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Obstructed and channelized viscoplastic flow in a Hele-Shaw cell

Published online by Cambridge University Press:  02 February 2016

D. R. Hewitt ,
M. Daneshi ,
N. J. Balmforth  and
D. M. Martinez
D. R. Hewitt*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2, Canada
M. Daneshi
Affiliation:
Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, V6T 1Z3, Canada
N. J. Balmforth
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, V6T 1Z2, Canada
D. M. Martinez
Affiliation:
Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, V6T 1Z3, Canada
*
†Email address for correspondence: drh39@cam.ac.uk
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Abstract

A theoretical study is presented of the flow of viscoplastic fluid through a Hele-Shaw cell that contains various kinds of obstructions. Circular and elliptical blockages of the cell are considered together with stepwise contractions or expansions in slot width, all within the simplifying approximation of a narrow gap. Specific attention is paid to the flow patterns that develop around the obstacles, particularly any stagnant plugged regions, and the asymptotic limits of relatively small or large yield stress. Periodic arrays of circular contractions or expansions are studied to explore the interference between obstructions. Finally, viscoplastic flow through a cell with randomly roughened walls is examined, and it is shown that constructive interference of local contractions and expansions leads to a pronounced channelization of the flow. An optimization algorithm based on minimization of the pressure drop is derived to construct the path of the channels in the limit of relatively large yield stress or, equivalently, relatively slow flow.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows Non-Newtonian Flows: Non-Newtonian Flows Non-Newtonian Flows: Plastic materials
Type
Papers
Information
Journal of Fluid Mechanics , Volume 790 , 10 March 2016 , pp. 173 - 204
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Copyright
© 2016 Cambridge University Press 

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