Thermophysical and Electrical Properties of Ethylene Glycol-Based Nanofluids Containing CaCO₃

Abstract

The thermophysical properties of various types of nanofluids are often studied to find more effective working fluids for heat transfer applications. In this paper, the mass density, isobaric heat capacity, thermal conductivity, dynamic viscosity surface tension, and electrical properties of calcium carbonate-ethylene glycol (CaCO${}_3$-EG) nanofluids were investigated. The samples with mass fractions of 0.01, 0.02, and 0.03 were prepared with a two-step method and studied as well as pure base fluid (ethylene glycol). The measurements were conducted at temperatures between 283.15 and 313.15 K and the obtained results show the impact of CaCO${}_3$ nanoparticles on the thermophysical and electrical properties of ethylene glycol.

1. Introduction

Nanofluids, as a relatively new group of materials, have attracted the attention of scientists and engineers, especially those who deal with heat exchange systems. The unflagging interest, reported in several recent papers [1,2], is due to the unusual properties given by the combination of nanoparticles and base fluid. Such fluids are called nanofluids [3] and generally have much better thermophysical properties than the base fluid itself.

The most impressive improvement of thermophysical properties usually is observed in the thermal conductivity of nanofluids, which is potentially interesting to improve the heat transfer performance of several thermal systems. Due to this reason, thermal conductivity is one of the most often investigated properties of nanofluids [4]. The number of publications concerning this topic is huge, and so far there have been at least a dozen review articles on the subject [5,6,7,8,9,10]. Also, viscosity is one of the key parameters determining the real-life applicability of nanofluids, which is reflected in the number of publications on the subject [4] as well as many review articles concerning viscosity properties of nanofluids [11,12,13,14,15].

Theoretically, there is a large number of possible combinations of nanomaterials and base fluids that could be utilized to develop nanofluids. Nevertheless, due to the most possible directions of its applications, most research focuses on nanofluids based on ethylene glycol [16], water [17], and their mixtures [18]. On the other hand, the dispersed phases in the thermal fluid can be oxides [19,20,21], metals [22,23], and nitrides [24,25] as well as various carbon-based structures [26,27], which are either not always friendly to the environment and human health, or their impact is not yet known [28,29]. Therefore, in recent years, work aimed at the use of natural, inert, or environmentally friendly nanoparticles has become increasingly important. One of these materials is calcium carbonate (CaCO${}_3$), which is commonly used in many branches of industry such as buildings [30], papers [31], paints, coatings, rubber industry, agricultural, environment treatment [32], personal health [33,34,35], food production, as well as plastics and oil industries [36,37,38,39]. Work is also underway on the use of CaCO${}_3$ nanoparticles in drug delivery, medical imaging [40], or other biomedical and biological applications [35].

The physical properties of nanofluids containing CaCO${}_3$ nanoparticles have so far not been widely investigated. Only a dozen papers considering such nanofluids are available in the publicly scientific literature, most of which focus on their practical application, omitting a deeper analysis of their individual properties.

Prakash [35] prepared nanofluids based on water with 80 nm particles of CaCO${}_3$ dispersed with a two-step method in a volume fraction of 0.02–0.1. They observed an increase in both heat transfer (HT) performance and thermal conductivity (TC) with the rising content of nanoparticles. The noted enhancement was from 10 to 40% and 12 to 57% for thermal conductivity and heat transfer, respectively. Thermal conductivity of CaCO${}_3$ water-based nanofluids were also studied by Zhu et al. [41]. They prepared five samples with a volume concentration between 0.12 and 4.11% using the two-step method and CaCO${}_3$ paste instead of dry nanoparticles. Similarly to Prakash [35], they noted a linear increase in thermal conductivity with the increasing nanoparticle content. The obtained results showed good agreement with Chen’s model. The CaCO${}_3$ nanoparticles were also used to prepare hybrid nanofluids (TiO${}_2$/CaCO${}_3$-W, CaCO${}_3$/TiO${}_2$/Cu-W/EG) with increased thermal conductivity [42,43].

The effect of CaCO${}_3$ nanoparticles on the viscosity of the base fluid has also been noted by researchers. Zhao et al. [36] prepared nanofluids based on two types of nanoparticles with different sizes (30 and 100 nm) and found that dispersion with bigger nanoparticles causes a slightly lower increase in viscosity with the increasing content of CaCO${}_3$ nanoparticles. Additionally, the authors stated that both types of nanofluids are Newtonian. The Newtonian behavior of CaCO${}_3$ nanofluids as well as the increase in viscosity with the increasing load of nanoparticles were also confirmed by Zhu et al. [41] and Liñeira et al. [44]. On the other hand, Villada et al. [39] showed non-Newtonian behavior nanofluids based on CaCO${}_3$ nanoparticles dispersed in water/bentonite.

In contrast to thermal conductivity and viscosity, the effect of CaCO${}_3$ nanoparticles on the mass density of nanofluids is limited and observed changes are close to linear [40,45,46], while the effect on the electrical conductivity of the base fluid can be significant [47].

In the context of numerous works on various types of nanofluids, the study of thermophysical and electrical properties of nanofluids based on calcium carbonate and ethylene glycol is very scarce. Thus, the main challenge of this work is to determine the thermophysical and electrical properties of such systems and fill the existing gap. Additionally, in contrast to metal or metal–oxide nanofluids, calcium carbonate nanofluids can provide a more environmentally friendly alternative in heat exchange systems. It is therefore important to know the properties of CaCO${}_3$-EG nanofluids. In the present study, CaCO${}_3$ nanoparticles were used to prepare ethylene glycol-based nanofluids. Their physical properties such as (a) mass density, (b) isobaric heat capacity, (c) thermal conductivity, (d) dynamic viscosity, (e) surface tension, (f) electrical properties, and (g) dielectric permittivity were investigated. The effect of CaCO${}_3$ nanoparticles’ loading as well as temperature on those physical properties were experimentally evaluated and discussed.

2. Materials and Methods

2.1. Materials and Sample Preparation

The CaCO${}_3$ nanoparticles utilized in this study were supplied by PlasmaChem GmbH (Berlin, Germany). Based on the manufacturer’s data, these nanoparticles have a cubic particle shape and belong to the calcite crystal form with a rhombohedral crystal class. They have a minimum purity level of 98% on an inorganic basis, ensuring their high quality and minimal impurities. The CaCO${}_3$ nanoadditives are in the form of a dry, white powder. As declared by the manufacturer, the nanoparticles present an average size of 90 ± 15 nm as well as specific surface areas of approximately 20 m${}^2$·g${}^{-1}$.

In the experiments, ethylene glycol (EG), with a purity higher than 99% and provided by Chempur (Piekary Ślaskie, Poland), was employed as the base fluid. All dispersions prepared for this work were produced in 50 mL vials following the two-step method.

In this approach, the initial step involves mechanically mixing the nanoparticles with the base liquid to create a heterogeneous suspension characterized by limited dispersion of the nanoparticles. Within this colloid, agglomerates of nanoparticles tend to rapidly settle. To address this issue and achieve improved nanoparticle dispersion resulting in a homogeneous mixture, a secondary stirring method employing ultrasound was implemented. It is important to note that for this work, there were no surfactants used in the sample preparation of the nanofluids. Nanofluids at 1, 2, and 3 wt.% mass concentrations were produced. Using a density value of 2710 kg·m${}^{-3}$ for the CaCO${}_3$ nanopowder, the 0.01, 0.02, and 0.03 mass fractions, ${\phi }_{m,np}$, correspond to the 0.0041, 0.0083, and 0.0125 volume fractions, ${\phi }_{v,np}$, respectively.

The nanofluid preparation process was initiated with the precise measurement of the required quantity of nanoparticles, using an analytical balance (Pioneer Semi-Micro PX225DM, OHAUS Corporation, Parsippany, NJ, USA). Following this, ethylene glycol was added to attain the targeted mass concentration. Subsequently, the nanofluids underwent a 30-min mechanical premixing using an IKA Vortex 3 shaker (IKA, Staufen, Germany). To ensure a uniform mixture, the nanofluids underwent further blending with ultrasound using an Emmi 60 HC ultrasonic cleaner (EMAG, Moerfelden-Walldorf, Germany) operating at 450 W power and a 45 kHz frequency for a total of 200 min, effectively dispersing the agglomerates and eliminating air bubbles. The preparation of the sample was completed by subjecting the nanofluid to high-energy ultrasonic mixing using a Sonics Vibracell VCX130 ultrasound generator (Sonics & Materials Inc., Newtown, CT, USA) for 5 min. Considering the precision of the analytical balance, the uncertainty in the mass fraction was established to be 2% of its measured value. The nanofluid samples, prepared using the described steps, were then immediately tested.

2.2. Nanoparticles’ Characterization

The morphology of the nanoparticles was investigated via transmission electron microscopy (TEM). TEM images were taken using a JEOL JEM-1010 microscope (JEOL, Tokyo, Japan) at an accelerating voltage of 100 kV. The microstructure of the material was examined via energy-dispersive X-ray spectrometry (EDS). EDS microanalyses were made using an Inca Energy 300 spectrometer (Oxford Instruments, Oxford, UK) coupled to a JEOL JSM-6700F scanning electron microscope (JEOL, Tokyo, Japan). To check whether any substantial modification of the nanoparticles occurs due to their dispersion in the base fluid, TEM and EDS analyses were carried out for two types of nanopowder samples: as received from the supplier and after being part of a 1 wt% nanofluid (mechanical mixing, low-energy ultrasound, and high-energy ultrasound processes) and dried. Silica and copper grids were used for TEM and EDS measurements, respectively. A drop of each nanopowder dispersion in ethanol was placed on the corresponding grid, allowed to dry, and coated with carbon.

2.3. Nanofluids’ Stability Characterization

The hydrodynamic size distribution of dispersed CaCO${}_3$ nanoparticles was determined by means of a Zetasizer Nano ZS (Malvern Instruments, Malvern, UK), which works on the principle of the dynamic light scattering (DLS) technique. The device uses a He-Ne laser emitting at a wavelength of 633 nm with a power of 4 mW. Intensity fluctuations in scattered light were measured at a detector angle of 173° (backscatter) relative to the source. Following a similar procedure to that developed by Fedele et al. [48], for each nanofluid concentration, two different plastic cuvettes were filled with approximately 1 cm${}^3$ of sample. The dispersion of the first cuvette was analyzed without shaking the sample to assess possible changes in the size distribution due to nanoparticle sedimentation when stored under nearly static conditions. The second fluid was measured after being sonicated for 1 min using a low-power ultrasound bath in order to assess changes in the size distribution after mechanically recovering the settled particles. Static and sonicated samples were investigated for over a month to assess the temporal stability of the dispersions. Then, additional measurements were performed for the dispersions six months after their preparation. The reported results are based on a minimum of three parallel tests of 15 runs each. The experimental uncertainty in measuring the size of the suspended particles was estimated to be 2% [49].

2.4. Physical Properties of Base Fluid and Nanofluids

The mass density, isobaric heat capacity, thermal conductivity, dynamic viscosity, surface tension, and electrical properties of the base fluid and nanofluids were determined in the 283.15–313.15 K temperature range using well-recognized experimental methods. Each measurement was performed at least five times for all samples.

2.4.1. Mass Density Measurements

Using an automatic oscillating U-tube densitometer DMA 4100 M (Anton Paar, Graz, Austria), mass density measurements were performed. Calibration of the instrument was carried out using deionized water at a temperature of 293.15 K and atmospheric pressure. The temperature range for the density measurements of all samples spanned from 283.15 K to 318.15 K.

In the course of conducting a series of one hundred density measurements, the determined density value for distilled water was 0.9969 g cm${}^{-3}$, with a standard deviation of 0.0002 g cm${}^{-3}$. The literature value from [50] for water density at 298.15 K is 0.9971 g cm${}^{-3}$. The relative uncertainty of the density measurements is established as 0.1%.

2.4.2. Isobaric Heat Capacity Measurements

Isobaric heat capacity measurements were performed by utilizing a Q2000 differential scanning calorimeter (TA Instruments, Newcastle, UK) combined with an RSC90 cooling system. An amount of 15 ± 1 mg of base fluid/nanofluid and 8 ± 1 mg of nanopowder were placed in Tzero Pan+Tzero Hermetic Lid cells for the corresponding measurements. The tests were carried out in a N${}_2$1 atmosphere using the quasi-isothermal temperature-modulated differential scanning calorimetry method. The temperature was modulated around the reference following a sinusoidal program (period of 80 s and amplitude of 0.5 K). The reference temperature for the measurements ranged between 283.15 K and 313.15 K. The uncertainty of these measurements was previously set as 3% [51].

2.4.3. Thermal Conductivity Measurements

Thermal conductivity measurements were carried out using a TEMPOS thermal properties analyzer (METER group, Pullman, WA, USA) equipped with a KS-3 sensor working both as a heat source and as a temperature sensor (1.3 mm diameter, 60 mm length). An amount of 20 ± 1 mL of sample was placed in a vial with a cap and septum for each measurement. The temperature around the sample was controlled using a thermostatic bath. The reference temperature for the measurements ranged between 283.15 K and 313.15 K. The “low power” measurement mode was used, ensuring that slight heat was applied to the needle in order to prevent free convection in the liquids.

Prior to the measurements, a calibration with glycerin at 293.15 K was carried out. For twenty thermal conductivity measurements carried out each 15 min, the average value obtained was 0.285 W·m${}^{-1}$·K${}^{-1}$, with a standard deviation of 0.002 W·m${}^{-1}$·K${}^{-1}$. The value from [52] in the literature for glycerin thermal conductivity at 293.15 K is 0.282 W·m${}^{-1}$·K${}^{-1}$. The relative uncertainty of the thermal conductivity measurements is established as 3%.

2.4.4. Rheological Measurements

Dynamic viscosity was investigated using a Physica MCR 101 air-bearing rheometer (Anton Paar GmbH, Granz, Austria). A Couette-flow Searle-type configuration, which mainly consisted of a CC27/T200/SS cup (outer radius: 14.46 mm) and a smooth concentric B-CC27/P6 bob (inner radius: 13.33 mm, measuring length: 40.00 mm, and cone-tip angle: 120°), was selected to perform the experimental determinations. The temperature of the tested sample was stabilized and controlled from 283.15 to 313.15 K each 10 K by means of a C-PTD 200 Peltier system and an appropriate evaporator blocker system. Steady-state viscosities were obtained in the shear rate range from 1 to 100 s${}^{-1}$, taking 7 points per decimal. The estimated uncertainty of dynamic viscosity determinations was assumed to be below 4%.

2.4.5. Surface Tension Measurements

For the purposes of this article, the surface tension values of the nanofluids were determined using a PI-MT1A.KOM tensiometer (Polon-Izot, Warsaw, Poland) employing the Du Nouy ring method. Three series of ten measurements were taken for each nanofluid sample to obtain surface tension values, and the results given represent the average of these series. In order to evaluate the measurement uncertainty, ten measurements were made of pure ethylene glycol at 298.15 K. The obtained result was 47.49 mN·m${}^{-1}$ with a standard deviation of 0.03 mNm${}^{-1}$, which aligns with the literature values of 48.02 mN·m${}^{-1}$ [50], 48.07 mN·m${}^{-1}$ [53], and 47.89 mN·m${}^{-1}$ [54]. Analyzing the mentioned factors, the relative uncertainty of surface tension measurements was estimated at 1%.

2.4.6. DC Electrical Conductivity Measurements

The direct current (DC) electrical conductivity of CaCO${}_3$-EG nanofluids, as well as the pure base fluid (ethylene glycol), was investigated with electrical conductivity meter Multiline 3410, coupled with a conductivity probe LR 925/01 (WTW GmbH, Weilheim, Germany). Samples were tested at a temperature range of 283.15 to 313.15 K with 5 K and an accuracy of 0.2 K. The value of electrical conductivity at each temperature was obtained as an average taken from measurements conducted during 10 min every 10 s. As it was mentioned elsewhere [55], the electrical conductivity uncertainty was determined to be 2%.

2.4.7. Dielectric Properties’ Measurements

Dielectric properties of all samples were investigated using the broadband dielectric spectroscopy (BDS) device (Concept 80, Novocontrol Technologies GmbH, Montabaur, Germany) in a frequency range of 1 MHz to 0.1 Hz in logarithmic scale. To ensure good control of the sample temperature, Novocontrol Quatro Cryosystem (Novocontrol Technologies GmbH, Montabaur, Germany) was employed. Measurements were performed at a temperature range from 293.15 to 313.15 K with a 5 K step. The accuracy of temperature stabilization was set to be 0.2 K. According to the manufacturer’s recommendations, each measurement series was preceded by a calibration procedure using an ohmic standard.

3. Results

3.1. Nanoparticles’ Morphology and Composition

Figure 1 shows TEM images of the CaCO${}_3$ nanopowders in which a mostly prismatic nanoparticle shape is observed. Regarding size, it can be stated that the nanoparticles evidence dimensions in the range declared by the manufacturer, 90 ± 15 nm. The comparison of the images of the nanopowder as received from the supplier (Figure 1a) and that dried after being part of a 1 wt% nanofluid (Figure 1b) evidences similar shapes and sizes of the nanoparticles. Thus, it can be concluded that their dispersion process within the base fluid, which includes high-energy ultrasounds, does not cause morphological changes.

Figure 2 presents the EDS spectra of the CaCO${}_3$ nanopowder, in which the presence of C, O, and Ca is evidenced as expected. Negligible amounts of S, Na, or Si are also shown. The results for the nanopowder as received from the supplier (Figure 2a) and that dried after being part of a 1 wt% nanofluid (Figure 2b) are similar. Therefore, it can also be concluded that the dispersion process of the nanoparticles within the base fluid does not imply changes in their chemical composition.

3.2. Nanofluids’ Stability

Over a month, DLS measurements were performed for nanofluids stored under nearly static conditions and after being sonicated for 1 min using a low-power ultrasound bath (simulating a reproducible strong fluid mixing) just before conducting the experiments. Figure 3 shows some representative hydrodynamic size distributions of the 3 wt% dispersion, together with the average sizes recorded for the three studied concentrations over time. No significant variations were observed between the results of the three nanofluids, indicating that the hydrodynamic size trends are independent of the nanoparticle content in the investigated concentration range. This fact was also reported in the literature for other nanofluids prepared at low nanoparticle concentrations [56,57,58]. After the sonication of the samples following the procedure described in Section 2.1, dispersed particles showed hydrodynamic diameters in the range of 250–280 nm and polydispersity indexes of 0.26–0.29. DLS sizes almost triple the diameters observed in the TEM images. Such differences may evidence a certain degree of nanoparticle agglomeration when dispersed in the ethylene glycol. However, it may also be noted that DLS measurements are not direct size determinations of dry nanoparticles, but the hydrodynamic diameter of the suspended particles. In addition, registered size distributions are quite polydispersed and there is also a small secondary intensity peak at about 4 $\mathsf{\mu }$m (see Figure 3a). Therefore, the presence of large nanoparticles may contribute to a rise in scattered light, which in turn shifts the average size to larger values [59]. Regarding the temporal evolution (Figure 3b), DLS diameters measured for static samples decrease to 160–170 nm in the first 10 days and remain centered on this value for the rest of the investigated timeframe. This reduction in average size indicates a partial nanoparticle sedimentation, probably the largest in size as also shown by the disappearance of the 4 $\mathsf{\mu }$m peak in the size distribution of the 3 wt% static sample (Figure 3a). As for the nanofluids investigated after 1 min of sonication, no major changes were detected in the DLS diameter over time (neither through the first month nor six months after their preparation), suggesting the absence of further aggregation phenomena [60].

3.3. Mass Density

The results of the mass density measurements of tested CaCO${}_3$-EG nanofluid mass fractions are shown in Figure 4a.

For all the nanofluids examined in this study, it is observed that the mass density rises proportionally as the nanoparticle mass fraction increases, indicating a consistent dispersion of the nanoparticles within the ethylene glycol. The maximum enhancement (2%) was noted at 293.15 K for the highest tested mass fraction (0.03). Simultaneously, an inverse relationship is noted between density and temperature, with density decreasing linearly as temperature rises. Investigated CaCO${}_3$-EG nanofluids exhibit a density increase with the increasing mass fraction of nanoparticles. Nonetheless, all of the nanofluids behave in the same way when concentration and temperature changes are taken into account.

Pak and Cho [61] offered an equation to describe this relationship as follows:

$${\rho }_{nf}=(1-{\phi }_v){\rho }_{bf}+{\phi }_v{\rho }_p,$$

(1)

where ${\rho }_{nf}$ is the density of the nanofluid, ${\rho }_{bf}$ is the density of the base fluid, ${\rho }_p$ is the density of the particles, and ${\phi }_v$ is the volume fraction related to the mass fraction ${\phi }_m$ by

$${\phi }_v=\frac{{\phi }_m}{{\rho }_p\left(\frac{{\phi }_m}{{\rho }_p}+\frac{1-{\phi }_m}{{\rho }_{bf}}\right)}.$$

(2)

The authors used the principles of ideal gas-mixing theory to establish the correlation between the variables. According to the authors, this equation can model the density of nanofluids to within a few percent. Figure 4b shows a comparison of Equation (1) and the experimental values obtained for the mass density of the nanofluid tested at 298.15 K.

3.4. Isobaric Heat Capacity

Isobaric heat capacities, $c_p$, were determined for ethylene glycol, the nanofluids, and the CaCO${}_3$ nanopowder at temperatures from 283.15 to 313.15 K. Good agreement was observed between the $c_p$ data here presented for EG and those values from Nan et al. [62], Góralski and Tkaczyk [63], Zemánková et al. [64], and Zyła et al. [65] (average deviations of 3.5%, 2.5%, 1.8%, and 0.8%, respectively). Figure 5 shows the increasing trend of $c_p$ with the rising temperatures. Decreases can also be noted with respect to the base due to the dispersion of the CaCO${}_3$ nanopowder. These decreases are practically temperature-independent and reach 0.3%, 1.2%, and 1.9% for the 1wt%, 2wt%, and 3wt% nanofluids, respectively. Water-, EG- and EG/water-based nanofluids commonly show decreases in specific heat from pure fluid values. This is often attributed to the fact that the heat capacity of particulate materials is much lower than that of water or EG [66]. Values of 811, 833, 855, and 877 J·g${}^{-1}$·K${}^{-1}$ were here obtained for the CaCO${}_3$ nanopowder at 283, 293, 303, and 313 K, respectively. These heat capacities are approximately 66% lower than those of the EG.

The Pak and Cho model is often employed to predict the heat capacity of nanofluids based on the values for the base fluid and the nanoparticles:

$$c_{p,nf}=c_{p,bf}·(1-{\varphi }_{m,np})+c_{p,np}·{\varphi }_{m,np}$$

(3)

where ${\varphi }_m$ is the mass fraction and the subscripts $nf$, $bf$, and $np$ mean nanofluid, base fluid, and nanoparticles, respectively. Other authors claim that Equation (3) is only valid when the difference between the densities of the fluid and the nanoparticle is low and theorize that the following expression is more appropriate:

$$c_{p,nf}=c_{p,bf}·(1-{\varphi }_{v,np})+c_{p,np}·{\varphi }_{v,np}$$

(4)

where ${\varphi }_v$ is the volume fraction. The experimental values here presented are well predicted by both models, with maximum deviations of 0.3% and −1.2% from Equation (3) and Equation (4), respectively, which are within the experimental uncertainty in both cases.

3.5. Thermal Conductivity

Thermal conductivity, k, was obtained for ethylene glycol and the nanofluids at temperatures from 283.15 to 313.15 K. Great agreement was noted between our experimental k values for EG and those reported by Akilu et al. [67] and Huang et al. [68] (absolute average deviations of 1.3% and 2.2%, respectively). Figure 6 shows k increases with rising temperature both for nanofluids and the base fluid. Furthermore, the increasing CaCO${}_3$ concentration produces thermal conductivity increases. These increases are practically temperature independent and reach average percentages of 2.2%, 6.7%, and 14.8% for the 1 wt%, 2 wt%, and 3 wt% nanofluids, respectively. Particle agglomeration, liquid layering at the particle–fluid interface, fluid convection at microscale, and the thermophoretic effect or Brownian motion are the main mechanisms attributed to the thermal conductivity improvements of nanofluids [69].

Our group [70] has previously adapted the parallel model or upper Wiener bound to the prediction of the effective thermal conductivity of nanofluids based on the expression:

$$k_{nf}=k_{bf}·(1-{\varphi }_{v,np})+k_{np}·{\varphi }_{v,np}$$

(5)

Several authors reported a thermal conductivity value in the range of 2.2–2.7 W·m${}^{-1}$·K${}^{-1}$ for calcium carbonate (calcite) [71,72,73]. By using $k_{np}$= 2.7 W· m${}^{-1}$· K${}^{-1}$, Equation (5) predicts the $k_{nf}$ values of the 1 wt%, 2 wt%, and 3 wt% nanofluids with average deviations of −1.8%, −0.8%, and 2.2%, respectively, which are practically within the experimental uncertainty.

3.6. Rheological Behavior

Dynamic viscosity, $\mu$, flow curves were experimentally determined for ethylene glycol and the three nanofluids at temperatures from 283.15 to 313.15 K and shear rates between 1 and 100 s${}^{-1}$. Good agreement (absolute average deviations less than 5%) was observed between the $\mu$ results here obtained for EG and other values from the literature [74,75,76,77]. Figure 7 shows the shear rate–shear viscosity dependence of the investigated samples. Like the base fluid, nanofluids show a Newtonian behavior within the studied conditions. This may be considered as an indication of a lack of large agglomerates or aggregates in the prepared dispersions [78]. For example, Newtonian viscosities were also reported in the literature by Liñeira del Río et al. [44] for 0.05–0.20 wt% CaCO${}_3$ dispersions in polyalphaolefin 8 (PAO8) lubricant and by Zhu et al. [41] for aqueous nanofluids loaded with 0.12–4.11% volume contents of spherical CaCO${}_3$ nanoparticles with diameters of 20–50 nm. The effect of temperature on the dynamic viscosity of the base fluid and nanofluids is presented in Figure 7b. As can be observed, $\mu$ exponentially reduces with the rising temperature. This behavior can be described by means of the well-known Vogel–Fulcher–Tammann (VFT) equation:

$$ln\mu =ln{\mu }_0+\frac{D·T_0}{T-T_0}$$

(6)

where ${\mu }_0$, D, and $T_0$ are adjustable coefficients. Experimental values can be fitted with standard deviations of 1.1–1.6 mPa·s (absolute average deviations of $AADs\%$ = 1.9–2.3%) using Angell strength (D) values of ∼6.12, which correspond to “strong” liquids [79] and are in the same range to the results reported in the literature for ethylene glycol [80] or poly(ethylene glycol) [57] samples.

As is common in this type of colloidal dispersions, investigated nanofluids exhibit larger $\mu$ values in comparison to the base fluid. Even so, in the studied concentration range, the rises with the CaCO${}_3$ loading were moderate [15]. Thus, on average, the viscosity increases were 2.8%, 4.1%, and 6.8% for the ethylene glycol-based dispersions containing 1%, 2%, and 3% in the mass of CaCO${}_3$, respectively. Padole et al. [45] investigated the dynamic viscosity of methanol-based nanofluids loaded with SnO${}_3$ (size ∼12 nm), CaCO${}_3$ (∼63 nm), CaF${}_2$ (∼49 nm), ZnS (∼37 nm), and Ag (∼32 nm) nanoadditives. Even though other design parameters such as particle shape should also be taken into account, CaCO${}_3$/ethanol dispersions also showed dynamic viscosities much lower when compared to samples containing comparable amounts of the four nanopowders.

Several theoretical or semi-empirical models have been proposed in the literature to predict or describe the dynamic viscosity–volume fraction dependence of solid–liquid dispersions [15]. In the case of low-concentrated microsuspensions of rigid, spherical particles, Einstein [81] proposed a linear relationship between the increases in dynamic viscosity and the content of the dispersed phase:

$${\mu }_r=\frac{{\mu }_{nf}}{{\mu }_{bf}=1+2.5·{\varphi }_{v,np}}$$

(7)

where ${\mu }_r$ is the so-called reduced viscosity and ${\varphi }_{v,np}$ is the volume fraction of the dispersed particles. However, as the nanoparticle concentration rises, hydrodynamic and colloidal interactions start to show a significant impact on the shear viscosity. As a consequence, the viscosity of solid–liquid suspensions increases in a non-linear manner and, therefore, the Einstein equation usually underpredicts the experimental $\mu$ results. For concentrated dispersions, Chow [82] developed an equation that takes into account both the interactions between the particles and within the equilibrium microstructure. This relationship can be formally written as a virial series:

$${\mu }_r=\frac{{\mu }_{nf}}{{\mu }_{bf}}=1+\sum _{i=1}^N{c}_i·{\varphi }_{v,np}^i$$

(8)

where N is the expansion degree and $c_i$ are adjustable coefficients that depend on different parameters such as the nanoparticle shape, orientation, and volume fraction [82]. In our study, we have used the Chow [82] equation with N = 2, fixing $c_1$ = 2.5 and using $c_2$ as the fitting parameter. Figure 8 graphically compares the experimental relative viscosities and the values provided by the Einstein [81] and Chow [82] relationships. In the investigated system, values predicted using the Einstein equation [81] are, on average, 2.3% smaller than the experimental results. An $AAD\%$ of 0.5% was obtained when using the second-degree fitting based on Equation (8) with $c_2$ = 236.

3.7. Surface Tension

The measured surface tension values of all nanofluids investigated in this work were presented in Figure 9.

All prepared samples exhibit an increase in surface tension values compared to pure ethylene glycol. This is consistent with earlier investigations of the surface tension of nanofluids, which have also shown an increase in surface tension relative to the pure base liquid. However, in this study, the increase in surface tension remains constant despite an increase in the nanoparticle mass concentration.

Additionally, in this work, surface tension values were also investigated for mass fractions below 0.01. The experimental data of these studies are summarized in

Table 1. Experimental values of surface tension, $\gamma$, of CaCO${}_3$-EG nanofluids, at a pressure p = 0.10 MPa at temperatures from T = 298.15 K for different values of mass fraction, ${\phi }_m$.

${\mathit{\phi }}_{\mathit{m}}$/–	${\mathit{\gamma }}_{\mathbf{nf}}$/mN m${}^{-1}$
0.000	48.0
0.001	48.1
0.002	48.2
0.003	48.4
0.004	48.5
0.005	48.5
0.010	48.5
0.020	48.4
0.030	48.5

The estimated standard relative uncertainty $u_r\left({\phi }_m\right)$ = 0.01, $u_r\left(\gamma \right)$ = 0.01, $u\left(p\right)$ = 0.01 MPa, and $u\left(T\right)$ = 0.10 K.

.

It can be observed that for mass fractions between 0.001 and 0.005, the surface tension value increases with the increasing nanoparticle fraction. A model to describe the increase in the surface tension of nanofluids has been proposed in a previous paper [83]. This model is expressed by the following equation:

$${\gamma }_{nf}={\gamma }_{bf}+A\left(1-\frac{1}{{\mathrm{e}}^{\frac{({\phi }_m-C)}{B}}+1}\right),$$

(9)

where ${\gamma }_{bf}$ is the value of the surface tension of the base fluid, ${\phi }_m$ is the mass fraction, and A, B, and C are adjustable parameters. The experimental values obtained for the CaCO${}_3$-EG nanofluids are in good agreement with this model, which was presented in Figure 10 for nanofluids in the mass fraction in a range from 0.001 to 0.01 at 298.15 K. Additionally, the parameters that were used to fit the model to the experimental data are as follows: A = 0.4114 mN·m${}^{-1}$, B = 0.0005, and C = 0.00211. It can be noted that the acquired data confirm the proposed model of surface tension in ethylene glycol-based nanofluids.

3.8. DC Electrical Conductivity

The direct current (DC) electrical conductivity of CaCO${}_3$-EG nanofluids as a function of the mass fraction at various temperatures was presented in Figure 11. As can be seen, both increases in the content of CaCO${}_3$ nanoparticles and temperature have a visible impact on the DC electrical conductivity of CaCO${}_3$-EG nanofluids. The increase in the mass fraction of nanoparticles up to 2 wt.% causes simultaneous increases in electrical conductivity. Future enhancement of the nanoparticle load (up to 3%) causes no significant changes in the electrical conductivity of the nanofluid. The highest value of ${\sigma }_{DC}$ was noted at the highest tested temperature (313.15 K) and it was 5.85 $\mathsf{\mu }$S/cm, while at 283.15 K, the increase was only up to 1.99 $\mathsf{\mu }$S/cm. Based on the available literature, electrical conductivity enhancement was expected, as it was previously reported for many various types of nanofluids [84,85,86,87,88]. Also in the case of nano-liquids containing CaCO${}_3$ dispersed in methanol, Chimankar et al. [40] observed an enhancement in electrical conductivity values with the rising CaCO${}_3$ nanoparticle content in the base fluid. The most possible mechanism behind the electrical conductivity enhancement of nanofluids (including CaCO${}_3$-EG) is the occurring electrical double layer (EDL) around the nanoparticles, which results in the nanoparticles becoming carriers of an electrical charge. In addition, the temperature rise has a positive effect in this context, improving the mobility of the charge carriers. The introduction of additional charge carriers in the form of Ca${}^{2+}$ ions from CaCO${}_3$ nanoparticles into the base fluid is also important for improving electrical conductivity.

3.9. Dielectric Permittivity

The complex dielectric permittivity of CaCO${}_3$-EG nanofluids was studied at wide range of frequency spanning from 10${}^6$ Hz to 0.1 Hz at four different temperatures (283.15, 293.15, 303.25, and 313.15 K). The results for two representative temperatures (283.15 and 313.15 K) are presented in Figure 12. As can be seen, dielectric constant spectra can be split into two regions, low- and high-frequency. The first region (low frequency) is characterized by strong and visible dispersion in which a decrease in frequency causes an increase in the values of the dielectric constant. Observed behavior can be assigned to two phenomena: electrode polarization and Maxwell–Wagner polarization [89]. The dielectric constant is also affected by the nanoparticle addition, which is particularly visible in the low-frequency region, where a shift of a decade between the base fluid and nanofluids is clearly visible. The second region (high frequency) is not affected by frequency changes and values of the dielectric constant remain the same without any major changes. Additionally, the border between these areas is dependent on temperature changes, and an increase in temperature from 283.15 K to 313.15 K causes a slight shift towards higher frequencies. Furthermore, there is no strong difference between nanofluids containing CaCO${}_3$ nanoparticles in a mass fraction from 0.01 to 0.03.

Dielectric losses of CaCO${}_3$-EG nanofluids were presented in Figure 12b,d, where a constant change in the dielectric loss value with an increasing frequency for all the samples tested can be observed. In addition, as in the case of the dielectric constant, the effect of the addition of nanoparticles can also be seen for the dielectric loss, with an increase in the dielectric loss value of about a decade compared to pure ethylene glycol.

3.10. AC Electrical Conductivity

The alternating current (AC) electrical conductivity of CaCO${}_3$-EG nanofluids at two representative temperature were presented in Figure 13. The obtained results show behavior characteristic for nanofluids [90,91], with three well-differentiated regions. Starting at low frequencies, the phenomenon of electrode polarization can be observed: as the frequency rises, the electrical conductivity also increases gently. In the mid-frequency range, no effect of frequency changes on the value of the electrical conductivity is observed. This area is the so-called plateau and is related to DC electrical conductivity. Further, at the highest frequencies tested, a dispersion area is noticeable where an increase in frequency causes the electrical conductivity value to rise again. This region is particularly visible in the case of a pure base fluid (Figure 13).

Generally, the electrical conductivity of CaCO${}_3$-EG nanofluids increases with the addition of nanoparticles, however, the differences between various mass fractions are very small, while between the base fluid and CaCO${}_3$-EG nanofluids, it is over one order of magnitude. Additionally, a more visible effect is given by the temperature increase, which can be noticed by comparing Figure 13a,b.

Based on the plateau observed in the AC conductivity spectra (Figure 13), values of DC electrical conductivity were designated and presented in Figure 14. As can be seen, the increase in values of electrical conductivity with the load of CaCO${}_3$ nanoparticles is confirmed. Differences in values obtained by these two methods are not significant and can be assigned to the combined uncertainty of both devices.

3.11. Figures-of-Merit

The thermophysical properties of the fluids are closely related to their convective heat transfer efficiency. This relationship depends significantly on the operating conditions. For certain heat exchangers and heat transfer modes, the literature includes some figures-of-merit based on thermophysical properties that allow for the comparison of typical fluids with their alternatives [92].

For single-phase forced convection with a fully developed flow over a circular pipe, the Mouromtseff number, $Mo$, estimates the heat transfer efficiency as a function of $\rho$, k, $cp$, and $\mu$. For laminar flow, $Mo$ can be directly assumed as the thermal conductivity, so the ratio between the Mouromtseff numbers of the nanofluid and the base fluid, $M{o}_{nf}/M{o}_{bf}$, is assumed as [93]

$${\left(\frac{M{o}_{nf}}{M{o}_{bf}}\right)}_{\mathrm{laminar}\mathrm{flow}}=\frac{k_{nf}}{k_{bf}}$$

(10)

On the other hand, for turbulent flow, the $M{o}_{nf}/M{o}_{bf}$ ratio presents different versions depending on the author. Some of the most used in the literature include the Dittus–Boelter coefficients (for heating) [94] and the Simons coefficients [93]:

$${\left(\frac{M{o}_{nf}}{M{o}_{bf}}\right)}_{\mathrm{turbulent}\mathrm{flow}\mathrm{Dittus}-\mathrm{Boelter}}=\frac{\frac{{\rho }_{nf}^{0.8}·k_{nf}^{0.6}·c_{p,nf}^{0.4}}{{\mu }_{nf}^{0.4}}}{\frac{{\rho }_{bf}^{0.8}·k_{bf}^{0.6}·c_{p,bf}^{0.4}}{{\mu }_{bf}^{0.4}}},$$

(11)

$${\left(\frac{M{o}_{nf}}{M{o}_{bf}}\right)}_{\mathrm{turbulent}\mathrm{flow}\mathrm{Simons}}=\frac{\frac{{\rho }_{nf}^{0.8}·k_{nf}^{0.67}·c_{p,nf}^{0.33}}{{\mu }_{nf}^{0.47}}}{\frac{{\rho }_{bf}^{0.8}·k_{bf}^{0.67}·c_{p,bf}^{0.33}}{{\mu }_{bf}^{0.47}}}.$$

(12)

In both cases, the $M{o}_{nf}/M{o}_{bf}$ ratio is considered to be equivalent to the ratio between the convective heat transfer coefficients of the nanofluid and the base fluid under the described working conditions. Therefore, $M{o}_{nf}/M{o}_{bf}$ ratios greater than one imply that the nanofluid can successfully replace the base fluid.

Table 2. Mouromtseff number ratios in laminar (Equation (10)) and turbulent (Equations (11) and (12)) flow for CaCO${}_3$-EG nanofluids at different temperatures.

	Temperature/K	CaCO${}_3$-EG-1%	CaCO${}_3$-EG-2%	CaCO${}_3$-EG-3%
${\left(\frac{M{o}_{nf}}{M{o}_{bf}}\right)}_{\mathrm{laminar}\mathrm{flow}}$	283.15	1.025	1.064	1.144
	293.15	1.024	1.065	1.154
	303.15	1.020	1.067	1.146
	313.15	1.019	1.073	1.147
${\left(\frac{M{o}_{nf}}{M{o}_{bf}}\right)}_{\mathrm{turbulent}\mathrm{flow}\mathrm{Dittus}-\mathrm{Boelter}}$	283.15	1.011	1.028	1.064
	293.15	1.007	1.028	1.071
	303.15	1.002	1.027	1.064
	313.15	1.004	1.030	1.067
${\left(\frac{M{o}_{nf}}{M{o}_{bf}}\right)}_{\mathrm{turbulent}\mathrm{flow}\mathrm{Simons}}$	283.15	1.012	1.031	1.070
	293.15	1.007	1.030	1.078
	303.15	1.002	1.029	1.071
	313.15	1.003	1.033	1.074

shows the $M{o}_{nf}/M{o}_{bf}$ ratios for the designed CaCO${}_3$-EG nanofluids at different temperatures, determined according to Equations (10)–(12). As observed, the ratios are greater than one in all cases. For laminar flow (Equation (10)) over a circular pipe, enhancements of around 15% are expected for the 3% nanofluid. On the other hand, for turbulent flow over a circular pipe (Equations (11) and (12)), increases of around 7% are shown using the coefficients of the different authors. These $M{o}_{nf}/M{o}_{bf}$ results are higher than those of many works in the literature, where values less than one are commonly reflected [95,96]. Tests with these nanofluids on real heat exchangers to confirm these expectations can be the subject of future research.

4. Conclusions

The experimental research of calcium carbonate-ethylene glycol nanofluids’ thermal conductivity, isobaric heat capacity, mass density and surface tension, dynamic viscosity, and electrical characteristics were summarized in this paper.

In all investigated samples, a linear reduction in density is noted with the rising temperature, and the mass density increases linearly with the increasing nanoparticle mass fraction up to 2%. Additionally, the obtained results are in agreement with the Pak and Cho model.

The isobaric heat capacity decreases with the rising nanoparticle mass fraction up to 1.9% and increases with the increasing temperature. The obtained results agree with Equation (4). The thermal conductivity enhances with the increasing nanoparticle mass fraction and reaches a noticeable 14.8% for the 3 wt% concentration. Increases with the increasing temperature were also found. The obtained results agree with those predicted by the parallel model adapted to nanofluids.

In the investigated shear rate range, the prepared nanofluids exhibited a Newtonian behavior. Even if dynamic viscosity increases with the rising calcium carbonate content, average rises in this property reached 6.8% for 3 wt%.

The surface tension of the investigated nanofluids is in accordance with the model presented by Traciak et al. in the previous publication [83], which presupposes that the base fluid’s surface is saturated with nanoparticles.

The electrical conductivity of ethylene glycol is enhanced when the load of CaCO${}_3$ nanoparticles increases up to a 2% mass fraction, as well as when the temperature of nanofluids increases.

The dielectric constant and dielectric loss are also affected by CaCO${}_3$ nanoparticles and temperature. The higher the content of nanoparticles, the higher the values of complex dielectric permittivity, which is more pronounced at lower frequencies.

The ratios between the Mouromtseff numbers of the nanofluid and the base fluid are greater than one at all the studied conditions. According to these results, the enhancement of the convective heat transfer over a circular pipe can reach 15% and 7% for laminar and turbulent flow, respectively.

The physical profile observed for 1–3 wt% CaCO${}_3$ nanofluids makes them promising candidates for improving heat transfer efficiency in various systems. This is particularly relevant in applications where efficient heat dissipation or thermal management is crucial, such as in cooling systems for electronic devices, heat exchangers, and renewable energy technologies. Additionally, the eco-friendly nature of CaCO${}_3$ nanofluids positions them as greener alternatives to metallic counterparts, aligning with the increasing demand for sustainable and environmentally friendly heat transfer fluids.