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Yield limit analysis of particle motion in a yield-stress fluid

Published online by Cambridge University Press:  24 April 2017

Emad Chaparian  and
Ian A. Frigaard Open the ORCID record for Ian A. Frigaard [Opens in a new window]
Emad Chaparian
Affiliation:
Department of Mechanical Engineering, University of British Columbia, Vancouver, BC, V6T 1Z4, Canada
Ian A. Frigaard*
Affiliation:
Department of Mechanical Engineering, University of British Columbia, Vancouver, BC, V6T 1Z4, Canada Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada
*
†Email address for correspondence: frigaard@math.ubc.ca
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Abstract

A theoretical and numerical study of yield-stress fluid creeping flow about a particle is presented. Yield-stress fluids can hold rigid particles statically buoyant if the yield stress is large enough. In addressing sedimentation of rigid particles in viscoplastic fluids, we should know this critical ‘yield number’ beyond which there is no motion. As we get close to this limit, the role of viscosity becomes negligible in comparison to the plastic contribution in the leading order, since we are approaching the zero-shear-rate limit. Admissible stress fields in this limit can be found by using the characteristics of the governing equations of perfect plasticity (i.e. the sliplines). This approach yields a lower bound of the critical plastic drag force or equivalently the critical yield number. Admissible velocity fields also can be postulated to calculate the upper bound. This analysis methodology is examined for three families of particle shapes (ellipse, rectangle and diamond) over a wide range of aspect ratios. Numerical experiments of either resistance or mobility problems in a viscoplastic fluid validate the predictions of slipline theory and reveal interesting aspects of the flow in the yield limit (e.g. viscoplastic boundary layers). We also investigate in detail the cases of high and low aspect ratio of the particles.

JFM classification

Non-Newtonian Flows: Non-Newtonian Flows Multiphase and Particle-laden Flows: Particle/fluid flow Non-Newtonian Flows: Plastic materials
Type
Papers
Information
Journal of Fluid Mechanics , Volume 819 , 25 May 2017 , pp. 311 - 351
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Copyright
© 2017 Cambridge University Press 

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