### 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 language | English (US) |
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Pages (from-to) | 57-62 |

Number of pages | 6 |

Journal | Applied Mathematics Letters |

Volume | 11 |

Issue number | 6 |

DOIs | |

State | Published - Nov 1998 |

### Keywords

- Bubble interface
- Finger
- Front
- Saffman-Taylor

### ASJC Scopus subject areas

- Applied Mathematics

## Fingerprint Dive into the research topics of 'Selection in the Saffman-Taylor finger problem and the Taylor-Saffman bubble problem without surface tension'. Together they form a unique fingerprint.

## Cite this

*Applied Mathematics Letters*,

*11*(6), 57-62. https://doi.org/10.1016/S0893-9659(98)00103-7