John R. Melrose

Shear thickening and order–disorder effects in concentrated colloids at high shear rates

The rheology and microstructure of concentrated colloidal suspensions, within the shear thickening regime, are investigated using Stokesian dynamics. We consider systems stabilized by charge and/or polymer layers, at hard core volume fractions above 40%. At φv=0.44, charge stabilized systems show transitions from ordered to disordered flow, with only a small increase in suspension viscosity. At higher φv, we observe larger jumps in viscosity with changes between order and disorder and vice versa. At high shear rates, interparticle gaps can become very small. This work investigates two ways in which these gaps may be controlled: by modifying the charge interaction potential [Dratler et al. (1997)], or by including a model for the presence of a polymer brush [Potanin and Russel (1995)]. The thickening observed is dependent on the gaps of closest approach of particles, but only weakly for hard sphere lubrication forces. Strong thickening is only observed with the presence of an enhanced lubricating force, in...

A simulation technique for many spheres in quasi-static motion under frame-invariant pair drag and Brownian forces

We report on details of a simulation technique for particles under quasi-static motion determined by a balance of conservative and dissipative interactions acting at the pair level. We develop frame-invariant and linear viscous interactions between pairs of translating and rotating spheres in a form suitable for computation. We report an o(N) method for generating Brownian forces correlated with a pair resistance tensor and show how explicit finite difference schemes lead naturally to an algorithm with Brownian motion and an estimate of the Brownian stress. We justify the algorithm by appeal to the second-order Langevin equation. We discuss the choice of time step and imposition of boundary conditions. We assess a model of this kind as an approximation for colloid spheres concentrated in a fluid medium under shear flow. It is noted that the algorithm is also that required for simulation, in the diffusive limit, of a technique known as dissipative particle dynamics. We report on structural effects in Brownian sphere colloids and their sensitivity to the model details. We argue that the approximation has heuristic value in the study of the rheology in concentrated colloid systems. Its predictions for the rheology of suspensions are in semi-quantitative agreement with experiment.

Metastable states and the kinetics of colloid phase separation

We report on the results of extensive Brownian dynamics simulations of colloid phase separation due to depletion flocculation. We study in detail the effect of potential variation at fixed volume fraction of colloid and fixed range of interaction. We find a variety of nonequilibrium behaviors for quenches into the colloid fluid+crystal phase coexistence regime. We present clear evidence of metastability, of homogeneous nucleation, and of a kinetically arrested gel state. We also find evidence that suggests a density instability in the metastable colloid fluid preceding crystal nucleation. Our findings are consistent with a previous proposal that nonequilibrium behavior is determined by a metastable vapor+liquid binodal hidden in the fluid+crystal phase coexistence regime.

Continuous shear thickening transitions in model concentrated colloids—The role of interparticle forces

The role of interactions between close particles in the shear thickening of concentrated colloids is examined by using a Stokesian dynamics simulation of model systems. The interactions are repulsive thermodynamic forces and lubrication forces. Three different models are contrasted in their thickening behavior: Brownian spheres, polymer coated spheres, and Hookian spheres. Respectively, they show: a “mild” continuous thickening, a “strong” continuous thickening, and a strain thickening with loss of steady state. The relationship of order-disorder transitions and thickening is examined. Depending on the volume fraction and range of repulsive forces, thickening can be observed with or without an order-disorder transition at its onset. The different thickening responses arise from the dependence of the relaxation time of close particle contacts on interparticle gap. A time-scale based criterion for strong thickening is proposed and supported by the simulations. A simple theoretical model based the motion of ...

Contact networks in continuously shear thickening colloids

Many body effects that occur in continuous shear thickening of concentrated colloid suspensions are examined by using a Stokesian dynamics simulation of model systems of polymer coated particles. The shear thickening state is probed in a number of ways: computed scattering intensities, imaging of density variation using Voronoi constructions, examination of the distribution of interparticle forces, and computation of the fabric of contacts. The shear thickening transition in these systems is found to be associated with the growth of a network of close particle contacts and shear induced density variations. This paper focuses on the network of contacts. The distributions of force magnitude are found to be exponential. The network directly relates to the normal stress differences. Both the data and simple physical argument suggest that thickening can be viewed as an approach to “jamming.”

The rheology and microstructure of concentrated, aggregated colloids

The rheology of concentrated, aggregated colloidal suspensions is determined through particulate simulations. Aggregating systems experience a large viscous enhancement over nonaggregating systems, this being due to the increase in the component of the viscosity arising from the repulsive colloid (thermodynamic) forces when attractive forces are present. The shear behavior of aggregating systems, for colloid volume fraction 0.47⩽φc⩽0.57, is characterized in the steady state regime over a wide range in shear rate, and is found to be power law, shear thinning η∼f(φc)γ−α, where the shear thinning index α=0.84±0.01. The effect of volume fraction enters as f(φc)=(1−φc/φmax)−1, with φmax=0.64, the value of random close packing; similarly, the viscosity also scales with the potential well depth as a power law, of index α. Consequently, we are able to deduce the full constitutive relation for this power law behavior. The associated structural features which emerge as a result of the imposed shear are identified ...

Brownian dynamics simulations of aging colloidal gels

The aging of colloidal gels is investigated using very long duration Brownian dynamics simulations. The Asakura-Oosawa description of the depletion interaction is used to model a simple colloid polymer mixture. Several regimes are identified during gel formation. The intermediate scattering function displays a double decay characteristic of systems where some kinetic processes are frozen. The beta relaxation at short times is explained in terms of the Krall-Weitz model for the decorrelation due to the elastic modes present. The alpha relaxation at long times is well described by a stretched exponential, showing a wide spectrum of relaxation times for which the q dependence is tau(alpha)=q(-2.2), lower than for diffusion. For the shortest waiting times, a combination of two stretched exponentials is used, suggesting a bimodal distribution. The extracted relaxation times vary with waiting time as tau(alpha)=tau(0.66)(w), more slowly than in the simple aging case. The real space displacements are found to be strongly non-Gaussian, correlated in space and time. We were unable to find clear evidence that the gel aging was driven by internal stresses. Rather, we hypothesize that in this case of weakly interacting gels, the aging behavior arises due to the thermal diffusion of strands, constrained by the percolating network, which ruptures discontinuously. Although the mechanisms differ, the similarity of some of the results to aging of glasses is striking.

Continuum percolation and depletion flocculation

Using Brownian dynamics simulations, we investigate continuum percolation in a system of colloid particles aggregating due to depletion flocculation. For all values of aggregating potential, there is a lower threshold volume fraction of colloid particles at which a percolating cluster appears. This threshold defines a percolation “phase” boundary that crosses the phase boundary between the colloid fluid phase and colloid fluid+crystal coexistence. In the two-phase coexistence regime, the lifetime of percolated clusters increases dramatically, and therefore the percolation threshold may be related to a transient gel threshold reported from experiment. In the phase coexistence regime, there is evidence of aging due to the thermal restructuring of clusters, implying a finite lifetime for percolating structures.

Stress Distributions in Flowing Aggregated Colloidal Suspensions

Simulations of the flow of concentrated aggregated colloidal systems, at the particulate level, are used to investigate the distribution of stresses in the shear-thinning regime. It is found that the distribution of shear stress carried by interparticle bonds decays approximately exponentially at large stresses, but with a double-exponential distribution for values of positive stress. The microstructural mechanisms associated with large stresses are manifested in clusters which dominate the positive contribution to the stress in the system. Towards the end of shear thinning the highest forces occur along bonds defining rods of particles aligned approximately along the flow-compression direction. We propose that the rheology of such systems is determined by a rupture–reformation process of these clusters of stress concentration during the flow. The aggregation forces play the role of enhancing such stress concentration by stabilizing clusters against buckling.

A numerical model for simulating mechanical behavior of flexible fibers

A numerical method is developed for simulating the mechanical behavior of flexible fibers. A circular crossed fiber is represented by a number of cylindrical segments linked by spring dash-pot systems. Segments are lined up and bonded to each neighbor. Each bond can be stretched or compressed by changing the bond distance. Bending deflection and twist movement occur, respectively, in the bending and torsion planes. While the bending angle is determined by the positions of two neighboring bonds, a reference twist vector is introduced to record the torsion motion along the segment chain. Fluid drag forces are calculated based on the Stokes’ Law, where a free draining assumption is made. The motion of the fiber is determined by solving the translational and rotational equations of individual segments. Computer simulation has been conducted to verify the single fiber model with elastic theory and excellent agreements have been found between the simulation results and the theory in various situations such as b...