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Self-similar flows of multi-phase immiscible fluids

Published online by Cambridge University Press:  26 February 2001

A. OZTEKIN ,
B. R. SEYMOUR  and
E. VARLEY
A. OZTEKIN
Affiliation:
Department of Mechanical Engineering, Lehigh University, Bethlehem, PA 18017, USA
B. R. SEYMOUR
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2, Canada
E. VARLEY
Affiliation:
Department of Mechanical Engineering, Lehigh University, Bethlehem, PA 18017, USA
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Abstract

Exact analytical representations are obtained describing self-similar unsteady flows of multi-phase immiscible fluids in the vicinity of non-circular, but constant strength, fronts. It is assumed that Darcy's law holds for each phase and that the mobilities are known functions of the saturations. Equivalent representations are obtained for Hele-Shaw cell flows that are produced when a viscous fluid is injected into a region containing some other viscous fluid. The fluids may be Newtonian fluids or non-Newtonian fluids for which the coefficients of viscosity depend on the shear stress. Even though the flows are unsteady and two dimensional, the representations are obtained by using hodograph techniques.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 11 , Issue 6 , December 2000 , pp. 529 - 559
Copyright
2000 Cambridge University Press

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