Dynamic Simulations of Hard-Sphere Suspensions Under Steady Shear

Abstract

We have studied the flow of suspensions of solid spheres under steady shear using a newly developed flow simulator. For the first time, the complicated interplay between hydrodynamic interactions and solids' variable configuration under flo$ conditions in which large departures from equilibrium configurations occur can be simulated in full 3D. For volume fractions up to 35%, viscosities have been obtained that are in excellent agreement with experiments reported in the literature.Determining the steady-shear viscosity of a suspension of equally sized hard spheres in a Newtonian fluid may be regarded as a basic model problem for studying suspension behaviour. The monodisperse hard-sphere system has been extensively studied, experimentally [1,2], theoretically [3-91, and by computer simulations [lo, 111. The theoretical and simulation efforts up to now had to make simplifying assumptions, because full treatment of all relevant aspects, i.e. multibody hydrodynamic interactions, Brownian motion and temporal and spatial correlation of sphere positions in a flow field, is extremely difficult. Usually, one or more aspects are ignored, and the validity of the resulting viscosity data is limited to extreme (from a practical point of view less relevant) cases: dilute suspensions [3,4], equilibrium sphere configurations [4-lo], or sphere monolayers [ 111.In contrast, practical applications usually deal with concentrated suspensions at shear rates giving rise to nonequilibrium configurations. This can easily be seen by considering the two relevant time scales: 1) the time over which Brownian diffusion restores the equilibrium configuration, R 2 / D o (here R represents the sphere radius and Do = kT/6xpoR the single-sphere diffusion coefficient with po the solvent viscosity), and 2) the time needed for the flow to perturb the microstructure significantly: l/f (with i. the shear rate). The ratio between these two time scales, the Peclet number Pe = f R z /Do, measures the <<amount of departure. from equilibrium. Unless the suspended particles are of submicron size, the Peclet number-being proportional to R3-will be large compared to unity. This means that

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