Preprint of paper in J. Fluid Mechanics in lieu of annual report
The non–Newtonian rheology is calculated numerically to second order in the volume fraction in steady simple shear flows for Brownian spheres in the presence of hydrody- namic and excluded volume interactions. Previous analytical and numerical results for the low–shear structure and rheology are confirmed, demonstrating that the viscosity shear thins proportional to Pe2, where Pe is the dimensionless shear rate or P ́eclet num- ber, due to the decreasing contribution of Brownian forces to the viscosity. In the large Pe limit remnants of Brownian diffusion balance convection in a boundary–layer in the compressive region of the flow. In consequence, the viscosity shear thickens when this boundary–layer coincides with the near–contact lubrication regime of the hydrodynamic interaction. Wakes are formed at large P e in the extensional zone downstream from the reference particle, leading to broken symmetry in the pair correlation function. As a re- sult of this asymmetry and that in the boundary–layer, finite normal stress differences are obtained as well as positive departures in the osmotic pressure from its equilibrium value. The first normal stress difference changes from positive to negative values as Pe is increased when the hard–sphere limit is approached. This unusual effect is caused by the hydrodynamic lubrication forces that maintain particles in close proximity well into the extensional quadrant of the flow. The study demonstrates that many of the non– Newtonian effects observed in concentrated suspensions by experiments and by Stokesian Dynamics simulations are present also in dilute suspensions.