Lattice Boltzmann simulation of viscous fingering in a channel

In this paper, we use a lattice Boltzmann (LB) multiphase model to study the flow of binary fluid with different component viscosities. We first validate the approach for a two-dimensional layered flow. The velocity profiles and the relative permeability coefficients are compared with the analytic results. We then apply this method to study viscous fingering in a two-dimensional channel where one fluid is displaced by another. The effects of viscosity ratio, capillary number, and wettability are investigated. The simulation results show that with the increase of the viscosity ratio or capillary number, both the finger width and the slipping distance of the contact lines decrease, while the finger length increases, indicating that the finger structure is truly due to viscous fingering. We also find that the finger growth is enhanced when the displacing fluid is nonwetting to the wall and that the fingering is otherwise suppressed. An indented part near the beginning of the fingers is clearly observed when a wetting fluid is displacing a nonwetting one.