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Mass and momentum balance during particle migration in the pressure-driven flow of frictional non-Brownian suspensions

Published online by Cambridge University Press:  25 October 2024

Michel Orsi Open the ORCID record for Michel Orsi [Opens in a new window] ,
Laurent Lobry ,
Elisabeth Lemaire Open the ORCID record for Elisabeth Lemaire [Opens in a new window]  and
François Peters Open the ORCID record for François Peters [Opens in a new window]
Michel Orsi
Affiliation:
Université Côte d'Azur, InPhyNi, 06200, France
Laurent Lobry
Affiliation:
Université Côte d'Azur, InPhyNi, 06200, France
Elisabeth Lemaire
Affiliation:
Université Côte d'Azur, InPhyNi, 06200, France
François Peters*
Affiliation:
Université Côte d'Azur, InPhyNi, 06200, France
*
†Email address for correspondence: [email protected]
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Abstract

The transient shear-induced particle migration of frictional non-Brownian suspensions is studied using particle-resolved simulations. The numerical method – the fictitious domain method – is well suited to heterogeneous flows thanks to a frame-invariant formulation of the subgrid (lubrication) corrections that does not involve the ambient flow (Orsi et al., J. Comput. Phys., vol. 474, 2023, 111823). The paper aims to give an accurate quantitative picture of the mass and momentum balance during the flow. The various assumptions and local constitutive laws that together form the suspension balance model (SBM) are thoroughly examined. To this purpose, the various quantities of interest are locally averaged in space and time, and their profile across the channel is extensively studied, with specific attention to the time evolution of the different contributions, either hydrodynamic in nature or from contact interactions, to the shear and normal stresses. The latter, together with the velocity gradient in the wall-normal direction and the volume fraction profile, yield the local constitutive laws, which are compared with their counterpart obtained in homogeneous shear flow. A fair agreement is observed except in a layering area at the boundaries and at the very centre of the channel. In addition, the main assumption of the SBM, i.e. the local relation between the hydrodynamic force on the particles and the particle flux, is meticulously investigated. The hydrodynamic force is found to be mainly a drag, except in the lower range of the probed volume fractions, where a non-drag contribution is observed.

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 998 , 10 November 2024 , A16
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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