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

A. P. Aldushin*, B. J. Matkowsky

*Corresponding author for this work

Research output: Contribution to journalArticle

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)57-62
Number of pages6
JournalApplied Mathematics Letters
Volume11
Issue number6
DOIs
StatePublished - Nov 1998

Keywords

  • Bubble interface
  • Finger
  • Front
  • Saffman-Taylor

ASJC Scopus subject areas

  • Applied Mathematics

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