text{(aq)}}\tag{2}$$

#### 1.1.2. Thermodynamic Supersaturation

The determination of the thermodynamic supersaturation is based on estimating the activity coefficients of the ionic pair K+-SO4 <sup>2</sup><sup>−</sup> as a function of temperature in a mixture of electrolytes K+-Mg2+//Cl−-SO4 <sup>2</sup>−, based on the Pitzer model. The latter considers the ionic strength of the electrolyte mixture since supersaturation is the driving force that promotes nucleation and growth of crystals in crystallization processes.

Pitzer's model [38–41] requires the binary ionic interaction parameter values of *β*(0) *ij* , *<sup>β</sup>*(1) *ij* , *<sup>β</sup>*(2) *ij* , and *<sup>C</sup>*<sup>∅</sup> *ij* for reactant electrolytes and products as a function of temperature, where *i* and *j* represent the ionic pair cation and anion, respectively. The ionic interaction parameters of KCl(aq), MgCl2(aq), and MgSO4(aq) as a function of temperature are given in Table 1. They were obtained by Equations (S1)–(S3), whose empirical parameters are found in Tables S1–S3, established by Holmes et al. [42], De Lima and Pitzer. [43], and Phutela and Pitzer [44], respectively (see Supplementary Information (SI).


**Table 1.** Pitzer ionic interaction parameters of electrolytes KCl, MgCl2 and MgSO4 at different temperatures.

Once the activity coefficients of the ion pair K+-SO4 <sup>2</sup><sup>−</sup> are determined in the system K+-Mg2+//Cl<sup>−</sup>-SO4 <sup>2</sup>−, they are related to the molal concentration and the thermodynamic equilibrium constant Ksp of K2SO4, which was determined using the Pitzer model for isotherms of 5, 15, 25, 35, and 45 ◦C based on solubility data [45]. The Ksp data for K2SO4 estimated in this work are similar to those reported by Jiménez et al. [46] for isotherms of 15, 25, 35, and 45 ◦C. The Ksp results of K2SO4 found in Table S4 (SI) are replaced in Equation (3) to obtain the dimensionless degree of supersaturation "S" used in the reactive crystallization process of K2SO4. Then, S is given by:

$$S = \gamma\_{\pm} \left( \frac{m\_{+}^{v\_{+}} m\_{-}^{v\_{-}}}{K\_{sp}} \right)^{1/v} \tag{3}$$

where, *<sup>γ</sup>*<sup>±</sup> is the mean activity coefficient corresponding to K2SO4, *<sup>m</sup>v*<sup>+</sup> <sup>+</sup> *and mv*<sup>−</sup> <sup>−</sup> are the molal concentration of the K+ and SO4 <sup>2</sup><sup>−</sup> ions raised to their respective stoichiometric coefficients and *v* is the total coefficient of K+ and SO4 <sup>2</sup><sup>−</sup> (*v*<sup>+</sup> <sup>+</sup> *<sup>v</sup>*−).

#### 1.1.3. Crystallization Kinetics

The CLD measured by the FBRM probe differs from the CSD measured by sieving, laser diffraction, and PVM. However, using the mean or mode average of the squareweighted chord length was found to be comparable to conventional sizing techniques for the range of about 50–400 μm [35]. Therefore, on that basis, it is possible to determine the population density and then exploit it for crystallization kinetic studies [17,35]. The mathematical Equations that allow obtaining CSD-based moments from CLD are presented below [17,35].

The jth moments from CLD data are calculated with Equation (4) according to Trifkovic et al. [36]:

$$\mu\_{\dot{I}}(t) \equiv \int\_0^\infty L^{\dot{I}} n(L, t) \, dl \approx \sum\_{i=1}^{FBRM} L\_{\text{ave},i}^{\dot{I}} N\_i(L\_{\text{ave},i}, k) = N\_k \tag{4}$$

where *Li* is the chord length, *Ni* the number of particles in channel *i*, and *k* the discrete time counter. *Lave*,*<sup>i</sup>* is the arithmetic mean between the upper (*Li*) and lower (*Li*−1) channel size and is expressed as:

$$L\_{\text{ave},i} = \frac{L\_i + L\_{i-1}}{2} \tag{5}$$

Trifkovic et al. [36] used the total number of crystals in the entire FBRM size range (1 to 1000 microns) to calculate the nucleation rate. The number of particles as a function of time is given by Equation (6).

$$N(t) = \int\_0^\infty n(t)dL \approx \sum\_{i=1}^{FBRM} N\_{i,k} = N\_k \tag{6}$$

Furthermore, it is possible to determine the nucleation rate as a difference of the total number of particles at each moment per mass of solvent, according to Equation (7).

$$B\_{\exp}(t) = \frac{1}{M(t)} \frac{dN(t)}{dt} \equiv \frac{1}{M\_k} \frac{\Delta N\_k}{\Delta t} = B\_{\exp, k} \tag{7}$$

where *Bexp*,*<sup>k</sup>* and *Mk* are the nucleation rate and the total mass of solvent in the *k*th time interval. From this Equation, the ratio of the particle count to the mass of the solvent can be considered. However, by adopting Equation (4) to determine the 0th moment, this would become a summation of CLD of original FBRM data, which does not consider the conversion from CLD to CSD. According to the report of Heath et al. [35], the population density is considered via the conversion of CLD to CSD as counts of square-weighted chord lengths by the following Equation:

$$N\_{i,n} = N\_{i,0} \mathbb{C}\_{i,A}^{\prime} \tag{8}$$

where *Ni*,*<sup>n</sup>* is the number of n-weighted chord length counts in the *i*th channel, *Ni*,0 the count of unweighted chord lengths in the *i*th channel, and *C<sup>n</sup> <sup>i</sup>*,*<sup>A</sup>* is the geometric mean length of the *i*th channel given by:

$$\mathbb{C}\_{i,A} = (\mathbb{C}\_{i,\mu} \cdot \mathbb{C}\_{i,l})^{1/2} \tag{9}$$

with *Ci*,*<sup>u</sup>* and *Ci*,*<sup>l</sup>* the length of the upper and lower limit of the *i*th channel, respectively. Then, by combining Equations (4) and (8), Equation (10) is constituted to determine the moments based on the population density as a function of time per unit mass of solvent. *M* is the mass of the solvent (H2O).

$$\mu\_j(t) \equiv \int\_0^\infty L^j n(L, t) dl \approx \sum\_{i=1}^{FBRM} L\_{ave, i}^j N\_{i, n}(L\_{ave, i}, k) \ast \frac{1}{M} \tag{10}$$

Following the previous Equation, moments of the order 0, 1, 2, and 3 can be determined with the units (#/kgH2O), (μm/kgH2O), <sup>μ</sup>m2/kgH2O , and <sup>μ</sup>m3/kgH2O , respectively as a function of time, also for different degrees of initial local supersaturation reached at temperatures of 5, 15, 25, 35, and 45 ◦C.

Based on the population balance equation (PBE), different ordinary differential equations (ODE's) are obtained that allow for the determination of the nucleation and growth rate and suspension density with respect to time considering the conversion from CLD to counts of square-weighted chord lengths, which are presented below.

*Primary nucleation rate.*

In the reactive crystallization of K2SO4, primary and secondary nucleation (*Bb* and *B*, respectively) occur, whereas *Bb* results from the high supersaturation generated by the reaction. The nucleation rate (*B*) of K2SO4 is determined based on the 0th moment (*μo*) after conversion of the CLD to square-weighted counts [35] (Figures S1 and S2 (see SI)). Then, the B is estimated using the following Equation [47]:

$$\frac{d\mu\_o}{dt} = B\tag{11}$$

In the present work, *Bb* is related with the initial local supersaturation (*S0*) since it has been obtained from the thermodynamic approach when considering the activities of the species K<sup>+</sup> and SO4 <sup>2</sup><sup>−</sup> in the multicomponent system K+, Mg2+/Cl<sup>−</sup>, SO4 <sup>2</sup>−//H2O. To determine the kinetic parameters such as order and rate constant of primary nucleation rate, the following Equation [48] has been used:

$$B\_b = k\_b \cdot S\_o^{\
b} \tag{12}$$

where *b* is the primary nucleation order and kb is the primary nucleation rate constant. *Secondary nucleation rate.*

Secondary nucleation usually depends on suspension density (MT) and supersaturation (*S*). Furthermore, growth (*G*) is also a function of *S*. Then, the relationship of *B* with *G* and MT describes the secondary nucleation rate of K2SO4 in the reactive crystallization process with time and is given as follows [49]:

$$B = K\_R \cdot G^i \cdot M\_T^j \tag{13}$$

Their *i* is the nucleation relative to the order of growth, *j* the suspension density exponent, and *KR* the relative rate coefficient.

*Crystal growth rate.*

The crystal growth rate (*G*) of K2SO4 was simultaneously determined from the population density data, where *G* is linked to the 0th and first moment (Figure S3 (SI)), according to the following Equation [47]: <sup>1</sup>

$$\frac{1}{\mu\_o} \frac{d\mu\_1}{dt} = G \tag{14}$$

With the data of *G* for different degrees of initial supersaturation *S*0, the empirical fit parameters are determined according to [48]:

$$G = k\_{\mathcal{S}} \cdot \mathbb{S}\_0^{\mathcal{S}} \tag{15}$$

*Crystal suspension density.*

The suspension density as a function of time, based on the data of the total volume of crystals *μ*<sup>3</sup> (μm3) (Figure S5 (SI)), was determined as follows [35]:

$$\frac{dM\_T}{dt} = 3 \cdot k\_{\overline{\nu}} \cdot \rho\_{\overline{\epsilon}} \cdot G \cdot \mu\_2 \tag{16}$$

where *<sup>ρ</sup><sup>c</sup>* is the K2SO4 crystals density (2.66 × <sup>10</sup>−<sup>12</sup> g/μm3), *kv* is the volume shape factor (0.69 for K2SO4), and *μ*<sup>2</sup> is the second moment (Figure S4 (SI)). However, the empirical Equation (17) was specified gravimetrically to corroborate the behaviour of the suspension density and through the mass balance (Equation (18)) using data from the third moment as follows:

$$M\_{T\bar{\imath}} = \frac{\mu\_{3\bar{\imath}}}{\mu\_{3f}} M\_{Tf}. \tag{17}$$

where *μ*3i and *μ*3f are the initial and final total crystal volume, and *MTi* and *MTf* are the initial and final suspension density in the reactive crystallization. The mass balance Equation is given by [50]:

$$\mathbb{C}(t) = \mathbb{C}\_0 - M\_{Ti} \tag{18}$$

with *C*<sup>0</sup> being the initial concentration of the solute resulting from mixing both reactive solutions, *C*(*t*) the concentration of the solute over time, and *MTi* as given above.

*Secondary nucleation activation energy.*

In a chemical reaction, efficient collisions occur between atoms, molecules, or ions. The ions of the reciprocal system K+, Mg2+Cl<sup>−</sup>, SO4 <sup>2</sup>−//H2O require the minimum kinetic energy to form the active complex specified by the activation energy *Ea* and expressed by the Arrhenius Equation: 

$$K = A \cdot \exp\left(-\frac{E\_a}{RT}\right) \tag{19}$$

where *K* is the reaction rate constant, *A* is the frequency of molecular collisions, *R* is the universal gas constant, and T is the absolute temperature. Taking the logarithm, it gives:

$$
\ln K = \ln A + \left(-\frac{E\_a}{R}\right)\frac{1}{T} \tag{20}
$$

The graphical relationship of *lnK* versus 1/*T* is linear, with the slope equals (−*Ea*/*R*) and the intercept *lnA*. Thus, the activation energy *Ea* can be obtained from the slope of this plot. For reactive crystallization, the dependence of the secondary nucleation rate constant *KR* on the absolute temperature allows estimating the secondary nucleation activation energy (*E*) in [kJ/mol] [30].

#### **2. Materials and Methods**

#### *2.1. Reagents*

Magnesium sulfate (MgSO4) was purchased from Acros Organic (Geel, Belgium; purity > 97 wt%), potassium sulfate (K2SO4) from Carl Roth GmbH & Co. (Karlsruhe, Germany; purity ≥ 98 wt%), and potassium chloride (KCl) from Merck (Darmstadt, Germany; purity 99.5–100 wt%). All three reagents were used as received. Solid picromerite was obtained by slow evaporation, filtration, and drying. Deionized ultrapure water used as a solvent in all experiments was provided by a Merck Millipore, Milli-Q® Advantage A10 system.

#### *2.2. Experimental Setup and Process Analytical Technology (PAT)*

The experimental setup for reactive crystallization studies is shown in Figure 1. The applied PAT, additional optical process monitoring using the Technobis Crystalline PV system, and further implemented offline analytics will be discussed below.

**Figure 1.** Scheme of the experimental setup. 1 Temperature control system; 2 Universal stand; 3 250 mL-Jacketed glass crystallizer; 4 Glass impeller; 5 Reservoir for saturated solution of KCl; 6 Vacuum pump; 7 Buchner flask; 8 Buchner funnel; 9 Pt-100 sensor; 10 Syringe needle; 11 FBRM probe; 12 Overhead stirrer; 13 ATR-FTIR probe; 14 Disposable syringe filter; 15 Syringe; 16 Data acquisition system.

#### 2.2.1. Focused Beam Reflectance Measurement (FBRM)

For monitoring the change in the CLD of K2SO4 crystals during reactive crystallization, the Particle Track S400A FBRM® probe with focused beam reflectance measurement technology from Mettler Toledo, Gießen, Germany was used. It is based on the backscattering of a rotating laser beam tracking particles flowing in front of the probe window. Since particles can be scanned in parts smaller or larger than their average size, the detected value is called the "chord length". In this study, the terms chord length distribution and a "number of crystals" is used to determine the nucleation rate *B*, growth rate *G*, and suspension density *MT* of K2SO4, but in CLD. The CLD of the crystals was measured in real time and fell in 100 channels. The CLD by channels varies on a logarithmic scale from 1 to 1000 μm, allowing a higher resolution of the CLD of particles <100 μm with the ability to characterize the presence of uni and bimodal particle size distributions. The counts of CLD data were captured every 10 s during 60 min of reactive crystallization. The operational variables of the FBRM to collect data consisted in adjusting the FBRM with an angle of inclination of 82◦ that also acts as a deflector, with the focal position (window) located above the tip of the impeller at a height less than 8 mm. To ensure the presence of crystal samples with the impeller speed used, the pulp concentration should not exceed 20 wt/wt%, and the CLD collection was established in fine mode. In addition, mechanical stirring was kept constant at 317 rpm allowing for a good suspension of crystals. Higher stirring speed generates vortices, small and large bubbles near the edge of the propellant and on the surface of the solution, respectively, which is a problem for moment data reads. All previous operations were based on Heath et al. [35].

#### 2.2.2. Attenuated Total Reflectance-Fourier Transform Infrared (ATR-FTIR) Spectroscopy

The change in absorbance of the solution during reactive crystallization was monitored in real time using the Mettler Toledo ReactIR™ 15 ATR-FTIR probe (Mettler Toledo, Gießen, Germany). The probe immersed in the solution measured the absorbance every 60 s during the 60 min of the reactive crystallization process.

#### 2.2.3. Temperature Measurement

A Pt-100 sensor (Ahlborn Mess- und Regelungstechnik GmbH, Holzkirchen, Germany) was used to follow the temperature of the solution before and during reactive crystallization. Temperature data were collected and recorded with a measurement precision ± 0.01 ◦C. The FBRM-S400A, ATR-FTIR, and Pt-100 probes are shown in Figure 1 as the main components collecting process data on the reactive crystallization of K2SO4.

#### 2.2.4. Technobis Crystalline PV

For image monitoring of nucleation and growth of K2SO4 crystals, the Crystalline PV multi-reactor system with particle viewer module (Technobis Crystallization Systems, Alkmaar, The Netherlands) was used. Images were taken every 20 s during the 60 min of the reactive crystallization process of K2SO4. Digital photographic images of K2SO4 particles as a function of time are displayed directly on the computer screen.

#### 2.2.5. X-ray Powder Diffraction Phase (XRPD) Analysis

Powder samples of the reactive crystallization products were subjected to XRPD analysis using a PANalytical X'Pert-Pro diffractometer (PANalytical GmbH, Kassel, Germany) with an X'Celerator detector and Cu Kα radiation. Samples were measured in a 2-Theta range of 10–100◦ with a step size of 0.0167◦ and a counting time of 30 s per step.

#### 2.2.6. Chemical Analysis by Ion Chromatography (IC)

The concentrations of K+, Mg2+, Cl<sup>−</sup> and SO4 <sup>2</sup><sup>−</sup> were determined by ion chromatography using the Dionex ICS 1100 IC system (Thermo Fischer Scientific, Dreieich, Germany). For calibration, standard solutions of known composition were prepared for the anionic and cationic pairs Cl−-SO4 <sup>2</sup><sup>−</sup> and K+-Mg2+, respectively. These standards allowed determining the concentrations of the cations and anions, with priority for Mg2+ as an impurity in the K2SO4 product crystals to evaluate the product quality.

#### *2.3. Experimental Procedure*

#### 2.3.1. Preparation of the Saturated Solution of Magnesium Sulfate from Picromerite

There are two methods to prepare MgSO4(aq) from picromerite: (1) by dissolving the MgSO4 from the picromerite crystal lattice by addition of water and (2) by isothermal synthesis. Both methods are based on the phase diagram for the ternary system K2SO4- MgSO4-H2O at 25 ◦C (see Figure S6 (SI)). In this work, method (2) has been adopted to prepare MgSO4(aq) from pure reagents K2SO4, MgSO4 and H2O without the need to prepare the picromerite. Since the dissolution of picromerite is an incongruent process, it decomposes in the presence of water, according to Equation (1). As a result, a solid phase of K2SO4(s) is in equilibrium with a saturated liquid phase of K+, Mg2+and SO4 <sup>2</sup><sup>−</sup> ions in water. The solid potassium sulfate is filtered under a vacuum, and the resulting solution is used in the K2SO4 reactive crystallization process to determine the kinetic parameters. For the pulp synthesis according to point C in Figure S6 (see SI), pure reagents K2SO4(s), MgSO4(s) and H2O(l) were mixed to obtain a synthetic pulp constituted of 11.10, 12.54, and 76.34 wt/wt% of K2SO4, MgSO4, and H2O, respectively.

The pulp synthesis and the generation of the saturated MgSO4(aq) solution from picromerite was performed in a jacketed vessel. All the reagents were added on a precision analytical balance (± <sup>1</sup>× <sup>10</sup>−<sup>4</sup> g): 12.9660 g of K2SO4(s), 8.9700 g of MgSO4(s), and 54.5820 g of H2O(l). The vessel with the reagents was hermetically closed, taken into the thermostatted reactor at 25 ◦C and left stirring for 24 h to reach solid–liquid equilibrium and guarantee the pulp composition. The solid was separated from the pulp by vacuum filtration, and the particle-free solution was transferred to another closed vessel maintaining the temperature in a thermostatic bath. The product K2SO4(s) was allowed to dry at room temperature under a fume hood for 24 h. This synthesis procedure was repeated for all the reactive crystallization runs of K2SO4.

#### 2.3.2. Preparation of Saturated Solution of KCl

The KCl(aq) solution reacting with MgSO4(aq) from picromerite gives rise to the formation of crystals of K2SO4(s) according to Equation (2). A saturated solution of KCl(aq) was prepared at 25 ◦C with an excess of 1% of KCl(s) to guarantee solid–liquid equilibrium. The dissolution of KCl(s) in water was carried out separately with magnetic stirring.

#### 2.3.3. Operating Conditions of the Reactive Crystallization Process

The experimentation plan with the operating conditions used is given in Table S5 (SI). Based on Equation (1), the saturated solution of MgSO4(aq) from picromerite was prepared at 25 ◦C. For all the reactive crystallization runs, the concentration of 457 (g of solute/kg H2O) was kept constant where the solute concentration was composed only of (1 − n) K2SO4(aq) and MgSO4(aq) at 25 ◦C, with n = 0.38. On the other hand, the saturated solution of KCl(aq) was prepared according to Equation (2), the concentration was 343.98 (g solute/kg H2O), which also remained constant for all reactive crystallization runs.

#### 2.3.4. Mixing of Reagents and Generation of Initial Supersaturation (S0)

For performing reactive crystallization between the saturated synthetic solution of MgSO4(aq) from picromerite with KCl(aq), it is essential to determine the degree of initial supersaturation *S*<sup>0</sup> and the supersaturation profile with time *S* to derive the nucleation rates, growth rates, and the suspension density during the reactive crystallization of potassium sulfate at different temperatures.

The initial supersaturation *S*<sup>0</sup> was generated by mixing the MgSO4(aq) solutions from picromerite at 25 ◦C, and the saturated solution of KCl(aq), also at 25 ◦C. Mixing of both solutions was carried out at each of the temperatures under study (5, 15, 25, 35, and 45 ◦C) in the experimental setup shown in Figure 1. In each run, the change of CLD, absorbance and temperature was recorded using the FBRM, ATR-FTIR, and Pt-100 probes, respectively. For offline monitoring of the change of ion concentrations K+, Mg2+, Cl<sup>−</sup>, and SO4 <sup>2</sup><sup>−</sup> over time, aliquots of the solution were taken every 2.5 min until 5 min, then every 5 min until 30 min, and finally every 10 min until 60 min. The weight of the aliquots was 0.3291 g of particle-free solution. At the end of the reactive crystallization process programmed for 60 min, the crystallized solid was separated from the pulp by vacuum filtration and dried for 24 h at room temperature. Afterwards, samples of the products obtained were subjected to XRPD analysis to check the phase identity and to chemical analysis by IC.

For the optical reactive crystallization process monitoring of nucleation, growth, and crystal morphology via the Crystalline PV particle vision system, the same conditions described above were applied, with a difference in the reagent amounts. In this case, 4.00 g of MgSO4(aq) from picromerite with 2.19 g of a saturated solution of KCl(aq) were studied in a closed vessel using a hook type stirrer at 400 rpm.

#### **3. Results and Discussion**

#### *3.1. Absorbance and Temperature in the Reactive Crystallization Process*

The results of monitoring the change in absorbance of the solution by ATR-FTIR spectroscopy are shown in Figure S7 (SI). The absorbance decreases as a function of time as the reaction progresses and moves to smaller absolute values at lower temperatures, caused by the lower saturation concentrations of the solute. The absorbance peaks of SO4 <sup>2</sup><sup>−</sup> and H2O are found in the wavenumber range of 1080–1100 cm−<sup>1</sup> and 1645 cm<sup>−</sup>1, respectively. The corresponding temperature profiles are shown in Figure S8 (SI). As expected, after the addition of KCl(aq), stored at 25 ◦C, to the MgSO4 solution at 5, 15, 25, 35, and 45 ◦C, the temperature in the resulting solution increased for lower reaction temperatures of 5 and 15 ◦C to 10 and 17 ◦C, and, decreased for higher reaction temperatures of 35 and 45 ◦C to 32.5 and 41 ◦C, respectively, for a short time only. For the reaction isotherm at 25 ◦C, the temperature remained constant. However, in all cases, in less than 3 min, the initial reaction temperature is restored except for a slight difference at 45 ◦C.

#### *3.2. Supersaturation Profiles, Reactive Crystallization Images and CLD*

The supersaturation as a function of time, *S*, was determined based on the concentration of the ions K+, Mg2+, Cl<sup>−</sup>, and SO4 <sup>2</sup>−. Assuming that the Mg2+ and Cl<sup>−</sup> concentrations in the solution remain constant but K<sup>+</sup> and SO4 <sup>2</sup><sup>−</sup> concentrations vary due to the formation of K2SO4(s) crystals, the concentrations of K+ and SO4 <sup>2</sup><sup>−</sup> were obtained by subtracting those integrated into K2SO4(s) crystals from those entering the reaction. The molal concentrations of mK<sup>+</sup> , mSO2<sup>−</sup> 4 , mMg2<sup>+</sup> and mCl<sup>−</sup> obtained were used to determine the activity coefficients and S, according to Equation (3).

Figure 2 shows the trajectory of S starting from the initial supersaturation *S*0, images of solution/crystals captured by Crystalline PV, and the respective CLD as a function of time during the reactive crystallization of K2SO4 at 5 ◦C. The *S*<sup>0</sup> value in the reaction mixture was 5.15, showing a strong supersaturation as a precondition to initiate nucleation and growth. After an induction time of ~5 min where the reaction solution reached thermal equilibrium and became homogenized, the supersaturation decreased as a result of crystallization, reaching a minimum value of *S* = 2.30 at 20 min. The Crystalline PV system detected at 1.44 and 5 min of reaction (Figure 2a,b) embryo clouds and tiny pseudohexagonal crystals due to nucleation and growth. At the same time, after ~5 min, a low CLD in terms of crystals counted by the FBRM per s <2.5 crystals/s with a chord length of 20–30 microns and a rather unimodal CLD is determined. Once the driving force has been exhausted, after 20 min, the supersaturation remains constant and reactive crystallization is finished, which is corroborated by chemical analysis of the K+, Mg2+, Cl<sup>−</sup> and SO4 <sup>2</sup><sup>−</sup> shown in Figure S9 (SI). At ~10 min, Figure 2c shows growing K2SO4 crystals, separated from each other but overlapping in some parts with defined vertices, maintaining the pseudohexagonal and orthorhombic morphology. The crystal count reached 25 crystals/s with a chord length

between 30–40 microns. A few particles between 2 and 5 microns having a crystal count of 8 crystals/s also appear (Figure 2f), thus leading to a bimodal CLD.

**Figure 2.** Supersaturation *S,* crystal/solution images and CLD for a reaction isotherm of 5 ◦C as a function of time at (**a**) 1.44 min, (**b**) 5 min, (**c**) 10 min, (**d**) 20 min, (**e**) 60 min and (**f**) CLD.

With the time at 20 min (Figure 2d), the crystals grow with a considerable presence of fines whose crystal count reached 42.5 crystals/s in the size range of 30–50 microns and 15 crystals/s in the range of 2–3 microns, keeping the bimodal CLD. Finally, at 6 min (Figure 2e), the pulp contains a considerable amount of fines that obstruct the image viewer of the Crystalline PV equipment; the crystal count reaches 70 crystals/s in the size range of 40–50 microns and 30 crystals/s in the 2–3 microns size range shown in Figure 2f. As seen, the counts of CLD increase with time, specifying product crystals with a bimodal CLD, which is attributed to breakage, attrition by friction or collision of crystals, or crystals with the propeller blades. Thus, crystal count increased but not growth.

At a reactive crystallization temperature of 25 ◦C, an initial supersaturation of *S*<sup>0</sup> = 3.84 is generated (Figure 3), which remains constant for ~10 min and then decreases slowly, reaching the final S of 2.53 at 30 min. This implies that the supersaturation was consumed in 20 min and the crystallization process was stopped. Figure 3a,b show the presence of very tiny crystals with a crystal count <2.5 crystals/s in the chord length range of 10–40 microns (Figure 3e). After 30 min (Figure 3c), it is impossible to identify the crystals' morphology due to their tiny sizes, with a crystal count of 20 crystals/s in a chord length range of 20–30 microns and 15 crystals/s with the size of 9–10 microns. After 60 min (Figure 3d), many tiny crystals are observed with a crystal count of 30 crystals/s between 30–40 microns size and 18.5 crystals/s between 3–6 microns size. Thus, again a bimodal CLD was developed as a result of the generation of fine particles from secondary nucleation mechanisms.

Comparing the reactive crystallization processes of K2SO4 at the two temperatures of 5 and 25 ◦C, as expected, the initial degree of supersaturation is greater at lower temperature and vice versa. As a result, for higher initial supersaturation, de-supersaturation and induction times were shorter, and crystal growth was enhanced, leading to a defined morphology, and a higher crystal count was reached with bimodal CLD. As the crystal images provide qualitative proof of the crystallization progress, in this report, the moment data collected by the FBRM probe were considered to determine the crystallization kinetics. The supersaturation profiles for all reaction temperatures used are compiled in Figure S10 (SI). They confirm the reaction crystallization trends discussed above.

**Figure 3.** Supersaturation *S*, crystal/solution images and CLD for a reaction isotherm of 25 ◦C as a function of time at (**a**) 1.20 min, (**b**) 10 min, (**c**) 30 min, (**d**) 60 min, and (**e**) CLD.

The initial supersaturations *S*<sup>0</sup> generated by reactive crystallization in the reciprocal system are large with values of S0 = 5.15, 4.13, 3.84, 3.54, and 3.24 at 5, 15, 25, 35, and 45 ◦C, respectively. In contrast, the S0- values used in solution crystallization by cooling methods for the binary K2SO4-H2O system are usually lower. For example, Bari and Pandit [24] worked in a range of S0 = 1.07–1.11 when cooling a saturated solution of K2SO4-H2O from 60 ◦C to a temperature between 53–49 ◦C. Gougazeh et al. [25] worked with *S* ∼= 0.00913 at 50 ◦C and Lyczko et al. [51] with *S*<sup>0</sup> = 1.31 at 30 ◦C. Mohamed et al. [30] used an initial supersaturation of S0 = 1.07 for a controlled cooling in a temperature range of 63.5 to 24.6 ◦C. Furthermore, Garside and Tavare [52] applied S0 = 1.09, Mullin and Gaska [27] worked with S ∼= 1.07 at 20 ◦C, and Garside et al. [53] with S = 1.15 at 30 ◦C. On the other hand, in reactive crystallization processes of sparingly soluble salts, the S0 generated is much larger than for the reciprocal salt system studied in this work. Therefore, crystal nucleation and growth events occur within a few seconds of the induction time. Lu et al. [32] report an initial supersaturation of *S*<sup>0</sup> = 1596, with an induction time of 26 s at 15 ◦C to crystallize Mg(OH)2; Taguchi et al. [31] an S0 = 70 with an induction time of 60 s to crystallize BaSO4, Steyer C. [54] an *S*<sup>0</sup> = 500 to crystallize BaSO4, and Mignon et al. [33] values of S0 = 771 and 960 to crystallize SrSO4 and CaCO3, respectively. This results from the fact that sparingly soluble salts exhibit minimal values of the thermodynamic equilibrium constant (KSP). For example, the KSP of BaSO4 is 2.88 × <sup>10</sup>−<sup>10</sup> (mol/kg)<sup>2</sup> at 25 ◦C [31], compared with a KSP of 0.0162 (mol/kg H2O)3 for K2SO4 according to the solubility data [45].

Figure 4 presents the CLDs of K2SO4 crystals after 5 min and the final product after 60 min at the different reaction temperatures investigated. Usually, for an industrial mass crystallization product, a narrow and unimodal CLD, as far as possible free of fine crystals, is targeted. However, in the experiments, a unimodal CLD is only observed at the beginning after 5 min of reaction (Figure 4a), where crystal counts are very low (1 to 4 crystals/s) with crystal sizes between 10–100 μm and fines <10 μm, which is found for all the isotherms studied. Likewise, Figure 4b shows the CLDs of the final K2SO4 product with a bimodal distribution. The region of fines of size <10 μm is specified by crystal counts <2 crystals/s at 45 ◦C, 30 crystals/s at 5 ◦C, and 10–15 crystals/s for isotherms in-between. In the coarse region, the size of the crystals is 15–200 μm with crystal counts of 5 crystals/s at 45 ◦C, 70 crystals/s at 5 ◦C, and 25–35 crystals/s for isotherms between 15 and 35 ◦C. The bimodal distribution is attributed to the effect of secondary nucleation due to the suspension density or breakage and attrition of the crystals. The difference between Figure 4a,b is related to uncontrolled depletion of supersaturation during isothermal reactive crystallization. Therefore, supersaturation is independent and predominant in reactive crystallization as the crystals simultaneously grow while others are born due to the motive force. As a result, the final CLD of the K2SO4 product is not narrow and thus not favourable for subsequent downstream processes such as filtration, drying, storage and transport, and the resistance to relative humidity as well due to the presence of fines <10 μm that can generate lumps, dust release, moisture absorption, etc.

**Figure 4.** CLDs obtained (**a**) at 5 min and (**b**) at 60 min, i.e., the final product, for different reaction isotherms.

In this work, the maximum K2SO4 crystal size obtained according to the semiquantitative analysis of CLD was between 70 and 80 μm at 5 ◦C, which is small compared with crystallization from pure K2SO4-H2O solutions. For example, Bari and Pandit [24] reported an average size of 286 μm via the isothermal method for low supersaturation and Bari et al. [22] an average size of 250 μm by the cooling method. Jones et al. [55] received an average size of 500 μm without fines using seeding and cooling, while via salting out with acetone, they obtained crystal sizes <350 μm with a greater presence of fines and agglomerates. It is concluded that reactive crystallization of K2SO4 from the quaternary K+, Mg2+, Cl<sup>−</sup>, and SO4 <sup>2</sup>−system provides smaller crystals as obtained in K2SO4-H2O systems, which is due to the reaction-inherent high degree of initial local supersaturation.

#### *3.3. Primary Nucleation Rate Bb*

To determine the nucleation rate, the CLD data have been converted to CLD counts square-weighted as a function of time for each reaction isotherm. The results transformed to moment data of the order 0, 1, 2, and 3 by Equation (10) are shown in Figures S2–S5 (SI).

In the reactive crystallization of K2SO4, primary nucleation (*Bb*) and secondary nucleation (*B*) occur, while *Bb* results from the high supersaturation generated. The nucleation rate (*B*) of K2SO4 was determined by Equation (11). Bb is related with *S*<sup>0</sup> since it has been obtained from the thermodynamic approach when considering the activities of the species K+ and SO4 <sup>2</sup><sup>−</sup> in the multicomponent system K+, Mg2+/Cl<sup>−</sup>, SO4 <sup>2</sup>−//H2O. To determine the kinetic order and rate constant parameters of *Bb*, the nucleation rates obtained for each S0 were averaged and then fitted to Equation (12) presented in Figure 5. The fitting parameters derived are *b* = 3.61 and *kb* = 83.68 [#/min·kg H2O] with a coefficient of determination R2 = 0.89, verifying that the behaviour of *Bb* is proportional to *S*0.

The primary nucleation order obtained for the reactive crystallization of K2SO4 is lower than found for the single solute system K2SO4-H2O, as reported by Bari et al. [22], with *b* = 6.5 for the isothermal method (tind). Nemdili et al. [21] reported b = 4.10 and 4.68 when measuring MSZW and tind, respectively. Additionally, Bari and Pandit [24] reported b = 6.5 and 5.73 when determining MSZW via the conventional method and sonocrystallization, respectively. There, *b* is a physical parameter that describes the dependence of the MSZW on the cooling rate regardless of the method used. In contrast, high values for the primary nucleation order are observed in reactive crystallization kinetics of sparingly soluble salts, such as SrSO4 and CaCO3 with *b* = 36.0 and 12.0, respectively, reported by

Mignon et al. [33]. In this report, the empirical value of *b* = 3.61 for the reactive crystallization of K2SO4 has no relation to the MSZW but classifies into the range established by the value of the primary nucleation order for inorganic compounds obtained by cooling, which, as a general rule, are found between 0.98 and 8.3 [23].

**Figure 5.** Correlation of the primary nucleation rate with So for reactive crystallization of K2SO4.

#### *3.4. Secondary Nucleation Rate B*

The profiles of the nucleation rates B during reactive crystallization of K2SO4 at different temperatures are shown in Figure 6. At 5 ◦C (with *S*<sup>0</sup> = 5.15), B decreases from a maximum of 2.68 × <sup>10</sup><sup>6</sup> (#/min·kgH2O) at 3 min to a minimum of 8.35 × <sup>10</sup><sup>5</sup> (#/min·kgH2O) at 20 min, which implies the consumption of supersaturation due to spontaneous nucleation. The decrease in B is attributed to the presence of crystals within the solution since the growth of crystals consumes the supersaturation, the concentration resulting from the suspension density is higher, which is also observed for the 15 ◦C isotherms. However, at <sup>25</sup> ◦C (with *<sup>S</sup>*<sup>0</sup> = 3.84) B starts with 7.7 × <sup>10</sup><sup>4</sup> (#/min·kgH2O) at 10 min reaching a maximum of 8 × 105 (#/min·kgH2O) at ~30 min of crystallization. Clearly B increases, with the increase being slight and attributed to slow crystal growth consuming less supersaturation. The concentration resulting from the suspension density is lower, a behaviour also seen for the 35 and 45 ◦C isotherms. Therefore, it is concluded that the greater S0, the greater is B, and it is depleted in less time than with less S0. This statement agrees with the report by Bari and Pandit [24], also referring to reactive crystallization.

**Figure 6.** Experimental and calculated nucleation rates Bexp [#/min·kg H2O] (symbols) and Bcal (line) as a function of time for different S0 obtained at 5, 15, 25, 35 and 45 ◦C.

Once the nuclei appear, they become stable crystals and grow over time. However, nucleation persists assisted by crystals constituted as suspension density, supersaturation decreases to a low level, and it is there that secondary nucleation occurs (B). Therefore, secondary nucleation is often dependent on suspension density (MT) and supersaturation (S). Furthermore, growth (G) is also a function of S. Then, the relationship of B with G and MT describes the secondary nucleation rate of K2SO4 in the reactive crystallization process with time and is given by Equation (13). The parameters KR, *i*, and *j* are estimated by adjusting the experimental data of G and MT with time using multiple linear regression to obtain the secondary nucleation rate calculated (Bcal) for each So.

The results of *Bexp* and *Bcal* are shown in Figure 6. A good correlation of secondary nucleation with G and MT is observed for most of the isotherms. The *Bexp* and *Bcal* values have practically the same tendencies, superimposed, at 5, 15, 25 and 45 ◦C (*S*<sup>0</sup> = 5.15, 4.15, 3.84 and 3.24), with a coefficient of determination of R2 = 0.976, 0.997, 0.998, and 0.979, respectively, and a slightly lower correlation for the 35 ◦C isotherm (*S*<sup>0</sup> = 3.54), with R2 = 0.943.

The empirical parameters *KR*, *i*, and *j* obtained for each reaction isotherm are compiled in Table S6 (SI). From the results, it can be concluded that B depends on the density of the suspension, whose values of *j* are between 0.20 and 0.80. However, *i* has values of 1.18, 0.63 and 0.1 for the 5, 15, and 25–45 ◦C isotherms, which is attributed to the fact that B depends on G implied by the supersaturation, whose value of *i* is greater than *j* for isotherms of 5 and 15 ◦C. For the 25–45 ◦C isotherms, *i* is less than *j*, suggesting little dependence on B for G. On the other hand, the KR values show irregular behaviour, as seen in the trends of B in Figure 6.

To finally evaluate secondary nucleation via Equation (13), the *G* and *MT* values for different *S*<sup>0</sup> (Figure 6) were fitted to the following Equation:

$$B = 13810.83 \cdot G^{0.75} \cdot M\_T^{0.71} \tag{21}$$

This general description of secondary nucleation in the reactive crystallization process of K2SO4 leads to a relatively low coefficient of determination R2 = 0.11. Therefore it is difficult to attribute the dependence of *B* to the suspension density or crystal growth rate, whose values of *i* and *j* are 0.75 and 0.71, respectively, and thus, both are close to unity [20]. For the crystallization processes in the single solute K2SO4-H2O system via cooling and seeding, Mohamed et al. [30] reported *i* = 0.9 and *j* = 0.57 and concluded that *B* depends on S and MT.

The presence of K2SO4(s) in the reactive crystallization solution contributes to nucleation so that the exponents *i* and *j* take on characteristic values. However, the primary nucleation order (b) depends solely on the degree of supersaturation and the method of detecting the appearance of nuclei, so the nucleation order is greater than the secondary one. Bari et al. [22] reported the dependence of secondary nucleation order (b2) on supersaturation and MT. They found b2 = 2.25 and b = 6.5 for the K2SO4-H2O system, obtained by the isothermal method and, as evident, b2 <b. Taguchi et al. [31] observed in the reactive crystallization process of BaSO4, when mixing two equimolar solutions of BaCl2 and Na2SO4 at 25 ◦C, that secondary nucleation is influenced by the stirring speed (Ns), MT and S, whose exponents are 0.98, 0.84 and 1.72, respectively, with a multiple correlation coefficient of 0.61. The KR parameter implies the dependence of temperature, hydrodynamics, presence of impurities and the properties of the established crystals. Thus, the KR data obtained for each reactive crystallization isotherm of K2SO4 is used to estimate the secondary nucleation activation energy in the following.

#### *3.5. Crystal Growth Rate of K2SO4*

The crystal growth rate (G) of K2SO4 was simultaneously determined from the square weighted CLD data, according to Equation (14). Figure 7 shows the growth rate of K2SO4 crystals as a function of time during the reactive crystallization process for different S0. At 5 ◦C (with S0 = 5.15), G starts with a value of 231.06 μm/min determined at 4.01 min and reaches a minimum value of 4.94 μm/min after 20 min. The decrease in G is caused by the

decrease in supersaturation due to crystallization. At 25 ◦C (with S0 = 3.84), G has an initial value of 101.5 μm/min and decreases over time to 5.30 μm/min at ≈30 min.

**Figure 7.** The growth rate of K2SO4 as a function of time at different S0 generated by reactive crystallization isotherms at 5, 15, 25, 35 and 45 ◦C.

As seen in Figure 7, the crystal growth rate is low due to the predominance of 0th. moment values (μ0) according to Equation (14). It is estimated that the nuclei are in a metastable state; therefore, the decrease in supersaturation is slight. Then, G becomes predominant, and S decreases.

As expected, the initial growth rates in the K2SO4 reactive crystallization are significantly higher than observed in the binary K2SO4-H2O system. Bari and Pandit [24] reported a G of 8.82 μm/min at 49 ◦C studying K2SO4 growth by microscopy. Mohamed et al. [30] reported a maximum growth rate of 6 μm/min at 40 ◦C with seeding, based on population balance data measured in the multichannel Coulter Counter. Mullin and Gaska [27] reported single K2SO4 crystal growth rates of 4.68 and 5.16 μm/min for faces 100 and 001 at 20 ◦C, respectively. In the present report, a maximum growth rate of 231 μm/min was observed at 5 ◦C for the reciprocal quaternary system K+, Mg2+/Cl−, SO4 <sup>2</sup>−/H2O using the FBRM probe in situ, without the need to take samples and without seeding.

With the G data for different degrees of S0, the empirical fit parameters were determined according to Equation (15). As shown in Figure 7, the growth rates steadily decreased from an initial maximum to a minimum for all isotherms. However, for reaction isotherms 35 and 45 ◦C, G increased at the beginning and then diminished to the minimum due to depletion of supersaturation. Thus, the crystals grew, as seen in Figure 2a–c. To correlate G as a function of *S*0, the G values of each isotherm were averaged to estimate the empirical parameters *kg* and *g*. Figure 8 shows the correlation and adjustment of G versus S0, obtaining a value of *g* = 4.64 and *kg* = 0.028 (μm/min) with a coefficient of determination of R2 = 0.761.

In reactive crystallization, the high supersaturation promotes both nucleation and crystal growth, leading to a fast [31] and relatively uncontrolled decrease in supersaturation. Thus, *g* is much higher due to the higher growth rate that implies higher *S*0. However, in reactive crystallization processes for sparingly soluble salts, Taguchi et al. [31] correlated the G of BaSO4 with the stirring speed (N) and *S*0. They mention that the influence of N implies the occurrence of growth controlled by diffusion, while the order with respect to S0 indicates that both diffusion and surface reaction exert some influence on growth rates. Tavare and Gaikar [47] correlated the growth rate of salicylic acid crystals with solution concentration and stirring speed. They report that due to the complexity of determining supersaturation, S was omitted in the correlation. Therefore, the adjusting exponents of both the concentrations of salicylic acid and the agitation speed prevented the attribution of any mechanism of influence on growth.

**Figure 8.** The fit of the empirical parameters *g* and *kg.*

In this report, the value of g = 4.64 is strongly influenced by the initial supersaturation. When *S*<sup>0</sup> is higher for 5, 15, and 25 ◦C, a higher crystal growth rate is promoted. However, the growth rate is much lower for *S*<sup>0</sup> at 35 and 45 ◦C. Therefore, when adjusting G vs. *S*<sup>0</sup> (obtained for 5–45 ◦C) to an empirical Equation, the slope is greater than those known for the K2SO4-H2O systems attributable to growth mechanisms. Thus, for future studies, it is proposed to develop a strategy that allows determining the growth mechanism of K2SO4, taking advantage of the generation of supersaturation by reaction and the initial presence of fine crystals so that a cubic cooling profile can be used to control supersaturation. As a result, a fairly narrow CSD and acceptable average crystal size [56,57] would be feasible.

On the other hand, there are numerous reports for the K2SO4-H2O system for the isolated determination of the growth mechanisms in crystallization processes with low supersaturation controlled by a cooling technique. In these works, generally, the mechanism that controls the growth of K2SO4 is diffusion [21,25–27].

#### *3.6. Crystal Suspension Density MT*

The variation of the suspension density with respect to time was determined by Equation (16), with the results presented in Figure S11 (SI). However, the absolute suspension density was identified via empirical Equation (17) to relate the amount by weight of crystals obtained gravimetrically at the end of reactive crystallization. The results allowed estimating the amount of potassium and sulfate ions in the solution during the reaction to later be used to determine the supersaturation profile.

In Figure 9, the absolute suspension densities at different reactive crystallization isotherms are shown as a function of time. At 5 ◦C (*S*<sup>0</sup> = 5.15), the suspension density increased linearly from 6.84 g of K2SO4/kg H2O at 6 min to 108.45 g of K2SO4/kg H2O at the end of the reactive crystallization at 20 min. At 25 ◦C (*S*<sup>0</sup> = 3.84), an increase in MT from 3.95 g of K2SO4/kg H2O at 10 min to 56.68 g of K2SO4/kg H2O at the end of the reactive crystallization at 30 min is obtained. Thus, the higher *S*0, the higher the suspension density reached in less time. The final MT for the isotherms at 15, 35 and 45 ◦C, with the respective *S*<sup>0</sup> of 4.13, 3.54 and 3.24, were 67.41, 47.03 and 21.29 g of K2SO4/kg H2O, respectively.

The suspension density (*MT*) targeted by crystallization is limited by the solubility, and the S0 reached in the system under study. It depends on the crystallization method and is further affected by the morphology and size distribution of the crystals, filtration demands, and the cocrystallization of an undesired compound. Mohamed et al. [30] reported an MT between 58 and 95 (g of K2SO4 crystals/kg H2O) by cooling from 63.5 to 24.6 ◦C, and 75 (g of K2SO4 crystals/kg H2O) at 40 ◦C for a K2SO4-H2O solution with seeding. In this report of reactive crystallization, a maximum *MT* of 108.45 g of K2SO4/kg H2O at 5 ◦C was

obtained and was limited by the potential cocrystallization of another compound from the reciprocal salt pair.

**Figure 9.** Suspension density of K2SO4 as a function of time at different S0 generated by reactive crystallization isotherms at 5, 15, 25, 35 and 45 ◦C.

The product yield was estimated based on the suspension density data at the end of the reactive crystallization process. For the 5, 15, 25, 35, and 45 ◦C isotherms, the yields achieved were 72.6%, 45.2%, 37.9%, 31.5%, and 14.3% of K2SO4, respectively. As expected, the higher the *S*<sup>0</sup> in the system, the higher the yield and the less reactive crystallization time is required. The yield was determined by relating the amount of K2SO4 obtained experimentally with that calculated by stoichiometry. The mass balances of the reactive crystallization experiments established from the suspension density and the solute concentration (as obtained by Equations (17) and (18)) are depicted in Figure S12 (SI). While the solute concentration decreases, the suspension density increases due to the consumption of supersaturation by crystallization.

The solid K2SO4 obtained at 5 ◦C represents a solid concentration of 11 wt/wt% in the pulp, which is highly favourable for process monitoring by FBRM, as recommended by Senaputra et al. [58], who recommend a pulp concentration not greater than 20 wt/wt%.

#### *3.7. Activation Energy E*

As mentioned above, the dependence of the secondary nucleation rate constant *KR* on the absolute temperature enables estimating the secondary nucleation activation energy *E* via the Arrhenius Equation (20). The results for the reactive crystallization process studied are presented in Figure 10, specifying the secondary nucleation activation energy as *<sup>E</sup>* = 69.83 kJ·mol<sup>−</sup>1. However, to obtain *<sup>E</sup>*, the *KR* values were considered as a function of the temperature that best fit. In addition, the Excel solver has been used under the restrictions of *j* ≥ 1 for the isotherms of 5, 15, and 25 ◦C, also to *i* ≥ 1.5 and 0.12 for the isotherms of 35 and 45 ◦C, respectively, which improves the determination coefficient (R2 = 0.92) in the activation energy estimation. As seen in Figure 10, the secondary nucleation activation energy is higher in the 5–25 ◦C segment due to the higher S0 promoting secondary nucleation, while S0 is lower in the 25–45 ◦C range with the consequence of a lower E.

In general, the secondary nucleation activation energy of 69.83 kJ·mol−<sup>1</sup> obtained for the reactive crystallization process of K2SO4 obeys the principle of positivity. However, it is believed that the activation energy for reactive crystallization primary nucleation of K2SO4 would be much lower due to the rate K2SO4 nucleated from a crystal-free solution. As there are no similar works, they cannot yet be compared with other values related to the reactive crystallization kinetics of soluble salts. However, for reference, Luo et al. [23] reported the activation energy of primary nucleation for cooling crystallization in the K2SO4-H2O system to be 33.99 kJ·mol<sup>−</sup>1, much less than obtained for the secondary nucleation of K2SO4

by reactive crystallization in this work. On the other hand, for reactive crystallization of a poorly soluble salt, Lu et al. [32] reported a nucleation activation energy of 73.049 kJ·mol−<sup>1</sup> for Mg(OH)2. As seen, when nucleation depends only on supersaturation, the activation energy of primary nucleation is much lower, implying that nucleation is faster than obtained in the present report, where the activation energy of secondary nucleation depends on the density of suspension.

**Figure 10.** Dependence of the secondary nucleation rate constant *KR* on the reciprocal reaction temperature.

#### *3.8. K2SO4 Product Quality*

The crystals of K2SO4 obtained as a final product in the reactive crystallization experiments were subjected to X-ray diffraction analysis to be compared with the reagents K2SO4, KCl, and MgSO4 and synthesized picromerite. The diffractograms are compiled in Figure 11. In addition, the product crystals were analyzed regarding the presence of Magnesium as an impurity by ion chromatography. As a result, only very small contents of 0.51, 0.11, and 0.01 wt% of Magnesium were detected in the products of reaction temperatures 5, 15, and 25, 35, and 45 ◦C, respectively. The X-ray patterns in Figure 11 and the low residual Mg amounts in the crystals prove that the K2SO4 obtained is of high quality. The diffractogram obtained for the K2SO4 product at 5 ◦C exhibits several intense peaks that correspond to the patterns of K2SO4 and picromerite, verifying the somewhat higher Mg content in the respective product. K2SO4 is the majority phase, and no other crystalline phase is present, considering a detection limit of XRPD <1%. The presence of picromerite peaks might be attributed to mother liquor occluded between the K2SO4 crystals which, after filtration, crystallizes as picromerite when drying. In this work, the washing process of the K2SO4 product was omitted. Of course, when including washing after solid–liquid separation, a further increase of purity is possible but at the expense of yield. The washing process is essential to improve the quality of K2SO4, as accomplished in the crystallization process of K2SO4 from the KCl(s) picromerite(s)-H2O system reported by Fezei et al. [12–15].

It is important to mention the presence of the eutectic point in the system, which allows deriving the lowest feasible crystallization temperature. In this sense, despite the reactive crystallization of K2SO4 from the multicomponent system K+, Mg2+/Cl−, SO4 <sup>2</sup>−//H2O, the remaining solution still contains salts like MgSO4(aq), KCl(aq), and MgCl2(aq) that could provide more K2SO4 at reaction temperatures below 5 ◦C. The eutectic points of the salts with solubilities are 7.29 g of K2SO4/100 g of saturated solution at −1.9 ◦C, 19 g of MgSO4/100 g of saturated solution at −3.9 ◦C, 19.87 g of KCl/100 g of saturated solution at −10.8 ◦C, and 21.0 g of MgCl2/100 g of saturated solution at −33.6 ◦C [45].

**Figure 11.** X-ray powder patterns of K2SO4, MgSO4, picromerite and K2SO4 product obtained at reactive crystallization temperatures of 5, 15, 25, 35 and 45 ◦C (from bottom to top).

Based on the quality of the K2SO4 obtained by reactive crystallization at 5 ◦C and the eutectic points mentioned above, they allow working at reactive crystallization temperatures below 5 ◦C. In addition, this enables generating higher S0 to improve the process performance since the eutectic point of K2SO4 is −1.9 ◦C, and it is estimated that this temperature is even much lower in the presence of K+, Mg2+, Cl−, and SO4 <sup>2</sup><sup>−</sup> ions. In this regard, Song et al. [59] mention that the solubility of the precipitating compound in a reactive crystallization process increases in the presence of ions in the system; for example, for CaSO4, the solubility increases in the presence of Cl<sup>−</sup>, H+, Ca2+, and SO4 <sup>2</sup><sup>−</sup> ions at 60 ◦C.

#### **4. Conclusions**

Based on the research on the reactive crystallization kinetics of K2SO4 from KCl(aq) with MgSO4(aq) from picromerite, several conclusions can be drawn. The S0 obtained is inversely proportional to the reactive crystallization temperature of K2SO4 and, the S0 was sufficient to promote nucleation and crystal growth at all reactive crystallization conditions used. The CLD obtained at different S0 is unimodal in the first minutes of reaction and bimodal in the final K2SO4 product. The bimodal CLD can be attributed to growth, secondary nucleation, and suspension density due to the higher S0 generated by the reaction. The presence of bimodal CLD's is a reflection of the secondary nucleation effect and is unfavourable for subsequent processes such as filtration, drying, storage, etc. On the other hand, real time images captured during reactive crystallization evidenced the appearance and growth of crystals with pseudohexagonal morphology.

Online monitoring of the CLD and using square-weighted CLD counts shows that Bb, G, and MT are directly proportional to S0. The primary nucleation parameters were determined with the order b = 3.61 and constant kb = 83.68 [#/min·kg H2O] by correlation of Bb with S0. The b-value indicates that the primary nucleation strongly depends on the supersaturation generated by the reaction in the K+, Mg2+/Cl<sup>−</sup>, SO4 <sup>2</sup>−//H2O system and the primary nucleation rate quantification method. In addition, G has been correlated with S0 to estimate the empirical parameter g = 4.61. The allocation of one of the growth mechanisms, such as transport and surface reaction, to the mechanism controlling growth in the performed reactive crystallization of K2SO4 is generally challenging due to the rapid mass transfer of the solute to the solid phase in reactive crystallization processes. The K2SO4 crystals obtained were of high quality containing (unwashed) 0.01–0.51 wt% of magnesium as impurity under the conditions used.

In general, it can be concluded that it was possible to estimate the degree of S0 and the trajectories of S with time in the K+, Mg2+/Cl−, SO4 <sup>2</sup>−//H2O system at 25 ◦C by directly varying the reaction temperature to produce soluble salt crystals like K2SO4. Furthermore, all the S0 values obtained at different reaction isotherms were sufficient to promote the crystallization parameters. However, to improve the quality and performance of the crystals' CSD, it is suggested to apply a programmed cubic cooling profile to the studied system since the coexistence of crystals/solution, e.g., at 45 ◦C, could replace a seeding stage.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/ 10.3390/cryst11121558/s1. Table S1: Empirical values to determine the ionic interaction parameters of KCl, Table S2. Empirical values to determine the ionic interaction parameters of MgCl2, Table S3. Empirical values to determine the ionic interaction parameters of MgSO4, Table S4. Solubility product for potassium sulfate at different temperatures based on solubility data, Table S5. Experimentation plan for reactive crystallization of potassium sulfate in batch crystallization modea, Table S6. Summary of empirical parameters of secondary nucleation rate and coefficient of determination at different temperatures, Figure S1. CLD and square-weighted count, for the final product of K2SO4 crystals at 5 ◦C, Figure S2. 0th moments μ0(#/kg H2O) as a function of time for different So generated at 5, 15, 25, 35 and 45 ◦C during reactive crystallization of K2SO4. Based on square-weighted counts, Figure S3. First moment, μ1(μm/kg H2O) of K2SO4 as a function of time for different So generated at 5, 15, 25, 35 and 45 ◦C during reactive crystallization of K2SO4. Based on square-weighted counts, Figure S4. Second moment, μ2(μm2/kg H2O) of K2SO4 as a function of time for different So generated at 5, 15, 25, 35 and 45 ◦C during reactive crystallization of K2SO4. Based on square-weighted counts, Figure S5. Third moment, μ3(μm3/kg H2O) of K2SO4 as a function of time for different So generated at 5, 15, 25, 35 and 45 ◦C during reactive crystallization of K2SO4. Based on square-weighted counts, Figure S6. Dissolution process of picromerite in water at 25 ◦C. Figure S7. Absorbance profiles of the solution during reactive crystallization at different temperatures, Figure S8. Temperature profiles during reactive crystallization at different temperatures, Figure S9. Behavior of K+, Mg2+, Cl<sup>−</sup> and SO4 <sup>2</sup><sup>−</sup> (g. ion/kg H2O) as a function of time during the reactive crystallization process of potassium sulfate for S0 at 5 ◦C, Figure S10. Supersaturation profiles S as a function of time for different S0 generated at different reaction isotherms: (a) 5 ◦C, (b) 15 ◦C, (c) 25 ◦C, (d) 35 ◦C and (e) 45 ◦C, Figure S11. Suspension density rate of K2SO4 (dMT/dt) as a function of time for different degrees of local initial supersaturation obtained at 5, 15, 25, 35 and 45 ◦C, Figure S12. Suspension density, MT (grams K2SO4 crystals/kg H2O) and solute concentration, C (grams solute/kg H2O) as a function time for 5 to 45 ◦C isotherms.

**Author Contributions:** Conceptualization, A.A. and Y.P.J.; methodology, A.A., Y.P.J. and H.L.; formal analysis, A.A. and Y.P.J.; investigation, A.A.; writing—original draft preparation, A.A.; writing—review and editing, Y.P.J., T.A.G. and H.L.; visualization, A.A.; supervision, T.A.G. and H.L.; funding acquisition, A.A. and T.A.G.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Universidad Autónoma Tomas Frías from Potosí Bolivia 2016–2019.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We are thankful to Universidad Autónoma Tomás Frías (U.A.T.F.) from Potosí Bolivia for declaring the first author in commission via Consejo Carrera de Química, Consejo Facultativo de Ciencias Puras, Comisión Académica and the Honorable Consejo Universitario de la U.A.T.F. 2016–2019. Further, we thank the Universidad de Antofagasta (U.A.) Chile, Programa Doctorado en Ingeniería de Procesos Minerales and the Max Planck Institute for Dynamics of Complex Technical Systems in Magdeburg/Germany for the support of the research internship.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Izabela Betlej 1, Katarzyna Rybak 2, Małgorzata Nowacka 2, Andrzej Antczak 1, Sławomir Borysiak 3, Barbara Krochmal-Marczak 4, Karolina Lipska <sup>5</sup> and Piotr Boruszewski 5,\***


**Abstract:** The paper presents the results of research on the microstructure of bacterial cellulose (BC-SP) obtained on a medium containing sweet potato peel, which was compared to cellulose obtained on a synthetic medium containing sucrose and peptone (BC-N). The properties of cellulose were analyzed using the methods: size exclusion chromatography (SEC), X-ray diffraction (XRD), scanning electron microscope (SEM), and computer microtomograph (X-ray micro-CT). BC-SP was characterized by a higher degree of polymerization (5680) and a lower porosity (1.45%) than BC-N (4879, 3.27%). These properties give great opportunities to cellulose for various applications, e.g., the production of paper or pulp. At the same time, for BC-SP, a low value of relative crystallinity was found, which is an important feature from the point of view of the mechanical properties of the polymer. Nevertheless, these studies are important and constitute an important source of knowledge on the possibility of using cheap waste plant materials as potential microbiological substrates for the cultivation of cellulose-synthesizing micro-organisms with specific properties.

**Keywords:** bacterial cellulose; crystallinity; polymerization degree; porosity; sweet potato waste

#### **1. Introduction**

Bacterial cellulose (BC) is a polymer with great application potential, synthesized by aerobic micro-organisms. Due to its high mechanical strength, high crystallinity, and a much greater degree of polymerization than plant cellulose, it has become a promising polymer for use in various technical fields, and even in medicine.

The main quality parameters of cellulose, determining its desired properties, is the crystallinity and the degree of polymerization. Allomorph Iα is dominant in the bacterial polymer. Aleshina et al. [1] indicate that it may constitute from 70 to 100% of the morphological composition, and additionally the quality and composition of the culture medium on which cellulose is synthesized affects its level in cellulose. Skiba et al. [2] reported that the synthesis of cellulose on unconventional substrates from plant materials causes a reduction in crystallinity and a decrease in the content of Iα in the polymer. The same authors, referring to the works of other authors, indicated that cellulose synthesized on a substrate from agricultural waste in the form of grape bagasse is characterized by a content of allomorph Iα from 70 to 56%. Another important morphological parameter influencing the high tensile strength of cellulose is the degree of crystallinity. In addition, this parameter may vary depending on the method of culturing cellulose-synthesizing micro-organisms [3],

**Citation:** Betlej, I.; Rybak, K.; Nowacka, M.; Antczak, A.; Borysiak, S.; Krochmal-Marczak, B.; Lipska, K.; Boruszewski, P. Structural Properties of Bacterial Cellulose Film Obtained on a Substrate Containing Sweet Potato Waste. *Crystals* **2022**, *12*, 1191. https://doi.org/10.3390/cryst12091191

Academic Editor: Claudia Graiff

Received: 29 July 2022 Accepted: 23 August 2022 Published: 25 August 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the types of carbon source and other components of the medium [4], or the procedure and method of drying [5]. 6. Illa et al. [6] showed that in the case of conventional drying, the degree of crystallinity of bacterial cellulose was slightly higher than during drying by lyophilization. Particular attention is paid to the influence of the composition of the culture medium on the degree of crystallinity of the cellulose. Because the development of low-cost culture media, on which it will be possible to obtain high-quality polymer, additionally with high efficiency, can guarantee its commercial application. Xu et al. [7], using a substrate of sweet potatoes, obtained cellulose with a crystallinity ranging from 83 to 87%. Other authors report that cellulose obtained on substrates containing agricultural waste in the form of oil palm leaf juice [8] or sweet sorghum leaves [9] was characterized by much lower crystallinity.

The properties of bacterial cellulose are also inextricably linked to its degree of polymerization, which is much higher than that of its plant-based counterpart and can be up to 20,000 [10]. Like crystallinity, the degree of polymerization of cellulose can be influenced by various external factors accompanying the synthesis process by micro-organisms. Surma-Slusarska et al. [ ´ 11] obtained cellulose on a substrate with glucose and mannitol with a degree of polymerization of approximately 1700, while Betlej et al. [12] obtained a cellulose polymerization degree of 6080 on a substrate with sucrose and peptone.

The conditions for culturing cellulose-synthesizing micro-organisms, including the composition of the culture medium, have a significant impact on the structural features of cellulose, which will reflect its properties. One of the key features of a bacterial polymer, determining its potential utility, is tensile strength and porosity. Porosity seems to be of particular importance in the case of the use of cellulose in the form of medical dressings, being gas-permeable and thus preventing the growth of anaerobic bacteria in places protected by it [13].

However, it should be remembered that the guarantee of the production volume of bacterial cellulose and its global demand is the reduction of production costs, while maintaining excellent physical and mechanical properties. According to Rivas et al. [14], the cost of cultivation on standard microbiological media may account for approximately 30% of the total cost of the process, therefore, efforts should be made to search for alternative sources of nutrients in the processes of microbial cultivation. It seems that a good alternative to synthetic substrates may be waste from plant production, which are rich in sugars, proteins, vitamins, and microelements necessary for the development of cellulose-synthesizing micro-organisms. At the same time, the management and reuse of plant waste can bring many benefits, including by reducing the costs of exportation and disposal or the production of new products.

The aim of the study was to investigate the structural features of bacterial cellulose, such as crystallinity, degree of polymerization and porosity, obtained on the culture medium from sweet potato peel and to compare them to the characteristics of cellulose obtained on a semi-synthetic medium containing sucrose and peptone. The indirect goal of the study was therefore to determine the suitability of plant waste materials, grown in many countries on a large scale, as a low-cost substrate for the production of high-quality polymer for various applications. In this way, we indicate environmentally friendly methods of bacterial cellulose production, which can be used in many industrial areas.

#### **2. Materials and Methods**

Bacterial cellulose (BC) was synthesized by micro-organisms known as Symbiotic Culture of Bacteria and Yeast (SCOBY) grown on two types of media. SCOBY were obtained from the organic farm Wolanin (Wolanin, Szczawnik, Poland). According to literature data, the dominant bacterial cultures are the species *Acetobacter xylium*, *A.pasteurianus*, *A. aceti*, and *Gluconobacter oxydans* [15], among the fungi yeasts belonging to *Saccharomyces*, *Saccharomycodes*, *Schizosaccharomyces*, or *Zygosaccharomyces* [16] are the those that are dominant. The test cultures were stored on agar slants containing 0.03% peptone (Biomaxima SA, Lublin, Poland), 0.05% yeast extract (Biomaxima SA, Lublin, Poland), 2.5% glucose (PPF

HASCO-LEK S.A., Wrocław, Poland), and 2.5% agar (AphaVit, Biała Podlaska, Poland). Before starting the experiment, an inoculum of micro-organisms was taken and introduced into 100 cm<sup>3</sup> of a liquid medium containing peptone, yeast extract, and glucose and cultured for 14 days in a heat incubator. During this time, the formation of bacterial cellulose on the surface of the medium was checked. Cultures were carried out in glass beakers with a diameter of 5 cm. The test culture was homogenized and used for inoculation of the media used in the test.

The reference medium contained 10% sucrose (Krajowa Spółka Cukrowa SA, Toru ´n, Poland) and 0.03% peptone (Biomaxima SA, Lublin, Poland). The second type of medium was based on ingredients of vegetable origin (sweet potato peel), treated as waste. The sweet potato tubers were stored at 4 ◦C before the start of the study. To prepare a broth medium based on plant material: 200 g of sweet potato peel, varieties 'Carmen Rubin', 'Purple' and 'Beauregard', grown in the field in Zyzn ˙ ów (49◦49 N 21◦50 E, Poland) on the soil of the defective wheat complex, with a slightly acidic reaction (pH = 6.1, in 1N KCl), suspended in 500 cm3 of water and ground with a blender, model MMBM401W (Bosch, Gerlingen, Germany). Thus, a homogeneous homogenate was prepared. The individual sweet potato homogenates were combined and then mixed. The homogenate was then filtered through the filter paper using a water pump, separating the clear solution from the solids. A clear solution was used as a microbiological broth medium, divided into equal portions, and sterilized in a steam autoclave (Spółdzielnia Mechaników SMS, Warsaw, Poland) for 20 min at 121 ◦C. A total of 1 cm3 of the inoculum was sterile added to both types of media. Cultures were incubated in a heat incubator (J.P. Selecta Laboratory Equipment Manufacturer, Barcelona, Spain) for a period of 14 days. The incubation temperature was 26 ± 2 ◦C. After the end of the cultivation time, the cellulose was purified according to the procedure described by Betlej et al. [17]. Both the cellulose obtained on the standard medium (BC-N) and the cellulose obtained on the sweet potato peel medium (BC-SP) were washed several times with distilled water, then rinsed in 0.1% NaOH solutions (Avantor Performance materials Poland SA, Gliwice, Poland) and 0.1% citric acid (Avantor Performance Materials Poland SA, Gliwice, Poland). Distilled water was always used between uses of the individual alkali and acid solutions and at the end of the rinsing process. The polymer thus prepared was dried at a temperature of 24 ± 2 ◦C in a laboratory dryer (J.P. Selecta Laboratory Equipment Manufacturer, Barcelona, Spain) until obtaining the constant mass of the polymer. The total sugar content in individual sweet potato varieties was presented and described by Krochmal-Marczak et al. [18] in earlier studies (Table 1). Krochmal-Marczak et al. [19] in other studies reported that the average protein content in dry matter in the raw material used is 1.35 g 100 g−1, the average content of vitamin C is 22.86 mg 100 g−1, and macroelements (P, K, Ca, Mg, Na) are 0.26, 2.12, 0.51, 0.13, and 0.19 mg 100 g<sup>−</sup>1, respectively


**Table 1.** Total sugars in sweet potato with peel based on studies by Krochmal-Marczak et al. [16].

\* FM—fresh matter.

#### *2.1. Polymerization Degree and Crystallinity of Bacterial Cellulose*

The degree of polymerization of bacterial cellulose was determined by the size exclusion chromatography (SEC) method [20]. The degree of polymerization of bacterial cellulose were determined according to the methodology described by Antczak et al. [21] and Waliszewska et al. [22], with changes described by Betlej et al. [12]

The crystallinity of polymer was analyzed using a TUR M-62 X-ray diffractometer (Carl Zeiss AG, Jena, Germany) with the method described by Betlej et al. [12]. On the basis of XRD tests, the structural parameters of cellulose were determined:


$$\mathbf{D} = \frac{\mathbf{k} \cdot \lambda}{\beta \cdot \cos \theta} \tag{1}$$

where D is the crystallite size perpendicular to the plane; k-Scherrer constant; λ is the X-ray wavelength; β is the full-width at half-maximum in radians; and θ is the Bragg angle.


After the separation of X-ray diffraction lines, the relative crystallinity was determined by comparing the areas under crystalline peaks and the amorphous curve. Relative crystallinity (%) was calculated using Equation (2).

$$\text{Relative crystallineity} = \frac{\text{crystaline area}}{(\text{crystalline} + \text{amorphouss}) \text{area}} \tag{2}$$

#### *2.2. Microstructure of Bacterial Cellulose*

The microstructure of bacterial cellulose was examined using a Hitachi scanning electron microscope, (TM-3000, Hitachi Ltd., Tokyo, Japan). Gold was used as a sputter (Cressington 108 auto sputter coater, Netherlands). The cross-section was observed. The photos of the samples at accelerating voltages equal to 15 kV were taken with 500 and 1000 magnification, and the record was saved using SEM software (TM3000, Hitachi Ltd., Tokyo, Japan).

#### *2.3. Porosity Analysis*

To examine the porosity of bacterial cellulose, samples were analyzed using X-ray micro-CT Skyscan 1272 system (Bruker, Kontich, Belgium). The parameters of the process carried out were as follows: X-ray source, voltage at 40 kV, and 193 μA current. Scans were done with a rotation step of 0.3◦ and a resolution of 25 μm. NRecon software (Bruker, Kontich, Belgium) was used to reconstruct cross-section images from μCT projection into 3D images. The determination of porosity was done with the application of CTAnn software (Bruker). Raw images were binarized at a threshold value of 25–255, and custom processing with internal plugins (despeckle, ROI shrink-wrap, 3D analysis) were applied for the selected volume of interest. The images were binarized by means of assigning pixels with lower intensity as background (air, pores) and pixels with higher intensity as matter. Two samples of each experimental variant were scanned.

#### *2.4. Statistical Analysis*

TIBCO company software (STATISTICA program, version 13, Palo Alto, CA, USA) was used to conduct the ANOVA analysis. The samples of bacterial cellulose film were divided into homogenous groups with the use of Tukey's test (α = 0.05).

#### **3. Results**

#### *3.1. Characteristics of the Crystallinity and Degree of Polymerization of Bacterial Cellulose*

Bacterial cellulose is a polymer characterized by high crystallinity, which is a decisive feature influencing the mechanical and physical properties of the polymer. XRD analysis is a key method for imaging crystallinity to verify the effect of various nutrient media on the crystallization properties of BC. X-ray patterns of the BC-N and BC-SP polymers presented in Figure 1 show significant differences in the heights as well as the widths of the diffraction peaks, which proves some changes in the supermolecular structure. In the case of BC-N obtained on a standard medium, typical diffraction maxima originating from the polymorphic variety of cellulose I were observed (Figure 1). The recorded diffraction peaks at the diffraction angles of 2θ corresponded to the crystal planes (100), (010), (110) of cellulose type Iα [1]. On the basis of the performed calculations, it has been shown that for bacterial cellulose from standard medium the value of the degree of crystallinity is 65%, which is close to the crystallinity value obtained on Hestrin–Schramm substrates, so far considered as reference substrates for cellulose-synthesizing micro-organisms [24]. The crystallinity of the cellulose obtained on the sweet potato medium was relatively low at 27%. Fan et al. [25] also observed lower crystallinity of cellulose obtained on media containing plant components.

**Figure 1.** XRD bacterial cellulose obtained from different medium. BC-N—bacterial cellulose from standard medium, BC-SP—bacterial cellulose from sweet potato peel medium.

The conducted research also showed significant differences in the determined sizes of crystallites in individual types of cellulose. It can be noted (Table 2) that bacterial cellulose from sweet potato peel medium is characterized by a much larger crystallite size (70–94 Å depending on the plane) compared to BC-N cellulose, where the crystallite size is in the range of approximately 44–56 Å) (Table 2). The reason for this phenomenon can also be seen as BC-SP is not a pure cellulose. On the subject, information can be found that bacterial cellulose contains up to 90–95% pure cellulose, the remaining components may be fractions of other polysaccharides, such as levane [26].


**Table 2.** Based structural properties of bacterial cellulose obtained from different medium broth.

\* SD—standard deviations in parentheses. The different lowercase letters in row show different homogeneous groups with the use of Tukey's HSD test with α = 0.05.

Despite its low crystallinity, BC-SP is characterized by a higher degree of polymerization compared to BC-N (Table 2). The reason for this can be seen in the greater availability of saccharides in the sweet potato medium than in the standard medium containing only sucrose. Sweet potatoes are a rich source of sugars, both mono and polysaccharides [27], and the latter can be broken down by enzyme into simple sugars, which are then used by micro-organisms not only for energy purposes but also in the process of polymer synthesis. In addition, the medium based on plant ingredients is rich in compounds such as vitamins, minerals, and enzymes, which can additionally regulate cellular processes or affect complex enzyme complexes involved in the biosynthesis of the polymer [28].

#### *3.2. Microstructure Identification Using SEM*

Figure 2 illustrates the surface cross-sections of bacterial cellulose. The cross-section of the polymer obtained on the sweet potato peel medium differs significantly from that obtained on the standard substrate. BC-N has a clearly layered structure in which the individual layers are significantly folded and clearly visibly separated from each other. Void spaces between the layers are observed. The cross-section of the BC-SP is completely different. The individual layers of the polymer clearly adhere to each other, creating a uniform structure. The cross-section structure is not folded, and the individual layers are flat and firmly integrated with each other.

**Figure 2.** Cross-section of bacterial cellulose imaging by SEM with ×500 and ×1000 magnification: (**a**) BC-SP; (**b**) BC-N.

#### *3.3. Porosity of Bacterial Cellulose*

Porosity is one of the most important morphological parameters of materials. It is particularly important for the application of bacterial cellulose in papermaking [29] or as a medical product [30]. Tang et al. [31] showed that the porosity of cellulose depends not only on the conditions and method of cultivation but also on the polymer drying process. BC-SP cellulose was characterized by a smaller number of pores than BC-N cellulose, which may correlate with a greater degree of polymerization and thus a greater amount of microfibers and a more compact structure, which was confirmed by SEM tests. The tested polymers were characterized by exceptionally low porosity (Table 3). The low porosity of the two types of polymers obtained may also be due to the mild drying conditions. Moreover, as reported by Tang et al. [31], the carbon sources in the medium also have an effect on the porous structure of cellulose. The observed morphological changes may be a consequence of the use of microbiological media with a specific composition. Molina-Ramírez et al. [32] by examining the different composition of the substrate on the morphology of the synthesized cellulose using SEM scanning microscopy, showed that the nutrients contained in the microbiological substrate affect the degree of porosity, which results from the density of the cellulose nanofiber network. Studies by other authors have shown that the synthesis of bacterial cellulose on various types of substrates does not affect the size of the produced nanofibers, but with some types of substrates a polymer is obtained with a larger amount of micro- and nanofibrils [33]. The same authors also report that crystallinity is inversely related to porosity. The larger the crystal size, the smaller the number of pores, which is consistent with the results of this study.

**Table 3.** Porosity of bacterial cellulose.


\* SD—standard deviations in parentheses. The different lowercase letters in row show different homogeneous groups with the use of Tukey's HSD test with α = 0.05.

In this study, the authors showed that cellulose obtained on the sucrose medium broth was characterized by a greater porosity than the polymer synthesized on the medium with sweet potato medium.

#### **4. Conclusions**

Culture media play a key role in the economic viability of bacterial cellulose synthesis. Striving to lower the costs of cellulose production on a large scale, readily available and cheap sources of carbon and nitrogen are sought. It seems that waste plant raw materials can successfully replace commercial microbiological substrates, while significantly reducing the costs of cellulose production for various applications. The sweet potato peel medium has proven to be suitable for the synthesis of cellulose with specific quality features. The research results presented in the paper show that the use of a microbiological medium broth based on plant-based ingredients as a medium for the synthesis of bacterial cellulose has an impact on the structural parameters of the polymer. In terms of polymer characteristics, such as degree of polymerization or porosity, it seems that this type of support is better than the standard, which is based solely on sucrose and peptone. The obtained polymer was characterized by a higher degree of polymerization, lower porosity, and a more compact structure. The degree of polymerization of SP-BC was over 14% higher than BC-N, and the percentage of porosity of cellulose obtained on the sweet potato substrate was over two times lower than BC-N. At the same time, from the point of view of crystallinity, the use of a microbiological medium based on sweet-potato peel gives worse results than on a sucrose and peptone based microbiological medium, which was only 27%. It can be concluded that the usefulness of the microbiological medium based on sweet potatoes is desirable, especially for applications of cellulose that should be characterized by a high degree of polymerization, and in this direction, it should intensify the process of polymer synthesis.

**Author Contributions:** Conceptualization, I.B.; methodology, I.B., A.A., K.R., K.L. and S.B.; validation, P.B. and I.B.; investigation, I.B. and B.K.-M.; writing—original draft preparation, I.B.; writing review and editing, I.B., P.B., A.A., S.B., M.N. and B.K.-M.; formal analysis, I.B. and P.B.; supervision, I.B. and P.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was performed by using research equipment purchased as part of the "Food and Nutrition Centre—modernisation of the WULS campus to create a Food and Nutrition Research and Development Centre (CZi ˙ Z)" co-financed by the European Union from the European Regional ˙ Development Fund under the Regional Operational Programme of the Mazowieckie Voivodeship for 2014–2020 (Project No. RPMA.01.01.00-14-8276/17).

**Acknowledgments:** The research was carried out thanks to funding from the Warsaw University of Life Sciences—SGGW.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Article* **Gypsum Seeding to Prevent Scaling**

**Taona Malvin Chagwedera, Jemitias Chivavava and Alison Emslie Lewis \***

Crystallization and Precipitation Research Unit, University of Cape Town, Rondebosch,

Cape Town 7700, South Africa; taona.chagwedera@alumni.uct.ac.za (T.M.C.); jemitias.chivavava@uct.ac.za (J.C.) **\*** Correspondence: alison.lewis@uct.ac.za

**Abstract:** Eutectic freeze crystallization (EFC) is a novel separation technique that can be applied to treat brine solutions such as reverse osmosis retentates. These are often a mixture of different inorganic solutes. The treatment of calcium sulphate-rich brines using EFC often results in gypsum crystallization before any other species. This results in gypsum scaling on the cooled surfaces of the crystallizer, which is undesirable as it retards heat transfer rates and hence reduces the yield of other products. The aim of this study was to investigate and understand gypsum crystallization and gypsum scaling in the presence of gypsum seeds. Synthetic brine solutions were used in this research because they allowed an in-depth understanding of the gypsum bulk crystallization process and scaling tendency without the complexity of industrial brines. A cooled, U-shaped stainlesssteel tube suspended in the saturated solution was employed as the scaling surface. This was because a tube-shaped surface enabled the introduction of a constant temperature cold surface in the saturated solution and most industrial EFC crystallizers are constructed from stainless steel. Gypsum seeding was effective in decreasing the mass of scale formed on the heat transfer surface. The most effective seed loading was 0.25 g/L, which reduced scale growth rate by 43%. Importantly, this seed loading is six times the theoretical critical seed loading. The seeding strategy also increased the gypsum crystallization kinetics in the bulk solution, which resulted in an increase in the mass of gypsum product. These findings are relevant for the operability and control of EFC processes, which suffer from scaling problems. By using an appropriate seeding strategy, two problems can be alleviated. Firstly, scaling on the heat transfer surface is minimised and, secondly, seeding increases the crystallization kinetics in the bulk solution, which is advantageous for product yield and recovery. It was also recommended that the use of silica as a seed material to prevent gypsum scaling should be investigated in future studies.

**Keywords:** gypsum; scaling; seeding; eutectic freeze crystallization; brine

#### **1. Introduction**

South Africa is an industrialized semi-arid country [1] that produces numerous saline solutions. Reverse osmosis (RO) is an economical and energy efficient way of treating these saline solutions. However, a highly concentrated brine stream (reverse osmosis retentate) is produced in the process, which must be treated before disposal. The brine production in South Africa is forecast to reach a peak daily production of 17,000 m3/day in 2030 compared to approximately 3000 m3/day in 2010 [2,3].

Conventional brine disposal methods in South Africa include discharging the brine into lined evaporation ponds, the use of mechanical evaporators, and injecting the brine into deep wells [3]. The main limitation of these methods is their inability to fully separate the brine into reusable products. As an example, evaporative methods result in the formation of a sludge, which is a mixture of salts that needs another disposal method [4]. In contrast, Eutectic Freeze Crystallization (EFC) is theoretically able to fully separate the brine into its constituents, thus having an advantage compared to evaporative methods.

Eutectic Freeze Crystallization (EFC) is a novel brine treatment process for separating the salts from water by cooling the brine to sub-eutectic temperatures. This results in

**Citation:** Chagwedera, T.M.; Chivavava, J.; Lewis, A.E. Gypsum Seeding to Prevent Scaling. *Crystals* **2022**, *12*, 342. https://doi.org/ 10.3390/cryst12030342

Academic Editor: Linda Pastero

Received: 29 October 2021 Accepted: 24 February 2022 Published: 2 March 2022

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the co-crystallization of ice and salts. The ice naturally floats to the top, because it is less dense than the brine, and the salts sink, because they are denser than the brine, making the products separable [5]. The salts produced can be sold depending on their purity and production quantities.

The treatment of calcium sulphate-rich brines, such as reverse osmosis retentates, using EFC, results in the formation of calcium sulphate dihydrate (gypsum) scale deposits on the cooled surfaces of the crystallizers and surfaces of ancillary equipment. This is due to the sparingly soluble nature of gypsum in water. Gypsum scaling is undesirable because the scale forms an insulating layer on the crystallizer heat exchange surfaces, thus retarding heat transfer rates and thereby lowering yields. Gypsum scaling also results in frequent stoppages to clean the scale layer.

Scaling or crystallization fouling is a process in which a deposit forms on a surface. This is due to either bulk crystallization followed by adhesion onto the surface or heterogeneous nucleation and growth on the surface [6]. Gypsum scaling due to adhesion is common for membrane processes [7–9]. Gypsum scaling on hot surfaces is a result of heterogeneous nucleation and growth [10,11]. There is no literature available for gypsum scaling mechanisms under cooling or freeze crystallization conditions, as previous studies [11–15] were conducted under heating crystallization conditions due to the recurrence of gypsum scaling in the handling of geothermal brines for energy production and water distillation.

Heterogeneous nucleation is a form of primary nucleation induced by foreign surfaces such as dust and vessel walls [16]. The nucleation energy barrier for heterogenous nucleation is higher than that for secondary nucleation. Secondary nucleation occurs in the presence of crystals of the material to be crystallized [17,18]. Seeding with parent crystals of the solute in a supersaturated solution lowers the nucleation energy barrier for the dissolved solute particles to crystallize [18].

Seed quality, seed surface area, and seed loading influence the effectiveness of a seeding protocol. Characteristics such as surface smoothness of seed crystals and the structural integrity of the seed crystals constitute the quality of the seeds. Jagadesh and co-workers [19] observed that precipitated potassium seeds were the most effective seed type to precipitate potassium alum from its solution compared to ground and commercial potassium seeds. This may have been due to the precipitated seed crystals having fewer strains in their crystal lattice, which are usually induced through milling. The strains in the crystal lattice are known to dampen the ability of crystals to grow [20].

Seed loading is a measure of the mass of seeds per unit volume of the supersaturated solution. The critical seed loading refers to the minimum amount of seeds required to promote growth without prior nucleation [21]. Doki and co-workers [22] give two correlations that can be used to determine the critical seed loading for a system. Equation (1) is used to determine the critical seed loading ratio using the mean seed crystal size, *Ls.*

$$C\_R^\* = 2.17 \times 10^{-6} \, L\_s^2 \tag{1}$$

where *C*∗ *<sup>R</sup>* = critical seed loading ratio;

*Ls* = mean seed crystal size (μm).

Equation (2) is then used to determine the critical seed loading of the system, using the critical seed loading ratio determined above, as well as the theoretical yield and the volume of the solution.

$$\mathbf{C}\_S^\* = \mathbf{C}\_R^\* \times \frac{\mathbf{W}\_T}{V} \tag{2}$$

where *C*∗ *<sup>S</sup>* = critical seed loading (g/L)

*WT* = theoretical yield of the salt (g)

*V* = volume of the solution (L)

It has been found that specific seed surface area plays an important role. Wang and co-workers [23] showed that 25 μm seed crystals were the most effective in enhancing bulk crystallization compared to larger crystals; 48 μm and 75 μm.

Higher seed loading introduces more surface area for nucleation and growth in the system and thus increases the crystallization rate of the target material. Liu and Nancollas [24] observed that the induction time for gypsum crystallization was shortened by increasing the seed loading from 0.42 to 1.89 g/L. However, the addition of an excessive number of seeds above the critical seed loading was observed to have no pronounced effect on gypsum crystallization kinetics [24].

Seeding has been employed in batch crystallization systems to control the crystal size distribution of the product crystals [19,21,22,25]. It is also an established method to enhance bulk crystallization of the target salt or ice in the EFC context [26–28]. Bulk crystallization of gypsum from a reverse osmosis brine was increased significantly when the brine was seeded with gypsum crystals [29].

A few studies on the use of seeding as a method to prevent scaling have been published. Adams and Papangelakis [30] observed that introducing gypsum seed crystals at 10 g/L in a laboratory scale neutralization reactor resulted in a 50% decrease in the mass of scale formed at 70 ◦C. Wang and co-workers [23] established that seeding was more effective in preventing scaling in brine transportation pipes compared to brine dilution. Gainey et al. [31] reported that seeding in evaporators resulted in the elimination of the calcium sulphate scale at the Rosewell laboratory and pilot plants. The actual details of the seed characteristics and seed loading were not published.

In this work, seeding was tested as a method to prevent scaling under cooling crystallization conditions. The aim of the study was to investigate and understand the interaction of gypsum crystallization in the bulk and gypsum scaling on the crystallizer surfaces in the presence of gypsum seeds.

#### **2. Materials and Methods**

#### *2.1. Experimental Equipment*

The experiments were conducted using the apparatus shown in Figure 1. A jacketed and insulated glass crystallizer with a working volume of 1.25 L was used. A U-shaped stainless-steel tube, 290 mm long with an outer diameter of 3.18 mm, was suspended from the lid into the supersaturated solution. The tube was maintained at 0.0 ◦C by a Lauda Proline PP855 thermostatic unit (Lauda, Germany), which circulated polydimethylphenylsiloxane (Kryo 51™) through it to cool the solution from 22.3 to 3 ◦C.

The jacket of the crystallizer was maintained at 2.5 ◦C by a Lauda ECO RE1050G thermostatic unit (Lauda, Königshofen, Germany), which circulated polydimethylphenylsiloxane (Kryo 51™, Lauda, Königshofen, Germany) through it. The temperatures of the bulk solution, coolant into and out of the tube, and coolant into and out of the jacket of the crystallizer were measured to an accuracy of ±0.01◦C, at 3-s intervals, using platinum resistance thermometers (Pt100) (Tempcontrol, Nootdorp, The Netherlands). The thermometers were connected to a CTR5000 precision bridge (ASL, Horsham, UK), which communicated with the computer via the ULog software (Ulog V6, ASL WIKA, Manchester, UK). A 4-blade pitched-blade impeller, attached to an overhead stirrer, was used to agitate the solution inside the crystallizer.

**Figure 1.** Batch crystallizer with cooled stainless-steel tubing suspended from the lid.

#### *2.2. Feed Solution Preparation*

The brine solution was prepared by reacting equal quantities of 0.11 M Ca(OH)2 (Merck, Modderfontein, South Africa) and 0.11 M H2SO4 (Sigma-Aldrich, Modderfontein, South Africa) in order to prepare a supersaturated calcium sulphate–water solution as illustrated by the reactions in Equation (3). The average concentration of the feed solution was 6.13 g/L CaSO4, as shown in Figure 7, resulting in an average starting supersaturation, S, of 7.71 that was calculated using the Debye–Huckel theory.

$$\text{Ca(OH)}\_{2}\text{(aq)} + \text{H}\_{2}\text{SO}\_{4} = \text{CaSO}\_{4}\text{(aq)} + 2\text{H}\_{2}\text{O} \tag{3}$$

Feed solution preparation was not possible through dissolving reagent grade gypsum powder in de-ionised water because of the sparingly soluble nature of gypsum. The suspension formed from the reaction was filtered through a 0.22 μm cellulose acetate membrane (Kimix Chemical and Lab Supplies, Cape Town, South Africa) held by a 250 mL Merck Millipore glass holder connected to a vacuum pump at room temperature (23.5 ◦C). However, this filtration step does not completely eliminate nano fraction particles as determined by Oshchepkov and co-workers [32]. The filtrate was used as feed solution due to technological limitations to further remove nano-sized particles.

#### *2.3. Seeds Preparation*

Gypsum seeds were precipitated by mixing equal quantities of aqueous 0.6 M sodium sulphate solution (Merck, Modderfontein, South Africa) and 0.6 M calcium chloride solution (Merck, Modderfontein, South Africa) as illustrated by Equation (4). The resistivity of deionised water used to prepare both solutions was 10.9 MΩ-cm.

$$\text{Na}\_2\text{SO}\_4\text{(aq)} + \text{CaCl}\_2\text{(aq)} + 2\text{H}\_2\text{O} = \text{CaSO}\_4\cdot2\text{H}\_2\text{O(s)} + 2\text{NaCl}\text{(aq)}\tag{4}$$

Calcium chloride solution was added one drop at a time to sodium sulphate solution at 70 ◦C to allow slow distribution of the supersaturation and precipitation of needle-type gypsum crystals. This method was adapted from Liu and Nancollas [24]. The suspension formed was filtered through a 0.22 μm cellulose acetate membrane held by a 250 mL Merck Millipore glass holder connected to a vacuum pump. Gypsum crystals were repeatedly washed with 0.50 L of deionised water to remove sodium chloride before they were dried.

#### *2.4. Experimental Procedure*

Briefly, 1.25 L of the feed solution was measured and transferred into the crystallizer. The overhead stirrer was set to 450 rpm, which is equivalent to a Reynolds number, (Re)

of 4.21 × <sup>10</sup>5, and the thermostatic units were switched on to start the experiment. Seed crystals with a mean size of 58 μm were added into the crystallizer at the start of the experiments in which seeding was employed.

At the end of the experiment, the thermostatic units and the overhead stirrer were switched off. The tube was removed from the lid and allowed to dry before it was weighed. The suspension in the crystallizer was filtered using the same apparatus as above and the filtrate was analysed for sulphate ion concentration.

#### *2.5. Measurement/Analytical Techniques*

The sulphate concentration for the feed solution and spent solution was analysed using the turbidimetric method. In this method, the sulphate ion is converted to barium sulphate through addition of barium chloride dihydrate (Merck, Modderfontein, South Africa) and the turbidity of the suspension is measured. A photometer (Merck Spectroquant Nova 60, Merck, Modderfontein, South Africa) set at a wavelength of 410 nm was used.

The mass of the scale was determined arithmetically from the difference between the mass of the scaled tube and the mass of the clean tube, which were both measured using a digital scale (Mettler™ Toledo ML204, Greinfensee, Switzerland) with an accuracy of ±0.0003 g.

Crystal size and morphology of the scaled tube were analysed using a Scanning Electron Microscope (Tescan™ MIRA3 Rise, TESCAN, Brno-Kohoutovice, Czech Republic).

#### **3. Results and Discussion**

#### *3.1. Seed Crystals*

Figure 2 shows SEM micrographs of the seeds. The seed crystals were a mixture of the needle-type habit and prisms.

**Figure 2.** Micrographs of the seed crystals. Scale bar = 100 μm in 4.2 (**a**) and 50 μm in 4.2 (**b**).

The crystal size distribution of the seed crystals is presented in Figure 3. An average of three samples was taken and most of the seed crystals (61%) were below 55 μm in size. The mean size of the seed crystals was 57 μm with a modal size of 26 μm.

**Figure 3.** Crystal size distribution of gypsum seed crystals.

#### *3.2. Preliminary Experiments*

It was established that the required experiment run time was 4 h for a measurable mass of gypsum scale to be deposited on the stainless-steel tube. The mass of gypsum scale recorded was 0.045 g. The bulk solution temperature was 3 ◦C at the time of stopping the experiment. There was negligible mass of gypsum scale on the inner wall of the crystallizer. A temperature of 3 ◦C was maintained in all experiments as this allowed the study of gypsum scaling, testing the effectiveness of gypsum seeding, without the complexity caused by ice formation.

Figure 4 shows the micrographs of the scaled tube after running the experiment. The lighter phase represents the stainless-steel tube surface and the darker phase represents gypsum crystals. There was also a very thin layer of finely grained crystals, which could have been due to the adhesion of gypsum crystals when the tube was left to dry.

**Figure 4.** Micrographs of a scaled tube after running the experiment for 4 h. Scale bar = 100 μm (**a**), 50 μm (**b**) and 20 μm (**c**) respectively.

The micrographs presented in Figure 4 show that the tube was not fully covered with scale after running the experiment for 4 h. Needle-type crystals grew normal to the plane of the tube into the bulk solution; although, the expectation was that they would grow along the cold tube surface, which provided high local supersaturation conditions. This was due to the difference in the crystallographic structure of stainless steel and gypsum, which inhibited the growth of crystals along the plane of the tube. It is also possible that the integration of gypsum lattice units into the scale crystals that crystallized first on the tube could have caused the gypsum crystals to grow into the bulk solution. There were tiny crystals that were lying parallel to the tube, possibly due to the adhesion of crystals precipitated in the bulk solution or shearing of crystals by fluid motion. The fluid motion around the tube was turbulent (Re = 4.21 × 105).

The experiment duration was increased further by 6 h to develop an understanding of how the scale crystals grew. The mass of scale deposited on the tube was 0.080 g and the final temperature of the solution was 3 ◦C. The longer experiment time did not change the predominant habit of crystals, with needle-type crystals of varying lengths constituting the scale layer. Growth of the crystals was also into the bulk solution, which resulted in small 'islands' of the tube that were not fully covered with gypsum scale.

An increase in the duration of the experiment to 24 h resulted in an increase in the mass of gypsum scale that deposited on the stainless-steel tube. However, the increase was not linear as was the case when the experiment duration was further increased to 48 h from 24 h. This was due to the decrease in the supersaturation of the system with time. Choi and co-workers [33] asserted that gypsum crystallization rates decrease in batch tests as the calcium ion concentration decreases. The mass of gypsum scale deposited on the tube after 24 h and 48 h was 0.179 g and 0.260 g, respectively. Figure 5 shows the increase in the mass of scale deposited on the tube as the run time was increased.

**Figure 5.** Mass of gypsum scale deposited on the stainless-steel tube as a function of time.

Figure 6 shows the micrographs of the scaled tube after 48 h. In the micrographs, the darker phase represents the stainless-steel tube surface, and the lighter phase represents gypsum crystals.

**Figure 6.** Micrographs of a scaled tube after running the experiment for 48 h. Scale bar = 100 μm (**a**), 50 μm (**b**) and 20 μm (**c**) respectively.

Figure 6a shows that the scale layer was predominantly composed of needle-type crystals varying in length between 40 and 100 μm. Most of the smaller sized crystals were on the top surface of the scale layer while the larger sized crystals were underneath. This was possibly because the underlying crystals crystallized first and had more time to grow and, hence, became larger than the top surface crystals.

Figure 6c shows attachment of smaller sized crystals to the larger crystals. This could have been due to the underlying crystals serving as growth sites for subsequent scale crystals. There was crystal twinning during scale layer growth as depicted in Figure 6a,b (white circles). The twinning may have resulted from the combination of moderate supersaturation conditions at the start of the experiment, prolonged growth time, and close contact with the cold tube surface where heat transfer was the highest.

Analysis of the micrographs of the scaled tube acquired after each preliminary experiment enabled the formulation of a possible mechanism of gypsum scaling on the tube, even though it was not conclusive. Gypsum scale layer was predominantly composed of needle-type crystals showing that the stainless-steel tube did not alter its habit under moderate supersaturation conditions present in the system. This is similar to what was observed by Amjad [10], although on a brass tube. The phenomenon would support the notion of gypsum scaling through adhesion. However, the plausible reasons for gypsum scaling through adhesion were outweighed by those for heterogeneous nucleation and supported by the micrographs.

It was proposed that gypsum scaling on the stainless-steel tube most likely proceeded via heterogeneous nucleation followed by growth. The growth of the scale layer crystals was into the bulk solution. Gypsum scaling was found to begin between 0 and 30 min. Based on this, it was decided that gypsum seeds would be added at the beginning of the experiment.

#### *3.3. Effect of Increasing Gypsum Seed Loading on Gypsum Scale Formation*

Synthetic gypsum seeds of the type described earlier were used. At the time the experiments were stopped, the calcium sulphate concentration was on average 5.33 g/L, which is above the thermodynamic equilibrium concentration of 2.27 g/L at 3 ◦C [34]. Since the calcium sulphate concentration in the spent solutions was double the equilibrium concentration, more gypsum may have theoretically crystallized from the solution if the experiments were run for longer. Gypsum crystallization kinetics were generally slow. Figure 7 is a graphical representation of the changes in solution concentration from feed to spent solution for 4-h run times plotted on the same axis for the different experiments.

**Figure 7.** CaSO4 concentration in solutions as a function of gypsum seed loading.

The graph shows that the average change in concentration between the feed solution and the spent solution for all seed loadings was 1.0 g/L CaSO4. At seed loadings less than 0.50 g/L, the least average change in concentration of 0.50 g/L CaSO4 was recorded while at 1.0 g/L this change in concentration was 1.76 g/L CaSO4. The significant concentration change at higher seed loading was a result of faster gypsum crystallization kinetics.

Figure 8 shows the mass of gypsum scale that deposited on the tube and the mass of gypsum that crystallized in the bulk solution as a function of gypsum seed loading. The x-axis is from a minimum value of −0.2 to show the data points at 0.0 g/L. Figure 8 shows that the mass of gypsum that deposited on the stainless-steel tube was several orders of magnitude less than the mass of gypsum that crystallized in the bulk solution.

The mass of gypsum that crystallized in the bulk solution increased rapidly as gypsum seed loading was increased due to faster gypsum crystallization kinetics. The increase in seed loading increased the available surface area with favourable energetics for gypsum growth to occur. In addition, the abundance of gypsum crystals in suspension increased crystal–crystal, crystal–impeller, and crystal–crystallizer surface collisions. These collisions increased the rate of secondary nucleation, which requires the lowest activation energy; thus, crystallization kinetics increased. The observed increase in crystallization rates as the seed loading was increased corroborated the results found by Choi and co-workers [33], where they observed that the induction time shortened in the presence of seeds compared to unseeded solutions.

Although the tube was the heat transfer surface area and the coldest part of the apparatus, causing high local supersaturation, less mass of gypsum crystallized on it than in the bulk solution. This is because the surface area provided by the tube (28.9 cm2) was very small compared to that provided by the bulk solution (1415 cm2) and the seed material. Surface area is a key determinant of crystallization rate processes. The surface area provided by the bulk solution was calculated using the internal dimensions of the crystallizer. It was difficult to quantify the surface area provided by gypsum seeds at the different seed loadings due to technological limitations. In addition, the surface area provided by the tube had poor energetics for gypsum nucleation and growth compared to the gypsum seeds.

**Mass of gypsum scale on tube Mass of gypsum crystallized in the bulk**

**Figure 8.** Seed loading against mass of gypsum scale deposited on the tube and mass of gypsum crystallized in the bulk solution.

A zoomed view of Figure 8 showing the change in the mass of gypsum scale with increase in gypsum seed loading is presented in Figure 9. The x-axis has a minimum value of −0.2 to show the data point at 0.0 g/L.

**Figure 9.** Seed loading against mass of gypsum scale deposited on the tube.

Figure 9 shows that the highest mass of gypsum scale deposited on the tube in the control experiment. The mass of scale deposited on the tube decreased in the presence of gypsum seeds because the added seeds consumed some of the available supersaturation to sufficiently low levels to decrease the rate of heterogenous nucleation on the tube, but still promoting secondary nucleation in the bulk solution. An increase in gypsum seed loading (specific surface area) decreased the mass of scale up to the seed loading of 0.25 g/L. Beyond the seed loading of 0.25 g/L, a further increase in gypsum seeds resulted in an increase in the mass of gypsum scale deposited. Although the mass of gypsum scale deposited on the tube increased at seed loadings greater than 0.25 g/L, it was still less than the amount deposited in the control experiment without seeding.

Contrary to expectation, the mass of gypsum scale deposited on the tube when the critical seed loading was employed was not the lowest. It was anticipated that the mass of gypsum scale deposited on the tube would be the least at the critical seed loading because this seed loading is associated with growth without any prior nucleation. Hence, at seed loadings greater than the critical seed loading the surface area provided by the seeds would have been in excess compared to the available supersaturation. Instead, the lowest mass of scale deposited on the tube was realised when a seed loading approximately six times higher than the critical seed loading (0.25 g/L) was employed. This deviation could have been because the surface area provided by the critical seed loading was too small to sufficiently reduce nucleation on the stainless-steel tube surface any further.

In addition, the calculated contact angle for gypsum nuclei to form on a stainless-steel surface was small. The contact angle calculation was done using Equation (A1) provided in the Appendix A together with the values from literature which were used (Table A1). A range of the contact angle was determined since the dispersive component of gypsum surface free energy was found as a range. The contact angle range found was 16◦ to 50◦. The lower limit of the contact angle range implies the degree of wetting was high, thus heterogeneous nucleation of gypsum on stainless-steel occurred easily. The respective surface energy reduction factors, *f*(∅), for the contact angles calculated using Equation (A2) (see Appendix A) were 0.001 and 0.08. This shows that the nucleation work on the stainlesssteel tube which needed to be overcame by the dissolved gypsum molecules was low.

The relative ease of gypsum to heterogeneously nucleate [17,18] on the stainless-steel tube as determined from the contact angle calculations may have hampered the ability of gypsum seed crystals to sufficiently reduce heterogeneous nucleation. Figure 9 shows that increasing gypsum seed loading six times from 0.04 to 0.25 g/L only resulted in a further 25% reduction in scale mass.

At seed loadings greater than 0.25 g/L, the specific surface area provided by the seeds could have been in excess for this system since the contact angle calculations showed that the degree of wetting on stainless-steel tube was relatively high, resulting in some of the seed crystals possibly adhering onto the tube surface. It should be noted that the scaling mechanism postulated for these experiments in which gypsum seeding was employed is different to the one for the preliminary experiments where there was no seeding. This is because the presence of gypsum seeds in relatively high quantities (0.50 and 1.0 g/L) made adhesion a possibility. However, this may not have been to a great extent since the mass of scale deposited on the tube in these experiments remained lower than that deposited in the control experiment.

The total amount of gypsum crystallized from the experiment was computed as the sum of the mass of gypsum scale and the mass of gypsum crystallized in the bulk solution. Figure 10 shows the total mass of gypsum crystallized as a function of gypsum seed loading.

The graph shows that the total mass of gypsum crystallized from the solution was much less than the theoretical yield expected. Theoretical yield was calculated using the feed solution concentration and the thermodynamic equilibrium concentration at 3 ◦C. This may have been due to slow gypsum crystallization kinetics stated earlier. Preliminary experiments, which were ran for 48 h, did not yield a spent solution concentration that is comparable to the thermodynamic equilibrium concentration.

Figure 11 shows the micrographs of the scaled tube at different seed loadings. The light phase represents the stainless-steel surface while the dark phase represents gypsum crystals.

**Figure 10.** Total mass of gypsum crystallized as a function of gypsum seed loading.

**Figure 11.** Micrographs of the scaled tube (**a**) control experiment, (**b**) *CS* = 0.04 g/L , (**c**) *CS* = 0.25 g/L, (**d**) *CS* = 0.50 g/L, (**e**) *CS* = 1.0 g/L. Scale bar = 100 μm.

The micrographs show that the predominant habit of the crystals that formed the scale layer was needles. An increase in gypsum seed loading led to fewer scale layer crystals per unit area of the tube because some of the available supersaturation was consumed by the seeds, leaving less available for heterogeneous nucleation and growth on the tube. Additionally, more gypsum seed crystals meant fewer prism-shaped crystals in the scale layer, as some of the supersaturation for growth of needle-type crystals into prisms was consumed by the gypsum seeds.

The growth direction of the crystals that formed the scale layer was comparable to that which was observed in the preliminary experiments at different durations. Figure 12 shows the normalized growth rate of the scale layer as a function of seed loading. The minimum on the x-axis (−0.2) was chosen to ensure the data point at 0.0 g/L would show clearly.

**Figure 12.** Normalized gypsum scale growth rate as a function of seed loading.

The graph shows that the normalised scale growth rate followed the same trend as was observed for the mass of scale deposited on the tube (Figure 9). The normalised scale growth rate was calculated by dividing the mass of gypsum scale by the product of the experiment duration and the tube surface area (same divisor). The experiment duration and the tube surface area were constants, hence the similarity in the trends.

The micrographs of the crystals recovered from the suspension at the end of each experiment are presented in Figure 13. The light phase represents the gypsum crystals and the dark phase represents the mounting glue.

The micrographs show that in the control experiment (Figure 13a), the crystals in the bulk solution were composed predominantly of needle-type crystals. There was evidence of some crystal twinning (white circles). The addition of 0.04 g/L seed crystals to the system decreased the proportion of needle-type crystals and the degree of twinning (Figure 13b). As the seed loading was increased, the habit of the crystals transformed from being predominantly needle-type to prisms. This was because in the absence of seeds, the supersaturation was relatively high and numerous crystallites were birthed. The available supersaturation was distributed among the crystallites for their growth, which resulted in needle-type habit. The presence of seeds and increase thereof possibly reduced the degree of nucleation and promoted crystal growth resulting in the formation of prisms.

**Figure 13.** Micrographs of the solid suspension at the end of the experiment (**a**) control experiment, (**b**) *CS* = 0.04 g/L, (**c**) *CS* = 0.25 g/L (**d**) *CS* = 0.50 g/L, and (**e**) *CS* = 2.01 g/L. Scale bar = 100 μm.

#### **4. Conclusions**

Gypsum scale formation on the cooled stainless-steel tube was most likely a result of heterogenous nucleation and growth. The micrographs of the scaled tube showed that the rough patches on the stainless-steel tube were nucleation sites for gypsum scale.

Gypsum seeding was effective in decreasing the mass of gypsum scale deposited on the stainless-steel tube. This was attributed to the gypsum seeds providing a surface area that had favourable energetics for gypsum crystallization compared to the tube surface. The most effective seed loading was 0.25 g/L.

The amount of gypsum crystallized in the bulk solution increased as gypsum seed loading was increased. This was due to the increase in specific surface area that had growth sites on which gypsum dissolved in solution could crystallize.

These findings are relevant for the operability and control of EFC processes, which suffer from scaling problems. By using an appropriate seeding strategy, two problems can be alleviated. Firstly, scaling on the heat transfer surface is minimised and, secondly, seeding increases the crystallization kinetics in the bulk solution, which is advantageous for product yield and recovery.

This is of great importance towards scaling-up EFC for industrial applications. Beyond that, seeding to prevent scaling has potential applicability in other processes where the scale is regarded a product and/or purity is of importance, thus making addition of polymeric scale inhibitors undesirable.

#### **5. Recommendation**

There is need to investigate the effect of silica as a seed material to prevent gypsum scale formation. The gypsum crystallized in the bulk solution was still to a greater extent composed of fines, which poses separation problems in EFC. Silica is a robust and inert material that can ideally maintain its structural integrity throughout the experiment. If gypsum dissolved in solution can crystallize on silica, then there is a possibility of yielding coarser silica-gypsum crystals that may be relatively easy to separate from ice during EFC.

**Author Contributions:** Data curation, A.E.L.; Investigation, T.M.C.; Methodology, J.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Julian Baring Scholarship and University of Cape Town grant number. The APC was funded by University of Cape Town.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** The authors would like to acknowledge and thank Gerda van Rosmalen, who gave us some very valuable input at the early stages of this work. The authors would also like to thank the Julian Baring Scholarship Fund, all members of the Crystallization and Precipitation Research Unit, and the Mechanical Workshop in the Chemical Engineering Department at the University of Cape Town. Special mention goes to Miranda Waldron, Electron Microscope Unit.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

$$
\gamma\_{sl} = \gamma\_{cs} + \gamma\_{cl}\cos\theta \tag{A1}
$$

$$
\Delta G\_{\text{Metroçenous}}^{\prime} = f(\mathcal{Q}) \Delta G\_{\text{Homøçenous}}^{\prime} \tag{A2}
$$

**Table A1.** Parameters used to calculate contact angle.


#### **References**

