Saffman-Taylor fingers with adverse anisotropic surface tension.

Abstract

Viscous fingering in a linear channel is investigated analytically in the presence of adverse anisotropy, i.e., when the directions of easy growth are at angle \ensuremath{\pi}/m away from the direction of the cell axis because of the anisotropy of the surface tension. The study is made in the limit of small surface tension and for a finger width which is around one-half of the cell width. The analytical investigation reveals the existence of an exceptional solution for the Saffman-Taylor finger which does not belong to the standard manifold. The origin of this exceptional solution is clarified by a WKB analysis of the problem. This finger has a width which grows with velocity in contrast with the standard situation. This is in agreement with experimental observation for the stable fingers and for the averaged unstable ones.