Fingers in a Hele-Shaw Cell with Surface Tension.
Abstract
Two dimensional flow in a porous medium may be studied by using an analogue proposed by Hele-Shaw. The analogue is based on the fact that the mean velocity in a two dimensional porous medium and the velocity of the flow between two parallel plates satisfy the same equations. In the present paper the author considers the steady two dimensional flow produced by a finger advancing between the two plates. The analogous porous medium flow occurs in oil recovery. This problem was first considered by Saffman and Taylor. They obtained an exact solution for zero surface tension. McLean and Saffman generalized the result of Saffman and Taylor by including the effect of surface tension at the interface. They solved the problem numerically and obtained one family of solutions. In the present paper the problem is solved by a different numerical scheme. The results suggest the existence of a countable number of solutions for non-zero surface tension. This infinite set of solutions contains the solution previously obtained by McLean and Saffman.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1983
- Accession Number
- ADA130548
Entities
People
- Jean-marc Vanden-broeck
Organizations
- University of Wisconsin–Madison