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Title

Revisiting plane Couette-Poiseuille flows of a piezo-viscous fluid

Author(s)

Suslov, Sergey A.;  Tran, Thien Duc

Abstract

We re-examine fully developed isothermal unidirectional plane Couette-Poiseuille flows of an incompressible fluid whose viscosity depends linearly on the pressure as previously considered in [J. Hron, J. Malek, K.R. Rajagopal, Simple flows of fluids with pressure-dependent viscosities, Proc. R. Soc. Lond. A 457 (2001) 1603-1622]. We show that the conclusion made there that, in contrast to Newtonian and power-law fluids, piezo-viscous fluids allow multiple solutions is not justified, and that the inflection velocity profiles reported in [J. Hron, J. Malek, K.R. Rajagopal, Simple flows of fluids with pressure-dependent viscosities, Proc. R. Soc. Lond. A 457 (2001) 1603-1622] cannot exist. Subsequently, we undertake a systematic parametric study of these flows and identify three distinct families of solutions which can exist in the considered geometry. One of these families has no similar counterpart for fluids with pressure-independent viscosity. We also show that the critical wall speed exists beyond which Poiseuille-type flows are impossible regardless of the magnitude of the applied pressure gradient. For smaller wall speeds channel choking occurs for Poiseuille-type flows at large pressure gradients. These features distinguish drastically piezo-viscous fluids from their Newtonian and power-law counterparts.

Publication type

Journal article

Source

Journal of Non-Newtonian Fluid Mechanics, Vol. 154, no. 2-3 (Oct 2008), pp. 170-178

Publication year

2008

FOR Code(s)

0203 Classical Physics

Keyword(s)

Applied pressure;  Boundary layers;  Fluids;  Gradient methods;  Hydrodynamics;  Incompressible fluids;  Multiple solutions;  Newtonian;  Packed beds;  Parametric studies;  Piezo-viscous fluid;  Plane Couette-Poiseuille flow;  Poiseuille flows;  Power laws;  Power-law fluids;  Pressure-dependent viscosity;  Pressure gradients;  Programmable logic controllers;  Speed;  Velocity profiling;  Viscosity;  Viscous flow;  Viscous fluids;  Walls

Publisher

Elsevier

ISSN

0377-0257

Publisher URL

http://dx.doi.org/10.1016/j.jnnfm.2008.04.010

Copyright

Copyright © 2008 Elsevier B.V. Authors' version reproduced in accordance with the copyright policy of the publisher.

Full text

Peer reviewed