Selection in the Saffman-Taylor finger problem and the Taylor-Saffman bubble problem without surface tension

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Abstract

We consider the Saffman-Taylor problem describing the displacement of one fluid by another having a smaller viscosity, in a porous medium or in a Hele-Shaw configuration, and the Taylor-Saffman problem of a bubble moving in a channel containing moving fluid. Each problem is known to possess a family of solutions, the former corresponding to propagating fingers and the latter to propagating bubbles, with each member characterized by its own velocity and each occupying a different fraction of the porous channel through which it propagates. To select the correct member of the family of solutions, the conventional approach has been to add surface tension σ and then take the limit σ → 0. We propose a selection criterion that does not rely on surface tension arguments. © 1998 Elsevier Science Ltd. All rights reserved.

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Aldushin, A. P., & Matkowsky, B. J. (1998). Selection in the Saffman-Taylor finger problem and the Taylor-Saffman bubble problem without surface tension. Applied Mathematics Letters, 11(6), 57–62. https://doi.org/10.1016/S0893-9659(98)00103-7

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