An Experimental Study of the Saffman Taylor Instability

Abstract

When a gas is pushed into a viscous fluid through a Hele-Shaw cell, one observes, after a long transient, the formation of a finger which propagates steadily along the channel. This simple situation defines the Saffman Taylor¹ problem. In spite of its simplicity, the limiting sizes of those fingers at large velocities and their stability has not been understood for a long time. A particularly striking fact observed in the experiments is that fingers occupy about one-half of the channel width at large velocities. In the model of Saffman and Taylor¹, where surface tension is neglected, all finger sizes are allowed. Moreover, fingers of size 1/2 are found linearly unstable, which is also in direct conflict with experiment. The problem was then to understand how surface tension acts to select finger sizes and to ensure stability.