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Flowing resistance and dilatancy of dense suspensions: lubrication and repulsion

Published online by Cambridge University Press:  07 November 2011

Pierre Grégoire Rognon ,
Itai Einav  and
Cyprien Gay
Pierre Grégoire Rognon*
Affiliation:
School of Civil Engineering, J05, The University of Sydney, Sydney, New South Wales 2006, Australia
Itai Einav
Affiliation:
School of Civil Engineering, J05, The University of Sydney, Sydney, New South Wales 2006, Australia
Cyprien Gay
Affiliation:
Matière et Systèmes Complexes, Université Paris Diderot – Paris 7, CNRS UMR 7057, Paris, France
*
†Email address for correspondence: [email protected]
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Abstract

The purpose of this study is to provide generic insights into the rheology of immersed particulate materials in dense configurations. We focus on a non-Brownian and Stokesian suspension of elastic spheres, as a way to identify the effect on the collective behaviour of two short-range interactions: lubrication and steric repulsion below a tunable range. The response of the material to shear under a prescribed shear rate and a prescribed normal stress is simulated using ‘soft dynamics’, a discrete element method which accounts for the dynamics of such a system. The material exhibits a visco-elastic behaviour, deforming elastically at high shear rates, and viscously at slower shear rates. When steady flow is established, the constitutive law can be expressed, as for dry grains, through a friction law and a dilatancy law, whose numerical constants depend in a non-trivial manner on the equilibrium gap. The analysis of the contribution of each interacting pair as a function of its distance and orientation sheds some light on this collective behaviour. Lubrication, which hinders grain approach, is responsible for a loss of contact and a low repulsion contribution to the stress. In contrast, lubrication viscously connects each grain to as many as 10 neighbours, which all contribute significantly to the shear stress. This forms a robust dynamic connected network controlling the collective resistance to flow. This study should be useful for modelling the rheological behaviour of real materials such as foams, emulsions and blood: beside the specific properties of their particles, these particulate fluids also involve lubrication and repulsion.

JFM classification

Granular media: Granular media Non-Newtonian Flows: Rheology Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 689 , 25 December 2011 , pp. 75 - 96
Copyright
Copyright © Cambridge University Press 2011

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