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 c
hanges 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.
Under an applied traction, highly concentrated suspensions of solid particles in fluids can turn from a state in which they flow to a state in which they counteract the traction as an elastic solid: a shear-jammed state. Remarkably, the suspension ca
n turn back to the flowing state simply by inverting the traction. A tensorial model is presented and tested in paradigmatic cases. We show that, to reproduce the phenomenology of shear jamming in generic geometries, it is necessary to link this effect to the elastic response supported by the suspension microstructure rather than to a divergence of the viscosity.
We consider extensional flows of a dense layer of spheres in a viscous fluid and employ force and torque balances to determine the trajectory of particle pairs that contribute to the stress. In doing this, we use Stokesian dynamics simulations to gui
de the choice of the near-contacting pairs that follow such a trajectory. We specify the boundary conditions on the representative trajectory, and determine the distribution of particles along it and how the stress depends on the microstructure and strain rate. We test the resulting predictions using the numerical simulations. Also, we show that the relation between the tensors of stress and strain rate involves the second and fourth moments of the particle distribution function.
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 volu
me 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 origin of the abrupt shear thickening observed in some dense suspensions has been recently argued to be a transition from frictionless (lubricated) to frictional interactions between immersed particles. The Wyart-Cates rheological model, built on
this scenario, introduced the concept of fraction of frictional contacts $f$ as the relevant order parameter for the shear thickening transition. Central to the model is the equation-of-state relating $f$ to the applied stress $sigma$, which is directly linked to the distribution of the normal components of non-hydrodynamics interparticle forces. Here, we develop a model for this force distribution, based on the so-called $q$-model that we borrow from granular physics. This model explains the known $f(sigma)$ in the simple case of sphere contacts displaying only sliding friction, but also predicts strong deviation from this usual form when stronger kinds of constraints are applied on relative motion. We verify these predictions in the case of contacts with rolling friction, in particular a broadening of the stress range over which shear thickening occurs. We finally discuss how a similar approach can be followed to predict $f(sigma)$ in systems with other variations from the canonical system of monodisperse spheres with sliding friction, in particular the case of large bidispersity.
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 cr
eate 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.
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 con
tact 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.
Dense suspensions are non-Newtonian fluids which exhibit strong shear thickening and normal stress differences. Using numerical simulation of extensional and shear flows, we investigate how rheological properties are determined by the microstructure
which is built under flows and by the interactions between particles. By imposing extensional and shear flows, we can assess the degree of flow-type dependence in regimes below and above thickening. Even when the flow-type dependence is hindered, nondissipative responses, such as normal stress differences, are present and characterise the non-Newtonian behaviour of dense suspensions.
We introduce a general decomposition of the stress tensor for incompressible fluids in terms of its components on a tensorial basis adapted to the local flow conditions, which include extensional flows, simple shear flows, and any type of mixed flows
. Such a basis is determined solely by the symmetric part of the velocity gradient and allows for a straightforward interpretation of the non-Newtonian response in any local flow conditions. In steady homogeneous flows, the material functions that represent the components of the stress on the adapted basis generalize and complete the classical set of viscometric functions used to characterize the response in simple shear flows. Such a general decomposition of the stress is effective in coherently organizing and interpreting rheological data from laboratory measurements and computational studies in non-viscometric steady flows of great importance for practical applications. The decomposition of the stress in terms with clearly distinct roles is also useful in developing constitutive models.
Dynamic particle-scale numerical simulations are used to show that the shear thickening observed in dense colloidal, or Brownian, suspensions is of a similar nature to that observed in non-colloidal suspensions, i.e., a stress-induced transition from
a flow of lubricated near-contacting particles to a flow of a frictionally contacting network of particles. Abrupt (or discontinuous) shear thickening is found to be a geometric rather than hydrodynamic phenomenon; it stems from the strong sensitivity of the jamming volume fraction to the nature of contact forces between suspended particles. The thickening obtained in a colloidal suspension of purely hard frictional spheres is qualitatively similar to experimental observations. However, the agreement cannot be made quantitative with only hydrodynamics, frictional contacts and Brownian forces. Therefore the role of a short-range repulsive potential mimicking the stabilization of actual suspensions on the thickening is studied. The effects of Brownian and repulsive forces on the onset stress can be combined in an additive manner. The simulations including Brownian and stabilizing forces show excellent agreement with experimental data for the viscosity $eta$ and the second normal stress difference $N_2$.
