L. Kondic, Michael J. Shelley and Peter Palffy-Muhoray, Non-Newtonian Hele-Shaw flow and the Saffman-Taylor instability, Phys. Rev. Lett. 80, 1433, 1998.

Abstract:

We explore the Saffman-Taylor instability of an air bubble expanding into a shear thinning liquid in a radial Hele-Shaw cell. Using Darcy's law generalized for non-Newtonian fluids (Phys. Rev. E {\bf 54}, 4536, 1996), we perform simulations of the full dynamical problem. The simulations show that shear thinning significantly influences the developing interfacial patterns. Shear thinning can suppress tip-splitting, and produce fingers which grow in an oscillating fashion and shed side-branches. Emergent length-scales show reasonable agreement with a general linear stability analysis.