https://doi.org/10.1140/epje/i2009-10530-7
Regular Article
Apparent viscosity and particle pressure of a concentrated suspension of non-Brownian hard spheres near the jamming transition
1
Laboratoire de Physique des Matériaux Diviseś et des Interfaces, UMR-CNRS 8108, Cité Descartes, Bâtiment Lavoisier, Université Paris Est, 5 bd Descartes, F-77454, Marne-la-Vallée Cedex 2, France
2
Centre de Recherche Paul Pascal, CNRS UPR 8641, Université Bordeaux 1, 115 Avenue Schweitzer, F-33600, Pessac, France
* e-mail: Pierre.Mills@univ-mlv.fr
** e-mail: snabre@crpp-bordeaux.cnrs.fr
Received:
16
June
2009
Revised:
11
September
2009
Accepted:
8
October
2009
Published online:
24
October
2009
We consider the steady shear flow of a homogeneous and dense assembly of hard spheres suspended in a Newtonian viscous fluid. In a first part, a mean-field approach based on geometric arguments is used to determine the viscous dissipation in a dense isotropic suspension of smooth hard spheres and the hydrodynamic contribution to the suspension viscosity. In a second part, we consider the coexistence of transient solid clusters coupled to regions with free flowing particles near the jamming transition. The fraction of particles in transient clusters is derived through the Landau-Ginzburg concepts for first-order phase transition with an order parameter corresponding to the proportion of “solid” contacts. A state equation for the fraction of particle-accessible volume is introduced to derive the average normal stresses and a constitutive law that relates the total shear stress to the shear rate. The analytical expression of the average normal stresses well accounts for numerical or experimental evaluation of the particle pressure and non-equilibrium osmotic pressure in a dense sheared suspension. Both the friction level between particles and the suspension dilatancy are shown to determine the singularity of the apparent shear viscosity and the flow stability near the jamming transition. The model further predicts a Newtonian behavior for a concentrated suspension of neutrally buoyant particles and no shear thinning behavior in relation with the shear liquefaction of transient solid clusters.
PACS: 83.10.-y Rheology: Fundamentals and theoretical – / 47.57.E- Suspensions – / 83.50.Ax Steady shear flows, viscometric flow – / 47.15.G- Low-Reynolds-number (creeping) flows –
© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg, 2009