Surface tension and dynamics of fingering patterns

Details Surface tension and dynamics of fingering patterns Surface tension and dynamics of fingering patterns

1997-07-25

arxiv.org/abs/patt-sol/9707005v1

Nonlinear Sciences

Pattern Formation and Solitons

4 pages, REVTEX, 1 postscript figures included

Scientific paper

10.1103/PhysRevE.57.R3707

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.

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