The threshold of the instability in miscible displacements in a Hele–Shaw cell at high rates

Abstract

For sufficiently large viscosity ratios and injection rates, miscible displacements in a vertical Hele–Shaw cell at high rates become unstable, leading to three-dimensional (3D) fingering patterns. Below the instability threshold, the base state is 2D in the form of a “tongue” of constant thickness. We apply the long wave Saffman–Taylor stability analysis to find an expression for the threshold of instability as a function of the viscosity ratio and the injection rate. The results are in agreement with the experimental data.