Brownian dynamics simulation of a hard-sphere suspension

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Abstract
In this paper we discuss the nonequilibrium shear viscosity of a suspension of hard spheres that is modeled by neglecting hydrodynamic interactions in a consistent way. The aim is to establish the true capabilities of this model in predicting the properties of real suspensions. A Brownian dynamics algorithm is used to simulate the movements of hard spheres immersed in a Newtonian solvent in a nonequilibrium steady shear flow. A new development is the treatment of the overlap of spheres as elastic collisions, to simulate the no-flux boundary condition on the surfaces of rigid particles. This algorithm is compared with other algorithms suggested in the literature, and is shown to be simple and accurate even for two spheres at close distance. This provides an algorithm that is very suitable for calculating the pair distribution function and especially its hard-sphere contact value, both in equilibrium and nonequilibrium simulations. The algorithm is used to study the nonequilibrium stationary shear flow in the low shear limit. The simulations correctly reproduce the exact low-density limit of the perturbation of the pair distribution function. The perturbation of the pair distribution function in shear flow can be extracted from the simulation data and used to compute the stationary shear viscosity for a system of diffusing hard spheres without hydrodynamic interactions. This yields a flow curve for this model system including the low shear limit. It is found that the model shear viscosity fails at intermediate and high shear rates as can be expected from the neglect of hydrodynamic interactions, but also in the low shear limit at small and moderate volume fractions.