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Viscous resuspension of non-Brownian particles: determination of the concentration profiles and particle normal stresses

Published online by Cambridge University Press:  25 January 2021

Enzo d'Ambrosio ,
Frédéric Blanc  and
Elisabeth Lemaire Open the ORCID record for Elisabeth Lemaire [Opens in a new window]
Enzo d'Ambrosio
Affiliation:
Université Côte d'Azur, CNRS, InPhyNi-UMR 7010, 06108 Nice CEDEX 2, France
Frédéric Blanc
Affiliation:
Université Côte d'Azur, CNRS, InPhyNi-UMR 7010, 06108 Nice CEDEX 2, France
Elisabeth Lemaire*
Affiliation:
Université Côte d'Azur, CNRS, InPhyNi-UMR 7010, 06108 Nice CEDEX 2, France
*
†Email address for correspondence: elisabeth.lemaire@unice.fr
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Abstract

We perform local measurements of both the velocity and the particle volume fraction to study viscous resuspension in non-Brownian suspensions for Shields numbers ranging from $10^{-3}$ to $1$. With this aim, a suspension of polymethacrylate spherical particles dispersed in a lighter Newtonian fluid (Triton X100) is sheared in a vertical Couette cell where both velocity and particle density mappings are performed. We show that the radial profiles of the velocity and of the particle volume fraction are inconsistent in the framework of local rheology of a Newtonian material and that these discrepancies disappear for a neutrally buoyant suspension. The vertical concentration profiles are used to deduce the third particle normal stress, $\varSigma _{33}^p$, by solving the Cauchy equation. The value of $\varSigma _{33}^p$ is shown not to vary linearly with shear rate but rather through a power law with an exponent close to $0.7$, irrespective of the value of the particle volume fraction, in accordance with the recent results of Saint-Michel et al. (Phys. Fluids, vol. 31, 2019, 103301). Finally, we compare our results with the results of previous studies where $\alpha _3=\varSigma _{33}^p/\eta _0\dot {\gamma }$ (with $\eta_0$ the viscosity of the suspending liquid and $\dot{\gamma}$ the shear rate) was deduced from the macroscopic measurement of the height of the resuspended layer. The agreement is satisfactory.

JFM classification

Granular media: Granular media Complex Fluids: Suspensions Multiphase and Particle-laden Flows: Particle/fluid flow

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A22
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© The Author(s), 2021. Published by Cambridge University Press

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