Saffman-Taylor fingers with anisotropic surface tension.

Abstract

We present complete results for the selected width of Saffman-Taylor fingers at large velocities with and without anisotropy in the surface tension. We solve a nonlinear eigenvalue problem to obtain the scaling laws and constants relating finger width, surface tension, and anisotropy. Excellent agreement with McLean's numerical solution of the full isotropic problem is obtained. The effect of anisotropy is to allow all finger widths. We discuss the relevance of these results to recent experimental findings.