Directional Growth in Viscous Fingering
During the past few years there has been a renewed interest in the Saffman-Taylor instability (Saffman and Taylor (1958)), as this instability between strongly viscosity-contrasted fluids gives rise to shape selection processes. Its dynamics is very similar to that of another pattern forming instability, the Mullins-Sekerka instability, occurring during the free growth of a crystal in an undercooled liquid (Mullins and Sekerka (1964)). The theoretical analogy between the growth of viscous fingers in Hele-Shaw cells and the growth of crystalline dendrites is now well-known (e.g. Langer (1988); Kessler and Levine (1988 a) for a review) and the similarity between the two phenomena has been demonstrated experimentally (Rabaud et al. (1988)). Both processes are free growths in which the non linear evolution of the pattern defines the field in which it keeps growing.
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