Three-Layer Hele-Shaw Displacement With an Intermediate Non-Newtonian Fluid

Abstract

We study the displacement of two Stokes immiscible fluids in a porous medium, approximated by the Hele-Shaw horizontal model. An intermediate non-Newtonian polymer-solute, whose viscosity is depending on the velocity, is considered between the initial fluids. The linear stability problem of this three-layer displacement does not make sense. If the intermediate viscosity depends on velocity and on the polymer concentration, we can obtain a minimization of the Saffman-Taylor instability.