A constitutive model for simple shear of dense frictional suspensions

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 the solid volume fraction ϕ increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed in a range of ϕ. When studied at controlled stress, the DST behavior is associated with nonmonotonic flow curves of the steady-state shear rate as a function of stress. Recent studies have related shear thickening to a transition from mostly lubricated to predominantly frictional contacts with the increase in stress. In this study, the behavior is simulated over wide ranges of concentration, dimensionless shear stress, and coefficient of interparticle friction. The simulation data have been used to populate the lubricated-to-frictional rheology model of Wyart and Cates [Phys. Rev. Lett. 112, 098302 (2014)], which is based on the concept of two viscosity divergences or “jamming” points at volume fraction ϕJ0=ϕrcp (random close packing) for the low-stress lubricated state, and at ϕJμ<ϕJ0 for any nonzero μ in the frictional state; a generalization provides the normal stress response as well as the shear stress, allowing a description of the full stress tensor. A flow state map of this material is developed based on the simulation results. At low stress and/or intermediate ϕ, the system exhibits CST, and DST appear at volume fractions below but approaching the frictional jamming point. For ϕ<ϕJμ, DST is associated with a material transition from one stress-independent rheology to another, while for ϕ>ϕJμ, the system exhibits DST to shear jamming as the stress increases.