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Register a new userMicroscopic origin of frictional rheology in dense suspensions: correlations in force space
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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 ($sigma_{xy}$) and packing fraction ($phi$). Using these microscopic correlations, we build a statistical theory for the macroscopic friction coefficient: the anisotropy of the stress tensor, $mu = sigma_{xy}/P$. We find that $mu$ decreases (i) as $phi$ is increased and (ii) as $sigma_{xy}$ is increased. Using a new constitutive relation between $mu$ 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 $mu$ that lead to the generic flow diagram of a DST fluid observed in experiments.
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The presence and the microscopic origin of normal stress differences in dense suspensions under simple shear flows are investigated by means of inertialess particle dynamics simulations, taking into account hydrodynamic lubrication and frictional contact forces. The synergic action of hydrodynamic and contact forces between the suspended particles is found to be the origin of negative contributions to the first normal stress difference $N_1$, whereas positive values of $N_1$ observed at higher volume fractions near jamming are due to effects that cannot be accounted for in the hard-sphere limit. Furthermore, we found that the stress anisotropy induced by the planarity of the simple shear flow vanishes as the volume fraction approaches the jamming point for frictionless particles, while it remains finite for the case of frictional particles.
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.
Dense suspensions of particles are relevant to many applications and are a key platform for developing a fundamental physics of out-of-equilibrium systems. They present challenging flow properties, apparently turning from liquid to solid upon small changes in composition or, intriguingly, in the driving forces applied to them. The emergent physics close to the ubiquitous jamming transition (and to some extent the glass and gelation transitions) provides common principles with which to achieve a consistent interpretation of a vast set of phenomena reported in the literature. In light of this, we review the current state of understanding regarding the relation between the physics at the particle scale and the rheology at the macroscopic scale. We further show how this perspective opens new avenues for the development of continuum models for dense suspensions.
Dense suspensions of hard particles in a Newtonian liquid can be jammed by shear when the applied stress exceeds a certain threshold. However, this jamming transition from a fluid into a solidified state cannot be probed with conventional steady-state rheology because the stress distribution inside the material cannot be controlled with sufficient precision. Here we introduce and validate a method that overcomes this obstacle. Rapidly propagating shear fronts are generated and used to establish well-controlled local stress conditions that sweep across the material. Exploiting such transient flows, we are able to track how a dense suspension approaches its shear jammed state dynamically, and can quantitatively map out the onset stress for solidification in a state diagram.
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 $phi$ increases above a critical volume fraction, and discontinuous shear thickening (DST) is observed for a range of $phi$. 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 $(phi,tilde{sigma}$, and $mu)$, with $tilde{sigma} = sigma/sigma_0$ the dimensionless shear stress and $mu$ the coefficient of interparticle friction: the dimensional stress is $sigma$, and $sigma_0 propto F_0/ a^2$, 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 jammingtextquotedblright points at volume fraction $phi_{rm J}^0 = phi_{rm rcp}$ (random close packing) for the low-stress lubricated state, and at $phi_{rm J} (mu) < phi_{rm J}^0$ for any nonzero $mu$ 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.
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