Self-similar flows of multi-phase immiscible fluids

Exact analytical representations are obtained describing self-similar unste ady flows of multiphase immiscible fluids in the vicinity of non-circular, but constant strength, fronts. It is assumed that Darcy's law holds for eac h phase and that the mobilities are known functions of the saturations. Equ ivalent representations are obtained for Hele-Shaw cell flows that are prod uced when a viscous fluid is injected into a region containing some other v iscous fluid. The fluids may be Newtonian fluids or non-Newtonian fluids fo r which the coefficients of viscosity depend on the shear stress. Even thou gh the flows are unsteady and two dimensional, the representations are obta ined by using hodograph techniques.