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Transient flows and migration in granular suspensions: key role of Reynolds-like dilatancy

Published online by Cambridge University Press:  23 September 2022

S. Athani ,
B. Metzger Open the ORCID record for B. Metzger [Opens in a new window] ,
Y. Forterre  and
R. Mari Open the ORCID record for R. Mari [Opens in a new window]
S. Athani*
Affiliation:
Université Grenoble–Alpes, CNRS, Laboratoire Interdisciplinaire de Physique (LIPhy), 38000 Grenoble, France
B. Metzger
Affiliation:
Aix Marseille Univ., CNRS, IUSTI, 13453 Marseille, France
Y. Forterre
Affiliation:
Aix Marseille Univ., CNRS, IUSTI, 13453 Marseille, France
R. Mari
Affiliation:
Université Grenoble–Alpes, CNRS, Laboratoire Interdisciplinaire de Physique (LIPhy), 38000 Grenoble, France
*
†Email address for correspondence: shivakumar.athani@univ-grenoble-alpes.fr
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Abstract

We investigate the transient dynamics of a sheared suspension of neutrally buoyant particles in pressure-imposed rheology configuration, subject to a sudden change in shear rate or external pressure. Discrete element method simulations show that, depending on the flow parameters (particle and system size, initial volume fraction), the early stress response of the suspension may differ strongly from the prediction of the suspension balance model based on the steady-state rheology. We show that a two-phase model incorporating the Reynolds-like dilatancy law of Pailha & Pouliquen (J. Fluid Mech., vol. 633, 2009, pp. 115–135), which prescribes the dilation rate of the suspension over a strain scale $\gamma _0$, captures quantitatively the suspension dilation/compaction over the whole range of parameters investigated. Together with the Darcy flow induced by the pore pressure gradient during dilation or compaction, this Reynolds-like dilatancy implies that the early stress response of the suspension is non-local, with a non-local length scale $\ell$ that scales with the particle size and diverges algebraically at jamming. In regions affected by $\ell$, the stress level is fixed, not by the steady-state rheology, but by the Darcy fluid pressure gradient resulting from the dilation/compaction rate. Our results extend the validity of the Reynolds-like dilatancy flow rule, initially proposed for jammed suspensions, to flowing suspension below the critical volume fraction at which the suspension jams, thereby providing a unified framework to describe dilation and shear-induced migration. They pave the way for understanding more complex unsteady flows of dense suspensions, such as impacts, transient avalanches or the impulsive response of shear-thickening suspensions.

JFM classification

Complex Fluids: Suspensions Low-Reynolds-number flows: Stokesian dynamics Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 949 , 25 October 2022 , A9
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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