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.

Particle-based simulations of discontinuous shear thickening (DST) and shear jamming (SJ) suspensions are used to study the role of stress-activated constraints, with an emphasis on resistance to gear-like rolling. Rolling friction decreases the volume fraction required for DST and SJ, in quantitative agreement with real-life suspensions with adhesive surface chemistries and "rough" particle shapes. It sets a distinct structure of the frictional force network compared to only sliding friction, and from a dynamical perspective leads to an increase in the velocity correlation length, in part responsible for the increased viscosity. The physics of rolling friction is thus a key element in achieving a comprehensive understanding of strongly shear-thickening materials.

The steady-state shear rheology of granular materials is investigated in slow quasistatic and inertial flows. The effect of gravity (thus the local pressure) and the often-neglected contact stiffness are the focus of this study. A series of particle simulations are performed on a weakly frictional granular assembly in a split-bottom geometry considering various magnitudes of gravity and contact stiffnesses. While traditionally the inertial number, i.e., the ratio of stress to strain-rate time scales, is used to describe the flow rheology, we report that a second dimensionless number, the ratio of softness and stress time scales, must also be included to characterize the bulk flow behavior. For slow, quasistatic flows, the density increases while the effective (macroscopic) friction decreases with increase in either particle softness or local pressure. This trend is added to the μ I ( )rheology and can be traced back to the anisotropy in the contact network, displaying a linear correlation between the effective friction coefficient and deviatoric fabric in the steady state. When the external rotation rate is increased towards the inertial regime, for a given gravity field and contact stiffness, the effective friction increases faster than linearly with the deviatoric fabric.

It is widely recognized in particle technology that adhesive powders show a wide range of different bulk behavior due to the peculiarity of the particle interaction. We use Discrete Element simulations to investigate the effect of contact cohesion on the steady state of dense powders in a slowly sheared split-bottom Couette cell, which imposes a wide stable shear band. The intensity of cohesive forces can be quantified by the granular Bond number (Bo), namely the ratio between maximum attractive force and average force due to external compression. We find that the shear banding phenomenon is almost independent of cohesion for Bond numbers Bo < 1, but for Bo ≥ 1 cohesive forces start to play an important role, as both width and center position of the band increase for Bo > 1. Inside the shear band, the mean normal contact force is always independent of cohesion and depends only on the confining stress. In contrast, when the behavior is analyzed focusing on the eigen-directions of the local strain rate tensor, a dependence on cohesion shows up. Forces carried by contacts along the compressive and tensile directions are symmetric about the mean force (larger and smaller respectively), while the force along the third, neutral direction follows the mean force. This anisotropy of the force network increases with cohesion, just like the heterogeneity in all (compressive, tensile and neutral) directions.

Simulations are used to study the steady shear rheology of dense suspensions of frictional particles exhibiting discontinuous shear thickening and shear jamming, in which finite-range cohesive interactions result in a yield stress. We develop a constitutive model that combines yielding behavior and shear thinning at low stress with the frictional shear thickening at high stresses, in good agreement with the simulation results. This work shows that there is a distinct difference between solids below the yield stress and in the shear-jammed state, as the two occur at widely separated stress levels, separated by a region of stress in which the material is flowable.Introduction: Concentrated or "dense" suspensions of particles in liquid are found in both natural [1] and industrial settings [2][3][4]. Under shear, non-Brownian suspensions display a number of non-Newtonian properties; considering just the shear properties, these mixtures may undergo yielding, shear thinning, shear thickening or even jamming [5][6][7][8]. Such non-Newtonian rheology arises from particle interactions [7], influenced by the solid-fluid interfacial chemistry and chemical physics of both phases [9][10][11], as well as from frictional interactions between particles [12][13][14] that are influenced by roughness [15,16]. Suspensions of particles interacting by attractive forces can exhibit a yield stress and at larger stresses shear thicken, and, as discussed here, possibly jam. Shear thickening (ST), the increase of relative viscosity η r with increasing shear rateγ, can occur as continuous shear thickening (CST) or discontinuous shear thickening (DST) in dense suspensions; here the relative viscosity is normalized by the suspending fluid viscosity η 0 , η r = η(φ,γ)/η 0 , where φ is the volume fraction. The viscosity varies continuously withγ in CST, while DST is characterized by dη r /dγ → ∞ at some stress, often resulting in orders of magnitude increase in viscosity. It has been demonstrated that if φ is sufficiently large, the suspension can even become a shear-jammed (SJ) solid [17]; this solid is fragile, in the sense that it is maintained in this state by the imposed load, and would, for example, fail if the load is applied in the reverse direction [18]. A recent body of work [19][20][21][22][23][24] has related shear thickening to a transition from lubricated to frictional interactions of particles above an "onset stress." An approach capturing this two-state model [19] based on a mean-field description of the fraction of particle interactions that are frictional has been shown [25] to be successful in describing both the relative viscosity η r and normal stress differences found in simulations of shear thickening frictional suspensions.

Wet granular materials in a quasistatic steadystate shear flow have been studied with discrete particle simulations. Macroscopic quantities, consistent with the conservation laws of continuum theory, are obtained by time averaging and spatial coarse graining. Initial studies involve understanding the effect of liquid content and liquid properties like the surface tension on the macroscopic quantities. Two parameters of the liquid bridge contact model have been identified as the constitutive parameters that influence the macroscopic rheology (i) the rupture distance of the liquid bridge model, which is proportional to the liquid content, and (ii) the maximum adhesive force, as controlled by the surface tension of the liquid. Subsequently, a correlation is developed between these microparameters and the steady-state cohesion in the limit of zero confining pressure. Furthermore, as second result, the macroscopic torque measured at the walls, which is an experimentally accessible parameter, is predicted from our simulation results with the same dependence on the microparameters. Finally, the steady-state cohesion of a realistic non-linear liquid bridge contact model scales well with the steady-state cohesion for a simpler linearized irreversible contact model with the same maximum adhesive force and equal energy dissipated per contact. B Sudeshna Roy

We develop a statistical framework for the rheology of dense, non-Brownian suspensions, based on correlations in a space representing forces, which is dual to position space. Working with the ensemble of steady state configurations obtained from simulations of suspensions in two dimensions, we find that the anisotropy of the pair correlation function in force space changes with confining shear stress (σxy) and packing fraction (φ). Using these microscopic correlations, we build a statistical theory for the macroscopic friction coefficient: the anisotropy of the stress tensor, µ = σxy/P . We find that µ decreases (i) as φ is increased and (ii) as σxy is increased. Using a new constitutive relation between µ and viscosity for dense suspensions that generalizes the rate-independent one, we show that our theory predicts a Discontinuous Shear Thickening (DST) flow diagram that is in good agreement with numerical simulations, and the qualitative features of µ that lead to the generic flow diagram of a DST fluid observed in experiments.

The phenomenon of shear-induced jamming is a factor in the complex rheological behavior of dense suspensions. Such shear-jammed states are fragile, i.e., they are not stable against applied stresses that are incompatible with the stress imposed to create them. This peculiar flow-history dependence of the stress response is due to flow-induced microstructures. To examine jammed states realized under constant shear stress, we perform dynamic simulations of non-Brownian particles with frictional contact forces and hydrodynamic lubrication forces. We find clear signatures that distinguish these fragile states from the more conventional isotropic jammed states.