Kinetic approach to non-linear soft-glassy rheology

2006

We review models for the rheology of soft glasses, a class of materials including e.g. emulsions, foams, colloidal glasses and possibly-but with substantial caveats-gels. The main focus is on the soft glassy rheology (SGR) model, and in particular on the occurrence of rheological aging effects. We first review appropriate definitions of rheological response functions suited to aging samples (in which time translation invariance is lost). These are then used to study aging effects within the SGR model. Its constitutive equations relate shear stress to shear strain among a set of elastic elements, with distributed yield thresholds, undergoing activated dynamics governed by a "noise temperature", x. For 1 < x < 2 there is a power-law fluid regime in which transients occur, but no aging. For x < 1, the model has a macroscopic yield stress. So long as this yield stress is not exceeded, aging occurs, with a sample's apparent relaxation time being of the order of its own age. The (age-dependent) linear viscoelastic loss modulus G (ω, t) rises as frequency is lowered, but falls with age t, so as to always remain less than G (ω, t) (which is nearly constant). Significant aging is also predicted for the stress overshoot in nonlinear shear startup and for the creep compliance. We discuss an extension of the model to include a proper tensorial description of stress and strain, and survey some related rheological models that have recently been developed.

Journal of Physics: Condensed Matter

Glassy solids may undergo a fluidization (yielding) transition upon deformation whereby the material starts to flow plastically. It has been a matter of debate whether this process is controlled by a specific time scale, from among different competing relaxation/kinetic processes. Here, two constitutive models of cage relaxation are examined within the microscopic model of nonaffine elasto-plasticity. One (widely used) constitutive model implies that the overall relaxation rate is dominated by the fastest between the structural (α) relaxation rate and the shearinduced relaxation rate. A different model is formulated here which, instead, assumes that the slowest (global) relaxation process controls the overall relaxation. We show that the first model is not compatible with the existence of finite elastic shear modulus for quasistatic (low-frequency) deformation, while the second model is able to describe all key features of deformation of 'hard' glassy solids, including the yielding transition, the nonaffine-to-affine plateau crossover, and the rate-stiffening of the modulus. The proposed framework provides an operational way to distinguish between 'soft' glasses and 'hard' glasses based on the shear-rate dependence of the structural relaxation time.

Soft Matter, 2010

In this paper, we investigate the rheological behavior of jammed emulsions in microchannels on the basis of microvelocimetry techniques. We demonstrate that velocity profiles in this confined geometry cannot be accounted for by the bulk-Herschel-Bulkley-rheological flow curve measured independently in a rheometer. A strong dependence of the flow behavior on the confinement, pressure drop and surface roughness is evidenced, which cannot be described by classical rheological descriptions. We show that these behaviors can be rationalized on the basis of a non local rheological model, introducing the notion of local fluidity as a key rheological quantity. The model reproduces the experimental velocity profiles for any confinements and any surface nature. The non-locality is quantified by a length, z, characterizing the flow cooperativity of jammed emulsions, and typically of the order of several emulsion droplet diameters. We study the influence of volume fraction, droplet diameter, and emulsions polydispersity on this length.

Physical Review Letters, 2012

Using confocal microscopy, we study the flow of a model soft glassy material: a concentrated emulsion. We demonstrate the micro-macro link between in situ measured movements of droplets during the flow and the macroscopic rheological response of a concentrated emulsion, in the form of scaling relationships connecting the rheological ''fluidity'' with local standard deviation of the strain-rate tensor. Furthermore, we measure correlations between these local fluctuations, thereby extracting a correlation length which increases while approaching the yielding transition, in accordance with recent theoretical predictions.

Soft Matter

Physical Review E, 2012

Mesoscopic models play an important role in our understanding of the deformation and flow of amorphous materials. One such description, based on the Shear Transformation Zone (STZ) theory, has recently been re-formulated within a non-equilibrium thermodynamics framework, and found to be consistent with it. We show here that a similar interpretation can be made for the Soft Glassy Rheology (SGR) model. Conceptually this means that the "noise temperature" x, proposed phenomenologically in the SGR model to control the dynamics of a set of slow mesoscopic degrees of freedom, can consistently be interpreted as their actual thermodynamic temperature. (Because such modes are slow to equilibrate, this generally does not coincide with the temperature of the fast degrees of freedom and/or heat bath.) If one chooses to make this interpretation, the thermodynamic framework significantly constrains extensions of the SGR approach to models in which x is a dynamical variable. We assess in this light some such extensions recently proposed in the context of shear banding.

Soft Matter, 2011

Physical Review E, 2013

The Soft Glassy Rheology (SGR) model is a mesoscopic framework which proved to be very successful in describing flow and deformation of various amorphous materials phenomenologically (e.g. pastes, slurries, foams etc). In this paper, we cast SGR in a general, model independent framework for nonequilibrium thermodynamics called General Equation for the Nonequilibrium Reversible-Irreversible Coupling (GENERIC). This leads to a new formulation of SGR which clarifies how it can properly be coupled to hydrodynamic fields, resulting in a thermodynamically consistent, local, continuum version of SGR. Additionally, we find that compliance with thermodynamics imposes the existence of a modification to the stress tensor as predicted by SGR.

Physical Review Letters, 2012

We explore numerically the shear rheology of soft repulsive particles at large volume fraction. The interplay between viscous dissipation and thermal motion results in multiple rheological regimes encompassing Newtonian, shear-thinning and yield stress regimes near the 'colloidal' glass transition when thermal fluctuations are important, crossing over to qualitatively similar regimes near the 'jamming' transition when dissipation dominates. In the crossover regime, glass and jamming sectors coexist and give complex flow curves. Although glass and jamming limits are characterized by similar macroscopic flow curves, we show that they occur over distinct time and stress scales and correspond to distinct microscopic dynamics. We propose a simple rheological model describing the glass to jamming crossover in the flow curves, and discuss the experimental implications of our results. PACS numbers: 62.20.-x, 83.60.La, 83.80.Iz

Nature, 2008

Physical Review Letters, 2009

A kinetic model for the elasto-plastic dynamics of a flowing jammed material is proposed, which takes the form of a non-local-Boltzmann-like-kinetic equation for the stress distribution function. Coarse-graining this equation yields a non-local constitutive law for the flow, introducing as a key dynamic quantity the local rate of plastic events. This quantity, interpreted as a local fluidity, is spatially correlated, with a correlation length diverging in the quasi-static limit, i.e. close to yielding. We predict finite size effects in the flow behavior, as well as the absence of an intrinsic local flow curves. These features are supported by recent experimental and numerical observations.

Physical Review Letters, 2011

We present an effective time approach to predict long and short time rheological behavior of soft glassy materials from experiments carried out over practical time scales. Effective time approach takes advantage of relaxation time dependence on aging time that allows time-aging time superposition even when aging occurs over the experimental timescales. Interestingly experiments on variety of soft materials demonstrate that the effective time approach successfully predicts superposition for diverse aging regimes ranging from subaging to hyper-aging behaviors. This approach can also be used to predict behavior of any response function in molecular as well as spin glasses.

2010

As the glass transition is approached from the high temperature side, viewed as a liquid, the properties of the ever more viscous supercooled liquid are continuous functions of temperature and pressure. The point at which we decide to classify the fluid as a solid is therefore subjective. This subjective decision does, however, have discontinuous consequences for how we determine the rheological properties of the glass. We apply the recently discovered relaxation theorem to the time independent, nondissipative, nonergodic glassy state to derive an expression for the phase space distribution of an ensemble of glass samples. This distribution is then used to construct a time dependent linear response theory for aged glassy solids. The theory is verified using molecular dynamics simulations of oscillatory shear for a realistic model glass former with excellent agreement being obtained between the response theory calculations and direct nonequilibrium molecular dynamics calculations. Our numerical results confirm that unlike all the fluid states, including supercooled liquids, a solid glass ͑in common with crystalline states͒ has a nonzero value for the zero frequency shear modulus. Of all the states of matter, a supercooled fluid approaching the glass transition has the highest value for the limiting zero frequency shear viscosity. Finally, solid glasses like dilute gases and crystals have a positive temperature coefficient for the shear viscosity whereas supercooled and normal liquids have a negative temperature coefficient.

Soft Matter, 2013

Journal of Rheology, 2020

Soft particle glasses are amorphous materials made of soft and deformable particles that are jammed above close-packing. They behave like weak solids at rest but they yield and flow under external mechanical constraints. Although soft particle glasses are widely used in applications, little is known about how the particle softness and microscopic dynamics determine the macroscopic rheology. Here we use three-dimensional particle dynamic simulations to analyze the dynamical properties of soft particle glasses at different scales. We demonstrate how the dynamics is determined by the persistence time and the magnitude of the fluctuating elastic forces that develop at contact in the flow. The shear-induced diffusion coefficient, the local structural relaxation times, the shear stress, and the normal stress differences are interconnected through simple relationships that allow the prediction of the macroscopic rheology from the microscopic dynamics.