We find the self-similar scaling behavior x{~}t3/5,y{~}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 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.
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Almgren et al. (1993) studied this question.
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