SURFACE-TENSION AND DYNAMICS OF FINGERING PATTERNS

We study the minimal class of exact solutions of the Saffman-Taylor pr oblem with zero surface tension, which contains the physical fixed poi nts of the regularized (nonzero surface tension) problem. New fixed po ints are found and the basin of attraction of the Saffman-Taylor finge r is determined within that class. Specific features of the physics of finger competition are identified and quantitatively defined, which a re absent in the zero surface tension case. This has dramatic conseque nces for the long-time asymptotics, revealing a fundamental role of su rface tension in the dynamics of the problem. A multifinger extension of microscopic solvability theory is proposed to elucidate the interpl ay between finger widths, screening and surface tension.