SAFFMAN-TAYLOR FINGERS WITH ADVERSE ANISOTROPIC SURFACE-TENSION

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 pi/m away from the direction of the cell axis beca use 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 whi ch does not belong to the standard manifold. The origin of this except ional solution is clarified by a WKB analysis of the problem. This fin ger has a width which grows with velocity in contrast with the standar d situation. This is in agreement with experimental observation for th e stable fingers and for the averaged unstable ones.