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oai:recercat.cat:2445/187702025-11-21T05:50:27Zcom_2072_1057col_2072_478823col_2072_478917

00925njm 22002777a 4500 dc Pauné i Xuriguera, Eduard author Magdaleno Escar, Francesc Xavier author Casademunt i Viader, Jaume author 2011-07-07T12:52:17Z 2011-07-07T12:52:17Z 2002 A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection. Dinàmica de fluids Fluid dynamics Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario