Tricoupled hybrid lattice Boltzmann model for nonisothermal drying of colloidal suspensions in micropore structures

A tricoupled hybrid lattice Boltzmann model (LBM) is developed to simulate colloidal liquid evaporation and colloidal particle deposition during the nonisothermal drying of colloidal suspensions in micropore structures. An entropic multiple-relaxation-time multirange pseudopotential two-phase LBM for isothermal interfacial flow is first coupled to an extended temperature equation for simulating nonisothermal liquid drying. Then the coupled model is further coupled with a modified convection diffusion equation to consider the nonisothermal drying of colloidal suspensions. Two drying examples are considered. First, drying of colloidal suspensions in a two-pillar micropore structure is simulated in two dimensions (2D), and the final configuration of colloidal particles is compared with the experimental one. Good agreement is observed. Second, at the temperature of 343.15 K ($70{}^{\circ }\mathrm{C}$), drying of colloidal suspensions in a complex spiral-shaped micropore structure containing 220 pillars is simulated (also in 2D). The drying pattern follows the designed spiral shape due to capillary pumping, i.e., transport of the liquid from larger pores to smaller ones by capillary pressure difference. Since the colloidal particles are passively carried with liquid, they accumulate at the small menisci as drying proceeds. As liquid evaporates at the small menisci, colloidal particles are deposited, eventually forming solid structures between the pillars (primarily), and at the base of the pillars (secondarily). As a result, the particle deposition conforms to the spiral route. Qualitatively, the simulated liquid and particle configurations agree well with the experimental ones during the entire drying process. Quantitatively, the model demonstrates that the evaporation rate and the particle accumulation rate slowly decrease during drying, similar to what is seen in the experimental results, which is due to the reduction of the liquid-vapor interfacial area. In conclusion, the hybrid model shows the capability and accuracy for simulating nonisothermal drying of colloidal suspensions in a complex micropore structure both qualitatively and quantitatively, as it includes all the required physics and captures all the complex features observed experimentally. Such a tricoupled LBM has a high potential to become an efficient numerical tool for further investigation of real and complex engineering problems incorporating drying of colloidal suspensions in porous media.

Figure 1

The relation between local particle concentration $\varphi$ and corresponding interaction potential $g\left(\varphi \right)$.

Figure 2

Simulation domain and setup of the two-pillar system (all dimensions are in lattice units).

Figure 3

Illustration of implementing no flux boundary condition at solid-liquid and solid-vapor interface. Solid purple line and dashed green line indicate first and second layer of solid object, respectively.

Figure 4

Comparison of bridge profiles (light gray) between experiment (a) from Ref. [6] and simulations of pillars (dark gray) with size $16\times 16$ (b), $12\times 12$ (c), and $8\times 8$ (d) $\mathrm{lattice}{\mathrm{s}}^2$, respectively.

Figure 5

Illustration of the spiral-shaped micropore structure (SMS) with dimensions: (a) side view; (b) top view. The red dashed-dotted array denotes the receding path of the main liquid-vapor meniscus.

Figure 6

Microscopic image of the experiment showing particle accumulation and deposition (bright white color) at the rough edges of SMS, while the solution is grayish. The experimental area that we considered is within the dashed blue line. This state is considered the initial state in the simulation.

Figure 7

Comparison of liquid configuration (light gray color) and particle accumulation and deposition (dark red color) at different nondimensional times during drying of colloidal suspensions in SMS. Left: experiment. Right: simulation.

Figure 8

Internal flow of colloidal liquid (capillary pumping) from large meniscus to small ones at nondimensional time $t_N=22.20$, driven by capillary pressure difference. The streamlines outside the colloid suspension indicate evaporated vapor flow. The contour represents the velocity magnitude of internal flow.

Figure 9

Comparison of normalized colloidal liquid mass between experiment (red solid square) and hybrid LBM simulation (green solid line) during drying of colloidal suspensions in SMS.

Figure 10

Comparison of colloidal liquid evaporation rate between experiment (red solid square) and hybrid LBM simulation (green solid line) during drying of colloidal suspensions in SMS.

Figure 11

Comparison of colloidal particle deposition area between experiment (red solid square) and hybrid LBM simulation (green solid line) during drying of colloidal suspensions in SMS.