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Plane Poiseuille flow of miscible layers with different viscosities: instabilities in the Stokes flow regime

Published online by Cambridge University Press:  26 September 2011

L. Talon  and
E. Meiburg
L. Talon
Affiliation:
Laboratoire Fluides Automatique et Systèmes Thermiques, Université Pierre et Marie Curie, CNRS (UMR 7608) Bâtiment 502, Campus Universitaire, 91405 Orsay CEDEX, France Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
E. Meiburg*
Affiliation:
Department of Mechanical Engineering, University of California at Santa Barbara, Santa Barbara, CA 93106, USA
*
† Email address for correspondence: meiburg@engineering.ucsb.edu
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Abstract

We investigate the linear stability of miscible, viscosity-layered Poiseuille flow. In the Stokes flow regime, diffusion is observed to have a destabilizing effect very similar to that of inertia in finite-Reynolds-number flows. For two-layer flows, four types of instability can dominate, depending on the interface location. Two interfacial modes exhibit large growth rates, while two additional bulk modes grow more slowly. Three-layer Stokes flows give rise to diffusive modes for each interface. These two diffusive interface modes can be in resonance, thereby enhancing the growth rate. Furthermore, modes without inertia and diffusion are also observed, consistent with a previous long-wave analysis for sharp interfaces. In contrast to that earlier investigation, the present analysis demonstrates that instability can also occur when the more viscous layer is in the centre, at larger wavenumbers.

JFM classification

Instability: Instability Low-Reynolds-number flows: Low-Reynolds-number flows

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 686 , 10 November 2011 , pp. 484 - 506
Copyright
Copyright © Cambridge University Press 2011

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