Scaling behavior in anisotropic Hele-Shaw flow

Abstract

We find the self-similar scaling behavior x∼${\mathit{t}}^{3/5}$,y∼${\mathit{t}}^{2/5}$ 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 obseve 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.