Particles suspended in a Newtonian fluid raise the viscosity and also generally give rise to a shear-rate dependent rheology. In particular, pronounced shear thickening may be observed at large solid volume fractions. In a recent article (R. Seto, R. Mari, J. F. Morris, and M. M. Denn., Phys. Rev. Lett., 111:218301, 2013) we have considered the minimum set of components to reproduce the experimentally observed shear thickening behavior, including Discontinuous Shear Thickening (DST). We have found frictional contact forces to be essential, and were able to reproduce the experimental behavior by a simulation including this physical ingredient along with viscous lubrication. In the present article, we thoroughly investigate the effect of friction and express it in the framework of the jamming transition. The viscosity divergence at the jamming transition has been a well known phenomenon in suspension rheology, as reflected in many empirical laws for the viscosity. Friction can affect this divergence, and in particular the jamming packing fraction is reduced if particles are frictional. Within the physical description proposed here, shear thickening is a direct consequence of this effect: as the shear rate increases, friction is increasingly incorporated as more contacts form, leading to a transition from a mostly frictionless to a mostly frictional rheology. This result is significant because it shifts the emphasis from lubrication hydrodynamics and detailed microscopic interactions to geometry and steric constraints close to the jamming transition.

Discontinuous shear thickening (DST) observed in many dense athermal suspensions has proven difficult to understand and to reproduce by numerical simulation. By introducing a numerical scheme including both relevant hydrodynamic interactions and granularlike contacts, we show that contact friction is essential for having DST. Above a critical volume fraction, we observe the existence of two states: a low viscosity, contactless (hence, frictionless) state, and a high viscosity frictional shear jammed state. These two states are separated by a critical shear stress, associated with a critical shear rate where DST occurs. The shear jammed state is reminiscent of the jamming phase of granular matter. Continuous shear thickening is seen as a lower volume fraction vestige of the jamming transition.Suspensions of particles at high volume fraction of solid, often termed dense suspensions, have a rich nonNewtonian rheology. This is particularly striking for the simple system of nearly rigid particles in a Newtonian fluid, which exhibits shear thinning, shear thickening, and normal stresses, the last associated with strong microstructural distortion, despite the dominant influence played in such mixtures by viscous (Stokes-flow) fluid mechanics [1]. The phenomenon of discontinuous shear thickening (DST) (see [2][3][4][5] and references therein) is especially fascinating. Suspensions exhibiting DST flow relatively easily with slow stirring, but become highly viscous or even seemingly solid if one tries to stir them rapidly. In a rheometer, the transition is seen at a critical shear rate for a given volume fraction. It is often found that DST is completely reversible [6]. DST typically occurs for a volume fraction that exceeds a threshold value φ c , which depends on the nature of the suspended particles: increased nonsphericity or surface roughness seem to lower φ c . Continuous shear thickening (CST) is observed below φ c , and becomes weaker with decreasing volume fraction. Although counterintuitive, the abrupt or discontinuous increase of viscosity with increase of shear rate is a generic feature of dense suspensions [3,7], occurring in both Brownian (colloidal) and non-Brownian suspensions. This ubiquity suggests the possibility of a single mechanistic basis applicable to the various types of suspension. DST has yet to be reproduced by a simulation method which can unambiguously point to the essential physical features necessary for its observation. This Letter presents a novel method able to identify these features.Several possible mechanisms have been proposed as the origin of DST. An order-disorder mechanism [8-10] describes a low shear rate ordered flow with few interactions between particles that becomes unstable at high shear rates and evolves to a disordered, highly interacting viscous flow. A hydroclustering [6,[11][12][13][14][15] or (hydro)contact network [16,17] mechanism attributes the thickening to clusters of particles "glued" together by the lubrication singularity. The competition between a force (Brown...

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), withσ = σ/σ 0 the dimensionless shear stress and µ the coefficient of interparticle friction: the dimensional stress is σ, and σ 0 ∝ 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.112, 098302 (2014)], which is based on the concept of two viscosity divergences or "jamming" points at volume fraction φ 0 J = φ rcp (random close packing) for the low-stress lubricated state, and at φ J (µ) < φ 0 J 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. At low stress and/or intermediate φ, the system exhibits CST, and DST appears at volume fractions below but approaching the frictional jamming point. For φ < φ µ J , DST is associated with a material transition from one stress-independent rheology to another, while for φ > φ µ J , the system exhibits DST to shear jamming as the stress increases.