The Saffman‐Taylor Fingers in the Limit of Very Large Surface Tension

Abstract

In long rectangular Hele‐Shaw cells the Saffman‐Taylor instability generates steady advancing fingers of the less viscous fluid. The structure of these fingers is determined by the solution of a system of nonlinear integrodifferential equations for two unknown functions of the curvilinear coordinate defined along the boundary of the finger. The surface tension appears in these equations through a dimensionless coefficient called k. I analyze the solution when this coefficient tends to infinity. In this limit, the inviscid fluid tends to fill almost completely the cell, except for a thin layer of viscous fluid left on the sides of thickness of order k−½.