TY - JOUR
T1 - Models of non-Newtonian Hele-Shaw flow
AU - Kondic, Ljubinko
AU - Palffy-Muhoray, Peter
AU - Shelley, Michael J.
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1996
Y1 - 1996
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevE.54.R4536
DO - 10.1103/PhysRevE.54.R4536
M3 - Article
AN - SCOPUS:0001655304
VL - 54
SP - R4536-R4539
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
SN - 1063-651X
IS - 5
ER -