Stability of finger patterns in Hele-Shaw cells

Abstract

The finger of fluid formed during the displacement of a more viscous fluid is a well-known example of nonequilibrium pattern formation. Previous efforts claimed that the steady-state solution discovered by Saffman and Taylor was linearly unstable, in contradiction with experimental observations. In this work, we present a new stability analysis which demonstrates stability and resolves the aforementioned conflict. We describe how this lends support to a new paradigm governing interfacial pattern-forming systems, that of ‘‘microscopic solvability.’’