We study the Saffman-Taylor instability of a non-Newtonian fluid in a Hele-Shaw cell. Using a fluid model with shear-rate dependent viscosity, we derive a Darcy’s law whose viscosity depends upon the squared pressure gradient. This yields a natural, nonlinear boundary value problem for the pressure. A model proposed recently by Bonn et al. @Phys. Rev. Lett. 75, 2132 ~1995!# follows from this mo...

We consider the problem of displacement processes in a three-layer fluid in a Hele-Shaw cell modeling enhanced oil recovery processes by polymer flooding. The middle layer sandwiched between water and oil contains polymer-thickened-water. We provide lower bounds on the length of the intermediate layer and on the amount of polymer in the middle layer for stabilizing the leading front to a specif...

We consider a setup in a Hele-Shaw cell where a fluid of constant viscosity l occupying a near-half-plane pushes a fluid of constant viscosity l occupying a layer of length L which in turn pushes another fluid of constant viscosity r occupying the right half-plane. The fluid upstream has a velocity U. Careful analysis of the dispersion relation arising from linear stability of the three-layer H...