Physicochemical Characterization

The mass of leaves, foam and powder were evaluated for the following physicochemical parameters: moisture content 103 ◦C/24 h; ash content determined by muffle incineration at 550 ◦C; Lipid content the soxlet was used; Protein was determined by kjedahl and total acidity by titration [17].

#### *2.2. Mathematical Modeling*

From the experimental data of drying kinetics, the values of the moisture content ratio were calculated according to Equation (1).

$$\text{RX} = \frac{\chi - \chi\_{\text{e}}}{\chi\_{\text{i}} - \chi\_{\text{e}}} \tag{1}$$

where: RX: moisture content ratio of the product, dimensionless; X; moisture content of the product (d.b.); Xi: initial moisture content of the product (d.b.); Xe: equilibrium moisture content of the product (d.b.).

Table 1 presents the mathematical models widely used to describe drying kinetics of vegetables. The models were fitted by nonlinear regression analysis using the Gauss-Newton method.

**Table 1.** Empirical and semi-empirical equations used to represent drying kinetics.


RX-Moisture content ratio of the product, dimensionless; k, k0, k1-Drying constants; h−1; a, b, c, n-Coefficients of the models; t-Drying time, h.

The preliminary criteria to select the model with best fit were: coefficient of determination (R2), relative mean error (P), estimated mean error (SE) and the mean chi-square (*χ*2).

$$\chi^2 = \sum \frac{\left(\chi - \hat{\chi}\right)^2}{\text{DF}} \tag{14}$$

$$P = \frac{100}{\text{n}} \sum \frac{|\mathbf{Y} - \mathbf{\hat{Y}}|}{\mathbf{Y}} \tag{15}$$

$$\text{SE} = \sqrt{\frac{\sum \left(\mathbf{Y} - \mathbf{\hat{Y}}\right)^2}{\mathbf{DF}}} \tag{16}$$

where: Y: experimental RX value; Y: RX value estimated by the model; n: number of ˆ observations; DF: degrees of freedom of the model (observations minus the number of model parameters).

In order to select a single model to describe the drying process under each condition, those models that preliminarily select (according to the criteria R2, P and SE) were subjected to the selection criteria of Akaike Information (AIC) and Schwarz's Bayesian Information (BIC).

The information criteria were determined by the following Equations:

$$\text{AIC} = -2\text{logL} + 2\text{p} \tag{17}$$

$$\text{BIC} = -2\text{logL} + \text{plog}(\text{N} - \text{r}) \tag{18}$$

where: p: number of model parameters; logL: logarithm of the likelihood function considering the estimates of the parameters; N: total observations; r: matrix X rank (incidence matrix for fixed effects).

Fick's diffusive model was fitted to the drying data considering the geometric shape of flat plate [18], with eight-terms approximation [19], according to Equation (19), for the determination of effective diffusivity.

$$\text{RX} = \left(\frac{8}{\pi^2}\right) \sum\_{\mathbf{n}=0}^{\infty} \frac{1}{\left(2\mathbf{n}+1\right)^2} \exp\left(-\left(2\mathbf{n}+1\right)^2 \pi^2 D \,\frac{t}{4\mathcal{L}\_0^2} \,\frac{S}{V}\right) \tag{19}$$

where: RX: moisture content ratio, dimensionless; D: effective diffusion coefficient, m<sup>2</sup> s −1; S: equivalent plate area, m2; V: equivalent plate volume, m3; L0: mass thickness, m; n: number of terms of the Equation; t: time, s.

The expression described by Arrhenius Equation (20) was applied, relating the dependence of effective diffusivity as a function of temperature.

$$\mathbf{D} = \mathbf{D}\_0 \exp\left(\frac{-\mathbf{E\_a}}{RT\_\mathrm{a}}\right) \tag{20}$$

where: Do: pre-exponential factor; Ea: activation energy, kJ mol−1; R: universal constant of gases, 8.314 kJ kmol−1. <sup>K</sup>−1; Ta: absolute temperature, K.

The linearization of the coefficients of the equationthe Arrhenius was used to calculate the activation energy from, applying the logarithm as follows:

$$\text{Ln D} = \text{LnD}\_0 - \frac{\text{E}\_\text{a}}{\text{R}} \cdot \frac{1}{\text{T}\_\text{a}} \tag{21}$$

#### *2.3. Thermodynamic Properties*

The thermodynamic properties of the drying process of the mass of leaves and foam determined were: enthalpy, entropy and Gibbs free energy, according to Equations (22)–(24), respectively.

$$
\Delta \mathbf{H} = \mathbf{E\_a} - \mathbf{R}. \,\mathrm{T\_a} \tag{22}
$$

$$
\Delta \mathbf{S} = \mathbf{R} \cdot \left[ \text{Ln}(\text{D}\_0) - \text{Ln}\left(\frac{\text{K}\_B}{\text{h}\_p}\right) - \text{Ln}(\text{T}\_\text{a}) \right] \tag{23}
$$

$$
\Delta \mathbf{G} = \Delta \mathbf{H} - \text{ T}\_{\mathbf{a}} \text{ } \Delta \mathbf{S} \tag{24}
$$

where: ΔH-specific enthalpy, J mol−1; ΔS-specific entropy, J mol−<sup>1</sup> <sup>K</sup>−1; ΔG-Gibbs free energy, J mol−1; KB-Boltzmann constant, 1.38 × 10−<sup>23</sup> J <sup>K</sup>−1; hp-Planck constant, 6.626 × 10–34 J s<sup>−</sup>1; T-temperature, ◦C.

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

#### *3.1. Physicochemical Characterization*

Table 2 shows the means of the evaluations of physicochemical composition of the mass of jambu leaves, foam and powder obtained at different temperatures.

The results found for the fresh mass of jambu leaves and foam showed that they have a significant contents of moisture and protein and reduced contents of lipids, ash and total titratable acidity. These contents are close to those described by Neves et al. [1], who found moisture content of 89% w.b., ash of 1.11%, lipids of 0.16%, proteins of 2.44%. The moisture contents obtained in the drying of the mass of jambu leaves ranged from 5.70 to 2.21% w.b. and showed a non-significant decrease with the increase in temperature. For the drying of the foam, there was a higher moisture retention, significant at temperatures of 60 and 70 ◦C when compared with the dried mass of leaves, with no significant influence of the increase in temperature.


**Table 2.** Mean values of the physicochemical composition of the mass of jambu leaves, foam and powder obtained under different drying conditions.

Lowercase letters in the column refer to the comparison between the different temperatures for the same material, and uppercase letters in the column refer to the comparison of the same temperature between the two materials, and the same letters do not differ from each other by Tukey test (*p* < 0.05). \* Tartaric Acid.

However, the fresh mass of leaves and foam of jambu showed relevant contents of protein (3.39% and 3.3%, respectively) and lipids (0.24 and 0.26%, respectively), so drying led to a reduction in moisture content that contributed to a significant increase in the contents of proteins and lipids, and the lipid content found in the foam after drying was higher than that found in the mass of leaves. Values similar to those obtained here were reported by Gomes et al. [16], who found that jambu powder had moisture contents between 4 and 6% w.b. and lipid and protein parameters of 7% and 27%, respectively, with no significant degradation under the studied conditions.

For the ash content of the fresh mass of jambu leaves and foam, there was no variation with the increase in temperature. It was found that the mass of leaves had higher percentages of ash, with values between 16 and 17%. The total acidity levels of the mass of leaves (0.26–0.29% tartaric acid) and foam (0.20–0.24 tartaric acid) after drying showed an acidic character compared with the fresh material (0.03 and 0.04% tartaric acid). The acidity content increased when temperature drying was applied, possibly due to the conversion of sugars into organic acids [11]. In the comparison of the materials before and after drying, there was a reduction in moisture content, while the protein and lipid contents increased, and the dried foam stood out with higher, values, differ dried mass of leaves. This increase may be linked to the addition of stabilizer and emulsifier used to obtain the foam.

Convective drying with forced air circulation is a method recommended for drying leaves because it helps reduce heat losses and improves drying quality [20]. The physicochemical parameters evaluated showed that the addition of stabilizers and emulsifiers did not cause significant changes in the mass of jambu composition. And foaming was a positive factor in the process as it reduced drying time, since this is a limiting factor for the drying conditions (temperature, speed and relative humidity of the air, as well as thickness), which must be controlled to maintain the quality of the final product and reduce moisture content [12].

#### *3.2. Mathematical Modeling*

To better understand the drying kinetics of the crushed mass of jambu leaves and foam, different mathematical models were evaluated. Table 3 shows the values of the estimated mean error (SE), relative mean error (P), coefficient of determination (R2) and chi-square test (χ2) for the mathematical models fitted to the experimental data of the drying kinetics of the mass of jambu leaves and foam at temperatures of 50, 60 and 70 ◦C and thickness of 1.0 cm Table 3.


*Agriculture* **2022**, *12*, 1252

**Table 3.** Estimated mean error (SE), relative mean error (P), coefficient of determination (R2) and chi-square test (χ2) for the twelve models

Wang & Singh, Midilli and Logarithmic models showed the best fits under all drying conditions according to the preliminary criteria of evaluation: R<sup>2</sup> higher than 99%, lower estimated mean error (SE) and chi-square test (χ2), as well as relative mean error (P) lower than 10%, which is considered as an adequate representation of the model [21].

Together with the previous statistical parameters (Table 3), the Akaike information criterion (AIC) and Schwarz's Bayesian Information criterion (BIC) were adopted as additional criteria to select the best model. The results of AIC and BIC for Wang & Singh, Midilli and Logarithmic models are described in Table 4.


**Table 4.** Akaike Information criterion (AIC) and Schwarz's Bayesian Information criterion (BIC) for the models that best fitted to the drying data of the crushed mass of jambu leaves.

Considering the lower values of the AIC and BIC information criteria as indication of better fit, Wang & Singh model showed the best fit to the experimental data for temperature of 50 ◦C of thin-layer and foam-mat drying. For the other treatment conditions, Midilli model obtained better fit to the experimental data. These results indicate that, regardless of the drying method used, the mathematical models fitted well to the data. Logarithmic and Midilli models were indicated as those with better fit to the experimental data of drying kinetics of the mass of jambu leaves [22].

Data of drying kinetics at different temperatures were analyzed in terms of moisture content ratio (RX), as shown in Figure 1. The moisture content ratio decreases continuously until the equilibrium is reached. The increase in air temperature resulted in a reduction in the time required to reach the equilibrium moisture content for the different conditions studied.

**Figure 1.** Moisture content ratio in the drying of crushed mass of jambu leaves, obtained experimentally and estimated by the Wang & Singh and Midilli models for the different drying conditions.

The moisture content ratio curve has been considered the best way to explain the behavior during the drying process [23]. Combined with the adequate model for drying kinetics, it is used to explain the total drying behavior [14]. As the model describes the mechanisms of heat and mass transport, it can be used to simulate other process conditions such as variation in thickness, foam composition and temperature, velocity and relative humidity of the air, among others [12].

The results indicated that just as air temperature played an important role in reducing drying time, the use of foam mat enhanced this reduction. The drying time was between 4 and 7 h in the drying of the mass of leaves and showed a considerable reduction in the drying of the foam, being 2 and 5 h.

Increase in drying temperature reduces the drying time due to molecular movement, thus increasing the rate of moisture content removal from the sample, which results in the reduction of drying time [11]. Franco et al. [12] report that the porous structure of the foam and the large surface area in contact with the drying air cause higher mass transfer rates, thus leading to a reduction in drying time and, therefore, a final product with better quality. The coefficients of fits of the mathematical equations obtained under the different experimental conditions of drying kinetics are presented in Table 5.

**Table 5.** Coefficients of the models that best fitted to the drying data of crushed mass of jambu leaves and foam.


The constant "k" increases with increasing temperature, since higher temperatures lead to higher drying rates [24], a behavior also observed. Considering that the parameter n is related to the internal resistance of the material to drying [25], with the addition of temperature the constant n of the Midilli and Wang and Sing model showed a tendency to increase with increasing temperature.

Figure 2 shows the values of the effective diffusion coefficient during the drying of the crushed mass of jambu leaves and foam. The effective diffusion coefficient showed higher values at the higher drying temperatures and with application of the foam mat.

The effective diffusion coefficient showed a trend of linear increase as the drying air temperature increased. The use of foam promoted higher values of the effective diffusion coefficient compared to the material without foam mat for the three temperatures analyzed. The same was observed for the hot air drying of mint leaves, whose effective diffusivity was slightly higher when the air temperature was increased from 60 ◦C to 70 ◦C [26]. Gomes et al. [22] described a trend of increase in diffusion coefficient with the increase in drying air temperature and material layer thickness when studying the mass of jambu leaves.

The increasing values of effective diffusivity with the increase in temperature can be attributed to the fact that water molecules are more weakly bound to the food matrix at higher temperatures, requiring less energy for diffusion [27].

The activation energy increased with the application of the foam mat, from 31 kJ mol−<sup>1</sup> (samples without foam mat) to 43–48 kJ mol−<sup>1</sup> (samples with foam mat). These differences in activation energy may result from the variation in effective diffusivity, depending on the variability and physical structure of the sample, chemical composition, geometry and air drying temperature [28].

**Figure 2.** Mean value of the effective diffusion coefficient (D) obtained in the drying of the crushed mass of jambu leaves and foam at temperatures of 50, 60 and 70 ◦C.

#### *3.3. Thermodynamic Properties*

The enthalpy values decreased with the increase in drying air temperature, and compared to the mass of jambu leaves, the smallest magnitudes are obtained with foam mat (Table 6). The lowest enthalpy value was observed with increased temperature, which indicates that the amount of energy needed to remove water bound to the product during drying was lower [27], showing that the foam-mat drying process required lower energy expenditure for water removal.

**Table 6.** Mean values of enthalpy (ΔH), entropy (ΔS) and Gibbs free energy (ΔG) obtained in the drying of the crushed mass of jambu leaves with and without foam mat at temperatures of 50, 60 and 70 ◦C.


Entropy was consistent with enthalpy, showing lower values for foam-mat drying. Such reduction indicates a lower excitation of water molecules and an increase in the degree of order of the water-foam system [29]. Regarding Gibbs free energy, the values were positive for both dried materials. According to Chen et al. [30], positive values of Gibbs free energy are characteristic of endergonic reaction, which indicates that the drying and absorption processes under the studied conditions were not spontaneous [27].

In a comparison of the thermodynamic properties for the different drying conditions, it is possible to observe that foam-mat drying shows a better performance. Drying is one of the most energy-consuming processes and is widely used in food industries, so

increasing efficiency has the potential to reduce the energy demand of drying operations and, consequently, of the industry [31].
