Surface tension and dynamics of fingering patterns

Abstract

We study the minimal class of exact solutions of the Saffman-Taylor problem with zero surface tension, which contains the physical fixed points of the regularized (non-zero surface tension) problem. New fixed points are found and the basin of attraction of the Saffman-Taylor finger is determined within that class. Specific features of the physics of finger competition are identified and quantitatively defined, which are absent in the zero surface tension case. This has dramatic consequences for the long-time asymptotics, revealing a fundamental role of surface tension in the dynamics of the problem. A multifinger extension of microscopic solvability theory is proposed to elucidate the interplay between finger widths, screening and surface tension.

4 pages, REVTEX, 1 postscript figures included

References in corpus (1)

• Selection of the Saffman-Taylor Finger Width in the Absence of Surface Tension: an Exact Result

Cited by in corpus (5)

• Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach
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• Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study
• Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario
• Two-finger selection theory in the Saffman-Taylor problem