NON-NEWTONIAN HELE-SHAW FLOW AND THE SAFFMAN-TAYLOR INSTABILITY

We explore the Saffman-Taylor instability of a gas bubble expanding in to a shear thinning liquid in a radial Hele-Shaw cell. Using Darcy's l aw generalized for non-Newtonian fluids, we perform simulations of the full dynamical problem. The simulations show that shear thinning sign ificantly influences the developing interfacial patterns. Shear thinni ng can suppress tip splitting, and produce fingers which oscillate dur ing growth and shed side branches. Emergent length scales show reasona ble agreement with a general linear stability analysis.