Models of non-Newtonian Hele-Shaw flow

Ljubinko Kondic, Peter Palffy-Muhoray, Michael Shelley

Research output: Contribution to journalArticle

Abstract

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 modified law. For a shear-thinning liquid, our derivation shows strong constraints upon the fluid viscosity - strong shear-thinning does not allow the construction of a unique Darcy's law, and is related to the appearance of slip layers in the flow. For a weakly shear-thinning liquid, we calculate corrections to the Newtonian instability of an expanding bubble in a radial cell.

Original languageEnglish (US)
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume54
Issue number5
StatePublished - 1996

Fingerprint

Hele-Shaw Flow
Non-Newtonian Flow
Shear Thinning
shear thinning
Viscosity
Darcy's Law
viscosity
fluids
Liquid
Hele-Shaw
Taylor instability
Non-Newtonian Fluid
Cell
Nonlinear Boundary Value Problems
Fluid Model
Pressure Gradient
liquids
cells
pressure gradients
boundary value problems

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

Models of non-Newtonian Hele-Shaw flow. / Kondic, Ljubinko; Palffy-Muhoray, Peter; Shelley, Michael.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 54, No. 5, 1996.

Research output: Contribution to journalArticle

Kondic, Ljubinko ; Palffy-Muhoray, Peter ; Shelley, Michael. / Models of non-Newtonian Hele-Shaw flow. In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 1996 ; Vol. 54, No. 5.
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