Applied Mathematics and Nonlinear PDE Seminar
Monday, February 2, 1998, 4:00pm, 120 Physics
Lou Kondic (Duke University)
Pattern Formation in Non-Newtonian Hele-Shaw Flow
Abstract:
We explore the morphology of patterns due to the Saffman-Taylor instability in Hele-Shaw cells and find that it can be dramatically altered by the non-Newtonian response of complex fluids such as liquid crystals and polymer solutions. The dense-branching morphology of Newtonian liquids may be replaced by dendritic fingers with stable tips and sidebranches. Starting from a very general viscoelastic fluid model, we find a distinguished limit where shear thinning effect is dominant. A Darcy's law leads to the nonlinear boundary value problem for the pressure in the fluid. Full numerical simulations show that shear thinning alone modifies considerably the pattern formation and can produce fingers whose tip-splitting is suppressed, in agreement with experimental results. These fingers grow in an oscillating fashion, shedding ``side-branches'' from their tips, closely resembling solidification patterns.

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