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Geometric scaling of a purely elastic flow instability in serpentine channels

Published online by Cambridge University Press:  01 October 2012

J. Zilz ,
R. J. Poole ,
M. A. Alves ,
D. Bartolo ,
B. Levaché  and
A. Lindner
J. Zilz
Affiliation:
PMMH UMR7636–ESPCI Paristech–CNRS–Paris 6–Paris 7, 10 rue Vauquelin F-75231 Paris CEDEX 05, France
R. J. Poole
Affiliation:
School of Engineering, University of Liverpool, Brownlow Hill, Liverpool L69 3GH, UK
M. A. Alves
Affiliation:
Departamento de Engenharia Química, Centro de Estudos de Fenómenos de Transporte, Faculdade de Engenharia da Universidade do Porto, Rua Doutor Roberto Frias, 4200-465 Porto, Portugal
D. Bartolo
Affiliation:
PMMH UMR7636–ESPCI Paristech–CNRS–Paris 6–Paris 7, 10 rue Vauquelin F-75231 Paris CEDEX 05, France
B. Levaché
Affiliation:
PMMH UMR7636–ESPCI Paristech–CNRS–Paris 6–Paris 7, 10 rue Vauquelin F-75231 Paris CEDEX 05, France
A. Lindner*
Affiliation:
PMMH UMR7636–ESPCI Paristech–CNRS–Paris 6–Paris 7, 10 rue Vauquelin F-75231 Paris CEDEX 05, France
*
†Email address for correspondence: [email protected]
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Abstract

A combined experimental, numerical and theoretical investigation of the geometric scaling of the onset of a purely elastic flow instability in serpentine channels is presented. Good qualitative agreement is obtained between experiments, using dilute solutions of flexible polymers in microfluidic devices, and three-dimensional numerical simulations using the upper-convected Maxwell model. The results are confirmed by a simple theoretical analysis, based on the dimensionless criterion proposed by Pakdel & McKinley (Phys. Rev. Lett., vol. 77, 1996, pp. 2459–2462) for onset of a purely elastic flow instability. Three-dimensional simulations show that the instability is primarily driven by the curvature of the streamlines induced by the flow geometry and not due to the weak secondary flow in the azimuthal direction. In addition, the simulations also reveal that the instability is time-dependent and that the flow oscillates with a well-defined period and amplitude close to the onset of the supercritical instability.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Microfluidics Non-Newtonian Flows: Viscoelasticity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 712 , 10 December 2012 , pp. 203 - 218
Copyright
©2012 Cambridge University Press

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