Recent Results of Experiments with Saffman-Taylor Flow

Abstract

In this paper we summarize our recent work on the viscous fingering problem^l,2. In its initially planar form, Saffman-Taylor flow³, viscous fingering represents the simplest of pattern formation problems. Thus the observation of its details provides a valuable opportunity for direct testing of the computer calculations which are now just becoming feasible for pattern formation⁴, Despite its extreme simplicity, Saffman- Taylor flow has much in common with the Mullins-Sekerka instability⁵ which gives rise to dendritic growth in alloys. In this paper we first discuss the formal similarity between the dispersion relations for the Saffman-Taylor and Mullins-Sekerka instabilities, then we set out some of our recent results on the Saffman-Taylor problem¹.