Interpolation for the lattice-Boltzmann method to simulate colloid transport in porous media

The lattice-Boltzmann method is convenient for simulating flow fields in porous media. However, due to its lattice characteristics, the velocity near a solid surface is not accurate, which results in significant errors when simulating colloid transport in porous media. Based on the general properties of a flow field close to a solid surface, we propose an alternative velocity interpolation method in which the velocity at a solid surface is strictly zero. Numerical simulation results show that the proposed method can give more accurate results than the usual bilinear interpolation. In addition, we use this method to simulate the contact efficiency of colloids in porous media and obtain a new power-law form of the contact efficiency.

Figure 1

Schematic diagram of lattice and solid boundary. The black circle represents a colloidal particle; the blue part represents a part of a spherical collector (grain).

Figure 2

Comparison of contact efficiency $\eta$ obtained from SDI and bilinear interpolation method for a single collector. $d/\mathrm{\Delta }x$ represents the ratio of collector diameter to node spacing.

Figure 3

Schematic diagram of porous media generated by the sedimentation-producing method. This porous medium is periodic, and water flows along the $z$ direction.

Figure 4

Simulated values of relative concentration $C\left(z\right)/C\left(0\right)$ along the direction of the water flow at $v={10}^{-4}\text{m/s}$. The linear relationship between $log\left(C\right(z)/C(0\left)\right)$ and $z$ indicates that the contact efficiency $\eta$ in Eq. (8) is a constant.

Figure 5

Comparison of contact efficiency $\eta$ obtained by SDI and bilinear interpolation for the colloid transport in porous media consisting of many collectors.

Figure 6

Simulated values (scatter markers) of contact efficiency $\eta$ of colloids transported in porous media. Dotted lines are fitted according to Eq. (9), and solid lines are the fitting results of the new power-law equation, Eq. (11).