The non-Newtonian rheology of dilute

The non-Newtonian rheology is calculated numerically to second order in the volume fraction in steady simple shear flows for Brownian hard spheres in the presence of hydrodynamic and excluded volume interactions. Previous analytical and numerical results for the low-shear structure and rheology are conrmed, demonstrating that the viscosity shear thins proportional to Pe2, where Pe is the dimensionless shear rate or Peclet number, owing to the decreasing contribution of Brownian forces to the viscosity. In the large Pe limit, remnants of Brownian diusion 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 Pe in the extensional zone downstream from the reference particle, leading to broken symmetry in the pair correlation function. As a result of this asymmetry and that in the boundary-layer, nite normal stress dierences are obtained as well as positive departures in the generalized osmotic pressure from its equilibrium value. The rst normal stress dierence changes from positive to negative values as Pe is increased when the hard-sphere limit is approached. This unusual eect 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 eects observed in concentrated suspensions by experiments and by Stokesian dynamics simulations are present also in dilute suspensions. 1