Accession Number : ADA130548
Title : Fingers in a Hele-Shaw Cell with Surface Tension.
Descriptive Note : Technical summary rept.,
Corporate Author : WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
Personal Author(s) : Vanden-Broeck,Jean-Marc
PDF Url : ADA130548
Report Date : May 1983
Pagination or Media Count : 13
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.
Descriptors : *Mathematical models, *Numerical analysis, *Two dimensional flow, Steady flow, Fingers, Plates, Potential flow, Interfaces, Nonlinear differential equations, Computations, Solutions(General)
Subject Categories : Numerical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE