Fingering with miscible fluids in a Hele Shaw cell

Abstract

Unstable, two‐fluid miscible displacements in a Hele Shaw cell of plate spacing b are analyzed by considering viscous dissipation of energy. A perturbation theory is presented that predicts the wavelength of fingers, λ, as λ≊4b. Experiments with a circular Hele Shaw cell are shown to support this result. In a porous medium, the analogous fingers are demonstrated to be the size of a pore, which is much larger than the corresponding fingers in the analogous Hele Shaw cell. These results provide the lower limits of finger wavelength for the theories of Saffman and Taylor, and Chuoke, van Meurs, and van der Poel.