Brownian dynamics simulations of model hard-sphere suspensions

Abstract

We compare the extensive experimental and simulation evidence for restructuring of colloidal systems under shear. New Brownian dynamics simulations are reported for the non-equilibrium phase behaviour of model dense suspensions under shear in the vicinity of 50% vol. fraction. We carried out simulations on two systems; particles interacting through the nearly hard-sphere continuous potential r − n , where n = 36, which we call the Continuous Potential Brownian Dynamics (CPBD) algorithm; and a new ‘potential-free’ algorithm designed to perform Brownian dynamics on model hard spheres. The latter Hard-Sphere Brownian Dynamics (HSBD) algorithm is stable to arbitrarily high Peclet Number (up to 12 000 at least, the maximum we tried). With this algorithm all the thermodynamic, mechanical and rheological properties reduce to simple expressions in terms of the pair-distribution function at contact g(σ) and a collision geometrical average matrix at contact of the spheres. The local structural changes under shear and the rheology are formally and simply related to one another as a result. At moderate volume fractions and high shear rate, the simulated hard-sphere suspensions manifest a shear-induced ordering into the so-called hexagonal shear-string (h.s.s.) phase but at higher volume fractions, we observe layers of particles normal to the shear gradient and, in some cases, regions of hexagonal ordering within the layer. Structure factors for the h.s.s. phase are consistent with neutron-and light-scattering data on sheared colloidal dispersions.