A constitutive model for simple shear of dense frictional suspensions

Abhinendra Singh; Romain Mari; Morton M. Denn; Jeffrey F. Morris

doi:10.1122/1.4999237

paper

A constitutive model for simple shear of dense frictional suspensions

arXiv:1708.05749 · doi:10.1122/1.4999237

Abstract

Discrete particle simulations are used to study the shear rheology of dense, stabilized, frictional particulate suspensions in a viscous liquid, toward development of a constitutive model for steady shear flows at arbitrary stress. These suspensions undergo increasingly strong continuous shear thickening (CST) as solid volume fraction $ϕ$ increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed for a range of $ϕ$ . When studied at controlled stress, the DST behavior is associated with non-monotonic flow curves of the steady-state stress as a function of shear rate. Recent studies have related shear thickening to a transition between mostly lubricated to predominantly frictional contacts with the increase in stress. In this study, the behavior is simulated over a wide range of the dimensionless parameters $(ϕ, σ ~$ , and $μ)$ , with $σ ~ = σ / σ_{0}$ the dimensionless shear stress and $μ$ the coefficient of interparticle friction: the dimensional stress is $σ$ , and $σ_{0} \propto F_{0} / a^{2}$ , where $F_{0}$ is the magnitude of repulsive force at contact and $a$ is the particle radius. The data have been used to populate the model of the lubricated-to-frictional rheology of Wyart and Cates [Phys. Rev. Lett.{\bf 112}, 098302 (2014)], which is based on the concept of two viscosity divergences or \textquotedblleft jamming\textquotedblright\ points at volume fraction $ϕ_{J}^{0} = ϕ_{rcp}$ (random close packing) for the low-stress lubricated state, and at $ϕ_{J} (μ) < ϕ_{J}^{0}$ for any nonzero $μ$ in the frictional state; a generalization provides the normal stress response as well as the shear stress. A flow state map of this material is developed based on the simulation results.

12 pages, 10 figures

A constitutive model for simple shear of dense frictional suspensions

Abstract

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