Kondic, L., Shelley, M., & Palffy-Muhoray, P. (1998). Non-Newtonian Hele-Shaw Flow and the Saffman-Taylor Instability (1–). Physical Review Letters. https://doi.org/10.1103/PhysRevLett.80.1433
Kondic, Ljubinko, Michael Shelley, and Peter Palffy-Muhoray. 1998. “Non-Newtonian Hele-Shaw Flow and the Saffman-Taylor Instability”. Physical Review Letters. https://doi.org/10.1103/PhysRevLett.80.1433.
Kondic, Ljubinko, et al. Non-Newtonian Hele-Shaw Flow and the Saffman-Taylor Instability. Physical Review Letters, 16 Feb. 1998, https://doi.org/10.1103/PhysRevLett.80.1433.
We explore the Saffman-Taylor instability of a gas bubble expanding into a shear thinning liquid in a radial Hele-Shaw cell. Using Darcy's law generalized for non-Newtonian fluids, 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 oscillate during growth and shed side branches. Emergent length scales show reasonable agreement with a general linear stability analysis.