Phase-field-based lattice Boltzmann model for liquid-gas-solid flow

Based on phase-field theory, we develop a lattice Boltzmann (LB) model for liquid-gas-solid flow from multiphase and particle dynamics algorithms. A modified bounce-back method is developed for the velocity-based LB approach. A curved boundary treatment with second-order accuracy based on velocity interpolation is developed. We propose a predictor-corrector scheme algorithm for specifying the three-phase contact angle on curved boundaries within the framework of structured Cartesian grids. In order to make the algorithm more stable, we combine the implicit particle velocity update scheme and the Galilean invariant momentum exchange method. The proposed method is validated through several single- and multicomponent fluid test cases. It was found the surface tension force associated with the interface acting on the solid structures can be captured. We simulate the sinking of a circular cylinder due to gravity, the numerical results agree well with the experimental data. Finally, we apply the method to the self-assembly process of multiple floating cylinders on water surface.

Figure 1

Schematic diagrams of the velocity interpolation rules: (a) $0\le q<1/2$, (b) $1/2\le q<1$.

Figure 2

Schematic depicting the interpolation to obtain the unknown phase-field value ${\varphi }_{i,j}$ of two schemes. (a) the common method, (b) the alternative scheme when the commom method fails.

Figure 3

The schematic diagram for a circular particle settling under gravity in an infinite channel.

Figure 4

Comparison of the vertical velocities of the particle during sedimentation for different particle densities. The number in the blanket of each case is the particle Reynolds number.

Figure 5

The contact angles on a stationary cylinder under two different wetting conditions: (a) $\theta ={60}^{\circ }$, (b) $\theta ={120}^{\circ }$.

Figure 6

Variations of the vertical capillary force of a stationary circular cylinder.

Figure 7

Geometry of a cylinder lying horizontally at the interface between water and air.

Figure 8

Snapshots of sinking motion for a cylinder at different times. In each subfigure the experimental data [39] (left) are placed side by side with the numerical results (right).

Figure 9

The position of the contact line as a function of nondimensional time $t$.

Figure 10

The cylinder's center position as a function of nondimensional time t.

Figure 11

Self-assembly movement of cylinders A, B, and C at different times $t=0.18$, $t=1.00$, $t=2.70$, and $t=3.25$.

Figure 12

The horizontal position of the cylinders vs time.

Figure 13

The vertical position of the cylinders vs time.