Structure, diffusion and rheology of Brownian suspensions by Stokesian Dynamics simulation

Abstract

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

A simple paradigm for active and nonlinear microrheology

“…Furthermore, this limit has been surprisingly effective in reproducing experimental measurements of the shear viscosity of colloidal suspensions, for which all particles are equivalent ͑a = b͒. [30][31][32][33] Remarkably, the effective shear viscosity derived from the infinite limit does not differ appreciably from the results for as small as 1.1. ͑Khair and Brady find this also holds for the microviscosity when a = b.…”

“…The volume fraction dependence of all hydrodynamic functions were captured by this simple rescaling and the remaining volume fraction dependence came from structural deformations ͑e.g., at low or high Péclet͒, which could be estimated from the pair problem; hydrodynamics could be neglected completely for shear thinning, while for shear thickening only knowledge of the boundary layer was necessary. 32 The structure of the microrheology problem suggests that this simple, but powerful, approximation should be applicable and we use it in what follows.…”

First normal stress difference and crystallization in a dense sheared granular fluid

“…For example, in non-Brownian viscous suspensions, N 1 changes sign at high Peclet number 31,32 . However, the reason for this effect is quite different in granular fluids as we show below.…”

Short-time transport properties in dense suspensions: From neutral to charge-stabilized colloidal spheres

“…Earlier applications of the non-accelerated (see, e.g., [16][17][18][19]) and accelerated Stokesian dynamics method [13,20] pioneered by Brady and coworkers, have dealt with systems of neutral hard spheres. In addition, short-time properties of colloidal hard spheres have been computed in earlier simulation work based on the hydrodynamic force multipoles method [21], and on the fluctuating Lattice-Boltzmann (LB) method [5,[22][23][24][25][26].…”