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

✍ Scribed by A.P. Aldushin; B.J. Matkowsky

• Book ID: 104350121
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 424 KB
• Volume: 11
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(98)00103-7

✦ Synopsis

we consider the %&man-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-S&man 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 (T and then take the limit u 4 0. We propose a selection criterion that does not rely on surface tension arguments.