Fingering in 2D Parallel Viscous Flow

Overview & Synopsis

We study the displacement of miscible fluids of different viscosities (viscosity ratio M) 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 ∼10, the interface becomes a well–defined finger, the reduced width of which tends to λ∞= 0.56 at large M. 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.