Steady states for viscous fingers with anisotropic surface tension

摘要

Pattern selection is considered for the case of viscous fingering in rectangular Hele-Shaw geometry in the presence of anisotropic surface tension, using solvability analysis and a boundary-integral method. We find that anisotropy introduced as a sinusoidal perturbation with a fourfold symmetry is irrelevant for small driving velocities and the usual steady-state finger width in the absence of the anisotropy is obtained. For sufficiently large driving velocities a new steady-state width is selected when the anisotropy makes the local interfacial tension a maximum at the finger tip. This is in agreement with recent experimental observations.