Immiscible displacement in a channel: simulations of fingering in two dimensions

In this paper, we use a lattice Boltzmann (LB) multiphase/multicomponent model to study the flow of two immiscible fluids with different viscosities. The approach is first validated 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 studying 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 slip distance of the contact lines decrease, while the finger length increases. With the decrease of the wettability of the displacing fluid, the finger length and its change rate with time increase while the slip distance of the contact lines and its change rate with time decrease, and the minimum capillary number to form a stable finger decreases. Hence the finger growth is enhanced when the displacing fluid is nonwetting to the wall and otherwise suppressed. An indented part near the beginning of the fingers is clearly observed when a wetting fluid is displacing a nonwetting one. The finger width, however remains nearly unchanged when the wettability of the fluids changes.