Effect of tangential interface motion on the viscous instability in fluid flow past flexible surfaces

Thaokar, RM and Shankar, V and Kumaran, V (2001) Effect of tangential interface motion on the viscous instability in fluid flow past flexible surfaces. In: European Physical Journal B, 23 (4). pp. 533-550.

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Abstract

The stability of linear shear flow of a Newtonian fluid past a flexible membrane is analysed in the limit of low Reynolds number as well as in the intermediate Reynolds number regime for two different membrane models. The objective of this paper is to demonstrate the importance of tangential motion in the membrane on the stability characteristics of the shear flow. The first model assumes the wall to be a spring-backed" plate membrane, and the displacement of the wall is phenomenologically related in a linear manner to the change in the fluid stresses at the wall. In the second model, the membrane is assumed to be a two-dimensional compressible viscoelastic sheet of infinitesimal thickness, in which the constitutive relation for the shear stress contains an elastic part that depends on the local displacement field and a viscous component that depends on the local velocity in the membrane. The stability characteristics of the laminar flow in the limit of low Re are crucially dependent on the tangential motion in the membrane wall. In both cases, the flow is stable in the low Reynolds number limit in the absence of tangential motion in the membrane. However, the presence of tangential motion in the membrane destabilises the shear flow even in the absence of fluid inertia. In this case, the non-dimensional velocity (At) required for unstable fluctuations is proportional to the wavenumber k (At~k) in the plate membrane type of wall while it scales as k2 in the viscoelastic membrane type of wall (At~k2) in the limit k-0. The results of the low Reynolds number analysis are extended numerically to the intermediate Reynolds number regime for the case of a viscoelastic membrane. The numerical results show that for a given set of wall parameters, the flow is unstable only in a finite range of Reynolds number, and it is stable in the limit of large Reynolds number.

Item Type:	Journal Article
Publication:	European Physical Journal B
Publisher:	Springer-Verlag
Additional Information:	Copyright for this article belongs to Springer-Verlag.
Keywords:	Deformation and flow;Stability of laminar flows;Flows in ducts;Channels;Nozzles;conduits
Department/Centre:	Division of Mechanical Sciences > Chemical Engineering
Date Deposited:	06 Sep 2004
Last Modified:	19 Sep 2010 04:16
URI:	http://eprints.iisc.ac.in/id/eprint/1911

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