Fingering in 2D Parallel Viscous Flow

Abstract

We study the displacement of miscible fluids of different viscosities (viscosity ratio AI) between two parallel plates, using the BGK lattice gas method. At high Peclet numbers, a symmetric interface develops in the gap between the plates. Above M +J 10, the interface becomes a well-defined finger, the reduced width of which tends to A~n = 0.56 at large AI. Assuming that a miscible displacement at high Peclet numbers is equivalent to an immiscible displacement at high capillary numbers, we extend the calculations of Reinelt & Saffman for immiscible fluids, and find the analytical shape of the finger. The result is compared to the celebrated Saffman-Taylor finger.