Deposition of colloidal particles in a microchannel at elevated temperatures

Abstract

This work reports an experimental study of the thermal effect on the deposition of microparticles onto a solid surface in a microfluidic system, which allows a precise control of the solution temperature and enables the real-time monitoring of the deposition kinetics at the increased temperature. The static particle deposition rate (Sherwood number) has been measured over a range of temperatures between 20 and 70 °C. It is found that the Sherwood number is monotonically increased up to 265 %, with the solution temperature within the test range. A model including the Derjaguin–Landau–Verwey–Overbeek theory-based colloidal surface forces and gravity force is employed, taking into account temperature effects, to qualitatively interpret the experimental findings. The model shows that, by increasing the solution temperature, the attraction energy (van der Waals force) between the particles and the solid surface is increased while the repulsive energy (electric double layer force) is decreased. These findings demonstrate the importance of thermal effects in various thermally driven deposition processes, such as the fouling of bacteria and milk proteins in microscale milk pasteurization units.

Appendix

It is known that the process of particle deposition from liquid media onto a solid surface consists of two sequential steps: transport and attachment. Gravity can influence the transport of particles from bulk suspension to the surface, while the mass diffusion of particles is another important factor in the absence of hydrodynamic flow as the case considered in this study. The final attachment onto surfaces (deposition) is mainly determined by colloidal forces (van der Waals force and electric double layer force) in the near-wall region.

In order to confirm whether gravity plays a dominant role or not in the enhanced particle deposition at elevated temperatures, we designed and conducted another set of experiments for the particle deposition on the top surface (upper wall) of the deposition channel. As shown in Fig. 10a, the experimental setup is similar to the one presented in the main text, but a new microchip consists of a smooth top plate (PMMA) and a grooved bottom plate (PMMA) with the deposition channel and heating channels as illustrated by Fig. 10b. Besides, an upright microscope (Zeiss) is used to facilitate the observation of particle deposition on the top surface. The tested sample contains the same particle volumetric number concentration (5.6 × 10⁶/ml) as that in the previous experiments in a 5 × 10⁻⁵ M NaCl electrolyte solution. The geometric dimensions of the channels and other experimental conditions and procedures are maintained as the same as those in previous experiments of the particle deposition onto the bottom surface presented in the main text.

Fig. 10

a Layout of the experimental setup, b detailed illustration of the two heating channels and the testing middle channel for observing particle deposition onto the top surface of the channel

Figure 11 shows that the dimensionless average particle deposition flux onto the top surface, Sherwood number, is monotonically increased with increasing the solution temperature. The Sherwood number is increased about 8 times, from 0.00022 to 0.00194, when the temperature of sample solution is increased from room temperature to 339.25 K. In Fig. 11, the dotted straight line presents the maximum possible deposition rate onto the top surface at various elevated temperatures if the increased gravity plays a dominant role in the deposition process. Since the gravity points downward, particles would be pulled away from the top surface and thus be prevented from deposition onto the top surface. However, the measured particle deposition rates versus elevated temperatures are much higher than such assumed maximum value. This suggests that the increased particle deposition at elevated temperatures is mainly dominated by the colloidal surfaces instead of gravity force. More specifically, the energy barrier and the competition between the electric double layer and the van der Waals force interactions significantly affect the deposition rate on the top surface. As we proposed in the main text, with increasing solution temperature the attractive potential (van der Walls interaction) is increased while the repulsive potential (electric double layer interaction) is reduced. Consequently, the energy barrier is decreased by increasing solution temperature. As a result, particles in the near-wall region have higher chances to overcome the barrier and deposit onto the surface.

Fig. 11

Dimensionless deposition rate (Sherwood number) onto the top surface of the channel at five different solution temperatures, 297.25, 317.35, 324.85, 331.85 and 339.25 K. The dotted line indicates the maximum deposition rate at elevated temperatures if the increased gravity plays a dominant role in the deposition process

Therefore, the experimental results presented in both the main text and the appendix suggest that gravity may affect the particle transport process, but it is the colloidal forces that determine the deposition at the attachment step. The enhanced particle deposition on the bottom wall at elevated temperature reported in this study is mainly attributed to the variation of colloidal forces in the near-wall region while the increased gravity facilitates the transport of particles from bulk suspension to the surface.

Furthermore, we plotted the electric double layer (EDL) interaction potential, the van der Waals (vdW) interaction potential and the gravity potential versus particle–surface separation distance by using the modified DLVO-based model with consideration of gravity at a solution temperature of 343.15 K, and the results are shown in Fig. 12. It can be seen clearly that the gravity effect is considerable at long range where the transport of particles occurs, but it becomes negligible when particles approach to the vicinity of the surface where the attachment happens.

Fig. 12

Dimensionless EDL, vdW and gravity interaction potential as a function of separation distance (T = 343.15 K). Curves are obtained with temperature-dependent water density, Hamaker constant, zeta potential and thickness of electric double layer. Inset shows the gravity plays a role at long range but becomes negligible in the near-wall region

In addition, the following provides a scaling analysis for the particle thermal energy versus the applied thermal energy. Given a particle, both the particle thermal energy, E _particle , and the applied thermal energy, E _applied , can be calculated from Eqs. (22) and (23), respectively.

$$E_{particle} = N_{p} {\kern 1pt} kT$$

(22)

$$E_{applied} = m_{p} c_{p} (T - T_{0} )$$

(23)

where N _p is the number of molecules contained in the particle, k is the Boltzmann constant (1.38 × 10⁻²³ J/K), T is the solution temperature, T ₀ is the reference temperature (293.15 K), and c _p is the specific heat of polystyrene particle, and its value is about 1.3 J/g·k, and m _p is the mass of particle. Furthermore, the number of molecules contained in one particle can be obtained from

$$N_{p} = {\kern 1pt} \frac{{m_{p} }}{{M_{w} }} \cdot N_{A}$$

(24)

where N _A is the Avogadro constant, M _w is the molecular weight of polystyrene particle and its value is 10,400 g.

Therefore, the ratio of E _applied to E _particle is given by

$$E_{applied} /E_{particle} = \frac{{c_{p} M_{w} \left( {T - T_{0} } \right)}}{{{\kern 1pt} N_{A} kT}}$$

(25)

Table 2 summarizes the estimated ratio of the applied thermal energy to the particle thermal energy at various elevated temperatures, and the results show that the applied energy by heating is significant compared to the particle thermal energy.

Table 2 Ratio of applied thermal energy to particle thermal energy at different temperatures (T ₀ = 293.15 K)