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A mechanism for oscillatory instability in viscoelastic cross-slot flow

Published online by Cambridge University Press:  10 March 2009

LI XI  and
MICHAEL D. GRAHAM
LI XI
Affiliation:
Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, WI 53706-1691, USA
MICHAEL D. GRAHAM*
Affiliation:
Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, WI 53706-1691, USA
*
†Email address for correspondence: [email protected]
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Abstract

Interior stagnation-point flows of viscoelastic liquids arise in a wide variety of applications including extensional viscometry, polymer processing and microfluidics. Experimentally, these flows have long been known to exhibit instabilities, but the mechanisms underlying them have not previously been elucidated. We computationally demonstrate the existence of a supercritical oscillatory instability of low-Reynolds-number viscoelastic flow in a two-dimensional cross-slot geometry. The fluctuations are closely associated with the ‘birefringent strand’ of highly stretched polymer chains associated with the outflow from the stagnation point at high Weissenberg number. Additionally, we describe the mechanism of instability, which arises from the coupling of flow with extensional stresses and their steep gradients in the stagnation-point region.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 622 , 10 March 2009 , pp. 145 - 165
Copyright
Copyright © Cambridge University Press 2009

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