Models of non-Newtonian Hele-Shaw flow

Journal Article · Fri Nov 01 04:00:00 EST 1996 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.54.R4536· OSTI ID:389293

Kondic, L; Palffy-Muhoray, P; Shelley, M J ^[1]

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1. Courant Institute of Mathematical Sciences, New York University, New York City, New York 10012 (United States)

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{close_quote}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 {ital et} {ital al}. [Phys. Rev. Lett. {bold 75}, 2132 (1995)] follows from this modified law. For a shear-thinning liquid, our derivation shows strong constraints upon the fluid viscosity{emdash} strong shear-thinning does not allow the construction of a unique Darcy{close_quote}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. {copyright} {ital 1996 The American Physical Society.}

• DOE Contract Number: FG02-88ER25053
• OSTI ID: 389293
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 5 Vol. 54; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
CORRELATIONS
DARCY LAW
FLOW MODELS
FLUID FLOW
INJECTION
MOLDING
PRESSURE GRADIENTS
USES
VISCOSITY