Saffman-Taylor finger width at low interfacial tension

Abstract

High-accuracy numerical results are shown which go against current conjecture that dimensionless finger width \ensuremath{\lambda} in the Saffman-Taylor problem is a monotonically increasing function of dimensionless surface tension \ensuremath{\tau}, asymptotically approaching 1/2 as \ensuremath{\tau}\ensuremath{\rightarrow}0. Specifically, quasi steady-state fingers are shown for finite \ensuremath{\tau} with \ensuremath{\lambda} significantly below 0.5. These solutions are consistent with published experimental results obtained in a Hele-Shaw cell, indicating that the Saffman-Taylor equations are sufficient to explain this phenomenon.