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Fast equilibration dynamics of viscous particle-laden flow in an inclined channel

Published online by Cambridge University Press:  19 September 2019

Jeffrey Wong Open the ORCID record for Jeffrey Wong [Opens in a new window] ,
Michael Lindstrom  and
Andrea L. Bertozzi
Jeffrey Wong*
Affiliation:
Department of Mathematics, Duke University, Durham, NC 27708, USA Department of Mathematics, University of California, Los Angeles, CA 90095, USA
Michael Lindstrom
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095, USA
Andrea L. Bertozzi
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90095, USA Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA
*
†Email address for correspondence: [email protected]
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Abstract

A viscous suspension of negatively buoyant particles released into a wide, open channel on an incline will stratify in the normal direction as it flows. We model the early dynamics of this stratification under the effects of sedimentation and shear-induced migration. Prior work focuses on the behaviour after equilibration where the bulk suspension either separates into two distinct fronts (settled) or forms a single, particle-laden front (ridged), depending on whether the initial concentration of particles exceeds a critical threshold. From past experiments, it is also clear that this equilibration time scale grows considerably near the critical concentration. This paper models the approach to equilibrium. We present a theory of the dramatic growth in this equilibration time when the mixture concentration is near the critical value, where the balance between settling and shear-induced resuspension reverses.

JFM classification

Interfacial Flows (free surface): Thin films Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 879 , 25 November 2019 , pp. 28 - 53
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Copyright
© 2019 Cambridge University Press 

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