Pseudopotential lattice Boltzmann equation method for two-phase flow: A higher-order Chapmann-Enskog expansion

In this paper, a higher order Chapmann-Enskog expansion technique is applied to pseudopotential lattice Boltzmann equation (LBE), and the contribution of third order error terms to pressure tensor is analyzed in detail. To be consistent with the thermodynamic theory, a force term is introduced to modify the coefficients in the pressure tensor. Some numerical simulations are conducted to validate the LBE, and the results show that the predictions of the present LBE agree well with the analytical solution and other predictions.

Figure 1

The coexistence curves predicted by LBE. (a) The comparison of the Guo et al. force scheme and the present LBE with $a=1$. (b) The prediction of the present LBE with different values of $a$.

Figure 2

The comparison of the minimum reduced temperature against with $\tau$ by Guo et al. scheme and the present LBE.

Figure 3

$\delta p$ vs 1/R predicted by LBE. (a) The effect of $\gamma$ with $a=1$; (b) the effect of $a$ with $\gamma =0.5$.

Figure 4

Flow pattern for $a=0.25,1$ with $\gamma =0.5$. (a) $a=0.25,T/Tc=0.6$; (b) $a=0.25,T/Tc=0.9$; (c) $a=1,T/Tc=0.6$; (d) $a=1,T/Tc=0.9$.

Figure 5

The magnitude of spurious currents with $a=0.25,0.5$, and 1. (a) The effect of density ratio; (b) the effect of parameter $\gamma$.

Figure 6

Evolution of the instantaneous density field for droplet splashing on a thin film at Re $=500, a=0.25$, and $\gamma =-1$.

Figure 7

Evolution of the instantaneous density field for droplet splashing on a thin film at Re $=500, a=0.5$, and $\gamma =-1$.

Figure 8

The snapshot of the density contour for $a=0.125$ and $\gamma =-0.5$ at Re $=500$, and $T_r=1.75$ with three different mesh sizes: $500\times 400, 1000\times 800$, and $1500\times 1200$.

Figure 9

The prediction of spread radius for $a=0.25$ and 0.5 at Re $=200,500$ and $\gamma =-1$.