SCALING BEHAVIOR IN ANISOTROPIC HELE-SHAW FLOW

We find the self-similar scaling behavior x is similar to t3/5, y is similar to t2/5 for the arms which form in radial Hele-Shaw flow with anisotropic surface energy, where x is the longitudinal and y is the transverse coordinate of each primary finger. We first observe this by direct numerical simulation using a boundary-integral method. Then we analytically derive the scaling law and the full asymptotic shape, by combining a simple boundary-layer analysis with previous results on velocity selection.