The non-equilibrium behaviour of concentrated colloidal dispersions is studied using Stokesian Dynamics, a molecular-dynamics-like simulation technique for analysing suspensions of particles immersed in a Newtonian fluid. The simulations are of a monodisperse suspension of Brownian hard spheres in simple shear flow as a function of the Péclet number, P e, which measures the relative importance of hydrodynamic and Brownian forces, over a range of volume fraction 0.316 6 φ 6 0.49. For P e < 10, Brownian motion dominates the behaviour, the suspension remains well-dispersed, and the viscosity shear thins. The first normal stress difference is positive and the second negative. At higher P e, hydrodynamics dominate resulting in an increase in the long-time self-diffusivity and the viscosity. The first normal stress difference changes sign when hydrodynamics dominate. Simulation results are shown to agree well with both theory and experiment. IntroductionSuspensions of small particles dispersed in a fluid occur in a variety of natural and industrial settings, such as slurries, paints, pastes, many foodstuffs, and ceramic sols. In these microstructured fluids the suspended particles interact through hydrodynamic, interparticle, and Brownian (or thermal) forces. The balance between thermal and interparticle forces determines the equilibrium behaviour. Under the action of an external driving force such as shear, hydrodynamic forces come into play and compete with thermal and interparticle forces to set the structure and determine properties. There have been a number of experiments on well-characterized model hard-sphere systems (de Kruif et al. 1985;Ackerson 1990; etc.) that have greatly advanced our understanding of colloidal dispersions, and, along with scaling theories for the behaviour at high solids concentration (Brady 1993b;Brady & Morris 1997) and Stokesian Dynamics simulations (Bossis & Brady 1984Brady & Bossis 1985, 1988Phung & Brady 1992;Phung 1993;Phung, Brady & Bossis 1996;Dratler & Schowalter 1996) a complete picture is emerging.In this work we report on Stokesian Dynamics simulation studies of rheology, diffusion, and structure of concentrated monodisperse suspensions of hard spheres. Stokesian Dynamics is a general molecular-dynamics-like method for simulating suspensions at low particle Reynolds number that accurately calculates the manybody interactions necessary to capture the hydrodynamic forces transmitted through the fluid. In a hard-sphere suspension particles interact through hydrodynamic and

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The behaviour of the long-time self-diffusion tensor in concentrated colloidal dispersions is studied using dynamic simulation. The simulations are of a suspension of monodisperse Brownian hard spheres in simple shear flow as a function of the Péclet number, Pe, which measures the relative importance of shear and Brownian forces, and the volume fraction, φ. Here, Pe =γa 2 /D 0 , whereγ is the shear rate, a the particle size and D 0 = kT /6πηa is the Stokes-Einstein diffusivity of an isolated particle of size a with thermal energy kT in a solvent of viscosity η. Two simulations algorithms are used: Stokesian Dynamics for inclusion of the many-body hydrodynamic interactions, and Brownian Dynamics for suspensions without hydrodynamic interactions. A new procedure for obtaining high-quality diffusion data based on averaging the results of many short simulations is presented and utilized. At low shear rates, low Pe, Brownian diffusion due to a random walk process dominates and the characteristic scale for diffusion is the Stokes-Einstein diffusivity, D 0 . At zero Pe the diffusivity is found to be a decreasing function of φ. As Pe is slowly increased, O(Pe) and O(Pe 3/2 ) corrections to the diffusivity due to the flow are clearly seen in the Brownian Dynamics system in agreement with the theoretical results of Morris & Brady (1996). At large shear rates, large Pe, both systems exhibit diffusivities that grow linearly with the shear rate by the non-Brownian mechanism of shear-induced diffusion. In contrast to the behaviour at low Pe, this shear-induced diffusion mode is an increasing function of φ. Long-time rotational self-diffusivities are of interest in the Stokesian Dynamics system and show similar behaviour to their translational analogues. An off-diagonal long-time self-diffusivity, D xy , is reported for both systems. Results for both the translational and rotational D xy show a sign change from low Pe to high Pe due to different mechanisms in the two regimes. A physical explanation for the off-diagonal diffusivities is proposed.

The rheology during the start-up and cessation of simple shear flow has been investigated for near hard-sphere colloidal suspensions. Simulations augmented by theoretical analysis are used to determine how the non-Newtonian stress development and relaxation depend on the microstructure. Accelerated Stokesian dynamics (ASD) and Brownian dynamics (BD) simulations are used for 0.05 Pe 500 in concentrated freely flowing suspensions; the P eclet number defining the ratio of shear to thermal motion is Pe ¼ 3pg_ ca 3 =kT with g the suspending fluid viscosity, _ c the shear rate, and kT the thermal energy. Theoretical predictions based on the Smoluchowski equation for dilute suspensions are made, and these are primarily used for comparison with results from BD simulations in which hydrodynamic interactions are neglected. For suspensions with hydrodynamics, simulations by ASD are used to probe start-up and flow cessation over a large range of Pe; these studies focus on solid volume fraction / ¼ 0:4, with more limited examinations at other /. The use of both BD and ASD simulations allows us to discriminate hydrodynamic interaction effects on the suspension rheology. The Brownian stresses computed by either method exhibit overshoots of their steady state value during the start-up of shear flow. The overshoots occur at strain amplitudes which depend on Pe, and the overshoot is described by a model based on extension of the concept of cage-breaking from glass dynamics. Results from the relaxation of a sheared suspension show that the distortion of the pair distribution function from its equilibrium form has a fast radial relaxation and a slow angular relaxation. The various rheometric functions (relative viscosity; first and second normal stress differences) are found to respond on different timescales, reflecting their different dependences on the flow-induced structure. A re-examination of steady shear flow allows us to find normal stress differences which tend properly toward zero at small Pe, unlike prior work; the discrepancy is found to be due to finite size scaling, as small simulations used in prior work resulted in excessively large normal stress responses at small Pe. V