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/σ0 the dimensionless shear stress and μ the coefficient of
interparticle friction: the dimensional stress is σ, and σ0∝F0/a2, where F0 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 ϕJ0=ϕrcp (random close packing) for the
low-stress lubricated state, and at ϕJ(μ)<ϕJ0 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.Comment: 12 pages, 10 figure