The role of contact angle in the thermal conductivity of microencapsulated phase change material suspensions

Abstract

The purpose of this article is to investigate the effect of the wettability on the thermal conductivity of microencapsulated phase change material suspensions. The wettability of the capsules, characterized by contact angle between solid capsules and carrier fluid, was modified by mixing two selected surfactants into the suspensions, that is, cetyltrimethylammonium bromide and sodium dodecyl sulfate, and changing such surfactants’ additive amount. Meanwhile, the static thermal conductivity of the microencapsulated phase change material suspensions was measured. The results indicated the effect of the cetyltrimethylammonium bromide is more significant than the sodium dodecyl sulfate when the mass fraction of surfactants falls into the range of 0–0.05 wt%. However, when the mass fraction of surfactants continues to increase from 0.05 wt%, the significance of the sodium dodecyl sulfate exceeded the cetyltrimethylammonium bromide. It was also found that the decrease in the contact angle led to the growth in thermal conductivity for Maxwell model and tested results. When the contact angle fell into the range of 45°–95°, the Maxwell model could predict the thermal conductivity with a good accuracy, but inversely, when the contact angles were smaller than 45°, a significant gap was found between the two results. To remove such gap a correction factor “A” which is associated with contact angles was proposed.

Introduction

Renewable energies will replace coal, oil, and gas significantly faster in order to halt climate changes. Solar energy will assume a major share. A crucial response to the dangers of global warming is the worldwide utilization of solar heat. By the end of 2013, an installed capacity of 374.7 GWth, corresponding to a total of 535 million squaremeters of collector area was in operation worldwide. The vast majority of the total capacity in operation was installed in China (262.3 GWth) and Europe (44.1 GWth), which together accounted for 82% of the total capacity installed. The remaining installed capacity was shared between the United States and Canada (17.7 GWth) as well as other countries. ¹ However, intermittency is inherently disadvantage of solar energy. Solar radiation varies throughout the day and through the seasons, and is affected by dust and cloud. Therefore, solar thermal systems make use of heat storage devices to help meet the transient thermal load of end users for a full day.

A phase change material (PCM) can handle much more heat at the same temperature than a single phase material. In addition to the higher heat storage capacity, a PCM can also act as a constant temperature heat source; this is because it can gain and release heat while remaining temperature constant in its phase change state. ² Thereby, the latent heat storage is an advantageous technology over sensible heat storage because it provides a better way of storing heat from renewable sources such as the sun and waste heat from industrial processes. The microencapsulated phase change material (MPCM) suspension is a new kind of multiphase thermal fluid fabricated by dispersing PCM microcapsules into carrying fluid, like water, adding one or more additives for long-term stability. High heat storage density and specific heat capacity allow it to be applied in thermal energy systems acting as excellent heat storage material and heat transfer enhancement medium simultaneously. Its excellent heat storage and heat transfer performance have attracted extensive concerns of many researchers.^3–5

A MPCM particle is a capsule with core-shell structure, involving solid–liquid PCM as core and a stable polymer as shell. The MPCM particles can be dispersed into the carry liquid to form a MPCM suspension. The heat transfer process of MPCM suspension is very complicated due to involving multiphase flow and phase change phenomenon. In recent years, extensive investigations have been done by many researches on the heat transfer of the MPCM suspension. In the study of Charunyakorn et al., ⁶ the particle shell thermal resistance was ignored, and the theoretical results of the wall temperature of the heated pipe based on the internal heat source model are 45% lower than the experimental results of Ahuja. ⁷ Zhang and Faghri ⁸ investigated the same case as Charunyakorn et al. ⁶ and Ahuja; ⁷ however, they considered the thermal resistance of the particle shell, so the error is reduced to 34%, 11% lower than Charunyakorn et al. ⁶ Zhang and Faghri’s work indicates that the error is reduced when the thermal resistance of the shell is under consideration in theoretical research. ⁸ Such error reducing process allowed creating an assumption that there could be an unknown thermal resistance between a particle and its surroundings. Such thermal resistance depends on the particles wettability characterized by contact angle between the particles and the carrier fluid. From the wettability point of view, particles’ surface is often modified by adding surfactant to improve the physical/mechanical stability^9,10 and reduce the flow resistance ¹¹ in the application of MPCM suspension. There could be a little residue air or even a minor air gap between the surface of a hydrophobic particle and its surroundings, leading to a “thermal hydrophobic resistance.” Such thermal hydrophobic resistance is analogous to the thermal contact resistance. However, as far as the authors know, no investigations have been reported about the relationship between wettability and suspensions thermal conductivity. This article develops the relationship between wettability and thermal conductivity of MPCM suspension.

Wettability and improvement of particle surface

Wetting is a process in which a fluid is replaced by another fluid on a solid surface. In a liquid–solid system, wetting is the process in which water replace air on a solid surface. ¹² The contact angle, usually expressed as θ, is the angle between the solid–liquid interface, characterizing wettability. It is one of the most direct indicators of wettability (Figure 1). When a liquid drop lies on the solid surface, its shape varies with wettability. The contact angle (θ) of the droplet in the stable or metastable state on the smooth surface can be obtained by Young’s equation ¹³

$${\gamma }_{\mathrm{sg}}={\gamma }_{\mathrm{sl}}+{\gamma }_{\lg }\cos \theta$$

(1)

where ${\gamma }_{\mathrm{sg}}$ , ${\gamma }_{\mathrm{sl}}$ , ${\gamma }_{\lg }$ are the tensions (the surface energy) between the solid–gas, solid–liquid, and the liquid–gas interface.

Figure 1.

Schematic diagram of contact angle and wettability.

The wettability of the particles depends on the interaction energy between the surface unsaturated bond and the liquid molecules and the association energy between the liquid molecules. It can be improved by surfactant modification method using surface modifiers. ¹⁴ In this article, sodium dodecyl sulfate (SDS) and 16 alkyl methyl ammonium chloride (cetyltrimethylammonium bromide (CTAB)) are applied as modifiers to change the wettability, and the modified results were observed with contact angle analyzer (Shanghai Zhongchen Digital Instruments, Ltd, JC2000DS2). SDS is a typical anionic surfactant, while CTAB presents cationic surfactant.

The melamine formaldehyde (MF) sheet was selected to observe the effect of different surfactants on the wettability(contact angle). Figure 2 shows the experimental results. Figure 2 indicates the contact angle between the melamine resin sheet, and water decreases with the increase in the mass fraction of the selected surfactants, SDS and CTAB. The contact angle decreases significantly with the mass fraction of SDS and CTAB when their mass fractions are less than 0.1. The contact angle nearly keeps constant when the mass fractions are greater than 0.1 for CTAB; however, for SDS, the contact angle nearly keeps constant when the mass fractions are greater than 0.1. It can also be seen from Figure 3 that CTAB can change contact angle more significantly than SDS.

Figure 2.

Effect of different surfactants and concentration on contact angle (20°C).

Figure 3.

Effect of the SDS mass fraction on contact angle of different shell materials (20°C).

Modified experiment of different materials

The wall materials of the microcapsules can influence the performance of the microcapsules, such as solubility and permeability. Commonly used shell materials include MF, polyvinyl acetate (PVAc), polystyrene (PS), polyethyl methacrylate (PEMA), polyurethane (PU, PUR), urea-formaldehyde (UF), and polymethyl methacrylate (PMMA). Table 1 presents some common shell materials and their properties.

Table 1.

Thermal and physical properties of the major shell materials.

Literatures	Materials	Density, kg/m3	Specific heat, J kg−1 °C−1	Thermal conductivity, W m−1 s−1	Decomposition temperature, °C	Melting point, °C
Fan et al., 15 Su et al., 16 Li et al., 17 and Zhang et al. 18	Melamine formaldehyde (MF)	1490	1670	0.42	−	−
Zhang et al. 19	Polyvinyl acetate (PVAc)	1190	101.86	0.159	150	−
Zhang et al. 19 and Alkan et al. 20	Polystyrene (PS)	1050	1220	0.111	347	240
Zhang et al. 19	Polyethyl methacrylate (PEMA)	1160	−	−	−	−
Inaba et al. 21	Polyurethane (PU, PUR)	1030	1700	0.14	−	200
Ai et al. 22 and Wang et al.23,24	Urea-formaldehyde (UF)	1490	1675	0.433	−	−
Zhang et al., 19 Zhang and Niu, 25 and Alvarado et al. 26	Polymethyl methacrylate (PMMA)	1190	1470	0.21	−	210

The typical materials, PS, MF, PU, and PMMA, were selected to test the contact angle when adding SDS into the water. Measurement results are as shown in Figure 3.

It can be seen from Figure 3 that the contact angle of the UF is 58°, smallest in all the selected shell materials without the addition of the SDS, indicating a good wettability. The contact angle of the PMMA reached 19.5°, the smallest one of all the selected shell materials at the SDS mass fraction of 0.6, indicating the best wettability. In contrast, the wettability of the PU is the worst, and the contact angle maintained at about 55° at the same SDS mass fraction.

Experimental study on thermal conductivity

Measurement procedure of the thermal conductivity of suspensions

Thermal conductivity of suspensions is measured by means of the transient plane source (TPS) technology. In this technology, the TPS element behaves both as temperature sensor and heat source. Such novel technology offers some advantages, for example, fast and easy experiments, wide range of thermal conductivities (from 0.02 to 200 W/mK), no sample preparation, and flexible sample size. The TPS element consists of an electrical conducting pattern of thin nickel foil (10 μm) in the form of double spiral, which resembles a hot disk embedded in an insulating layer made of Kapton (70 μm) (see Figure 4).

Figure 4.

Schematic diagram of a TPS sensor.

Different concentration MPCM suspensions were prepared, which were stirred thoroughly and ultrasonicated for more than half of an hour. A Kapton-insulated probe was successively dipped into the different suspensions. The diameter of the sensing spiral in the probe was around 2.001 mm, and the Kapton insulation on both sides of the spiral had a thickness of 13 μm. Then, the thermal conductivity was measured by a Hot Disk Thermal Constants Analyzer (Hot Disk, Inc., Uppsala, Sweden). The measurement was run at V = 0.02 V, T = 20°C with switch time at t = 50 s. Each experiment was repeated at least 10 times to calculate the mean value of the experimental data.

Before systematic experiments were performed on MPCM suspensions, the experimental system was tested with deionized water as the working fluid. The results with the deionized water will also serve as the basis for comparison with the results of suspensions (see Table 2). The uncertainty of our measurements is less than ±1.00%.

Table 2.

Thermal conductivity of deionized water.

T (K)	Kexp (W/mK)	Kref (W/mK)	(Kexp−Kref)/Kref(%)
283	0.5705	0.5741	−0.63
293	0.6008	0.5985	0.38
303	0.6231	0.6171	0.97

Results and discussion

In this work, the microcapsule is a commercial product MPCM 28 manufactured by Microtek Laboratories, Inc. (USA). The MPCM suspension was fabricated by dispersing such microcapsules into the carrier fluid. The concentration of such suspension depends on how many microcapsules are dispersed. In this work, a MPCM suspension with 10 wt% microcapsules content was prepared for thermal conductivity measurement. Meanwhile, the required quantity of surfactants SDS or CTAB were added to obtain corresponding contact angles based on the aforementioned experimental achievements in section “Modified experiment of different materials.” The thermal conductivity of MPCM suspension with mass fraction of 10 wt%^27–29 was tested using a thermal conductivity analyzer (Hotdisk 2500s; Hot Disk, Inc.). The testing results are shown in Figures 5 and 6. The theoretical value of suspensions thermal conductivity was also illustrated in figures, which was calculated using the Maxwell formula ³⁰

$${\mathrm{k}}_{\mathrm{b}}={\mathrm{k}}_{\mathrm{f}}\frac{2+{\mathrm{k}}_{\mathrm{p}}/{\mathrm{k}}_{\mathrm{f}}+2\alpha ({\mathrm{k}}_{\mathrm{p}}/{\mathrm{k}}_{\mathrm{f}}-1)}{2+{\mathrm{k}}_{\mathrm{p}}/{\mathrm{k}}_{\mathrm{f}}-\alpha ({\mathrm{k}}_{\mathrm{p}}/{\mathrm{k}}_{\mathrm{f}}-1)}$$

(2)

where ${\mathrm{k}}_{\mathrm{b}}$ is static thermal conductivity of MPCM suspension, ${\mathrm{k}}_{\mathrm{p}}$ is thermal conductivity of MPCM particle, ${\mathrm{k}}_{\mathrm{f}}$ is thermal conductivity of the carrier fluid (because of containing different concentrations of the surfactant, the thermal conductivity is different), and $\alpha$ is the volume fraction of MPCM particles in solid–liquid mixtures.

Figure 5.

Relationship between thermal conductivity and contact angle (MF modified by CTAB, 10 wt%, 20°C).

Figure 6.

Relationship between thermal conductivity and contact angle (MF modified by SDS, 10 wt%, 20°C).

It was found from the two figures (Figures 5 and 6) that thermal conductivity presents a downward trend with the increase in contact angle. In the range of 45°–95°, the measured thermal conductivity is in good agreement with the experimental values with the errors less than 5%. However, when the contact angle is smaller than 45°, the gap between the theoretical and experimental results are greater; the errors are in the range of 5%–12%, indicating that the Maxwell formula is more precise for the thermal conductivity calculation of the MPCM suspension if the contact angles fall into the range of 45°–95°. Comparatively, when the contact angle is smaller than 45°, the experimental results is greater than the Maxwell formula’s theoretical results. This may be because there could be an unknown “thermal hydrophobic resistance” between the exterior surface of the shell and the surrounded carrier fluid. Such unknown “thermal hydrophobic resistance” had been detected during the testing; however, it is not reflected in the Maxwell’s formula; as a result, perhaps the Maxwell formula only can be applied in a certain range of the contact angle. In this case, a correction to the Maxwell’s formula need to be found.

Yu and Choi ³¹ proposed a correction formula based on the Maxwell’s formula, as below

$${\mathrm{k}}_{\mathrm{b}}={\mathrm{k}}_{\mathrm{f}}\frac{2+{\mathrm{k}\prime }_{\mathrm{p}}/{\mathrm{k}}_{\mathrm{f}}+2\alpha ({\mathrm{k}\prime }_{\mathrm{p}}/{\mathrm{k}}_{\mathrm{f}}-1){(1+\beta )}^3}{2+{\mathrm{k}\prime }_{\mathrm{p}}/{\mathrm{k}}_{\mathrm{f}}-\alpha ({\mathrm{k}\prime }_{\mathrm{p}}/{\mathrm{k}}_{\mathrm{f}}-1){(1+\beta )}^3}$$

(3)

The correction coefficient β proposed by Yu and Choi ³¹ is the ratio of the interfacial layer thickness, h_layer, to the particle size, r_p; however, the thickness of the boundary layer led by the surfactants is hard to be obtained; thus, in current work, a correction coefficient A is proposed to modify the Maxwell’s formula, and the modified Maxwell formula is

$${\mathrm{k}}_{\mathrm{b}}={\mathrm{k}}_{\mathrm{f}}\frac{2+{\mathrm{k}}_{\mathrm{p}}/{\mathrm{k}}_{\mathrm{f}}+2\mathrm{A}\mathrm{\alpha }({\mathrm{k}}_{\mathrm{p}}/{\mathrm{k}}_{\mathrm{f}}-1)}{2+{\mathrm{k}}_{\mathrm{p}}/{\mathrm{k}}_{\mathrm{f}}-\mathrm{A}\mathrm{\alpha }({\mathrm{k}}_{\mathrm{p}}/{\mathrm{k}}_{\mathrm{f}}-1)}$$

(4)

The correction coefficient A is associated with the contact angles and can be obtained by

$$\mathrm{A}=\frac{({\mathrm{k}}_{\mathrm{b},\mathrm{t}}-{\mathrm{k}}_{\mathrm{f}})({\mathrm{k}}_{\mathrm{p}}+2{\mathrm{k}}_{\mathrm{f}})}{{\mathrm{k}}_{\mathrm{b},\mathrm{t}}({\mathrm{k}}_{\mathrm{p}}-{\mathrm{k}}_{\mathrm{f}})+2{\mathrm{k}}_{\mathrm{f}}({\mathrm{k}}_{\mathrm{p}}-{\mathrm{k}}_{\mathrm{f}})}$$

(5)

where ${\mathrm{k}}_{\mathrm{b},\mathrm{t}}$ is the measured results of the suspensions bulk dynamic thermal conductivity. As mentioned above, A is related to the contact angle. By data fitting (see Figure 7), such relationship can be given by

$$\mathrm{A}=-0.60957+1.48758\sin \theta -0.77425(\sin \theta {)}^2$$

(6)

Figure 7.

The correction coefficient A as a function of contact angle θ (R² = 0.9611).

Conclusion

The surface wettability of MPCM materials is of great significance to physical stability and heat transfer performance of MPCM suspensions. The experimental investigation indicates that addition of surfactants led to decrease in the contact angle; however, such angle would reach a constant minimum value with surfactants addition, not necessarily zero. For the cell material MF, the modification effect of the SDS on the surface wettability was better than that of the CTAB. It was also found that the hydrophilicity of PMMA was the most easiest to be modified in the selected common MPCM shell materials, and inversely, the hydrophilicity of the PU had a minimum variation. The further experiments indicate that the thermal conductivity of the MPCM suspensions increases with the decrease in the contact angle. In a certain range of contact angle (45°–95°), the Maxwell’s formula can predict its thermal conductivity at an acceptable error. However, when the contact angle is less than 45°, the thermal conductivity calculated by the Maxwell relation had a comparatively big gap with the experimental results. Thereby, based on the experimental results of the thermal conductivity of the MPCM suspensions selecting the UF as shell material, a coefficient A related to contact angles was proposed to enable the Maxwell formula to predict the MPCM suspensions thermal conductivity precisely in a wider range of contact angles. The equation of the coefficient A was obtained by data fitting.