Fingering in 2D Parallel Viscous Flow

(Received 15 July 1996, revised 16 October 1996, received in final form 30 April 1997, accepted 14 May 1997)

Abstract
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 , the interface becomes a well-defined finger, the reduced width of which tends to 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.