Normal viscosity and Viscous resuspension of non-Brownian suspensions

Normal stresses in sheared suspensions of non-Brownian particles are obtained from numerical simulations in the viscous regime. The stresses are determined in homogeneous shear of non-buoyant particles and by analyzing shear-induced resuspension of buoyant particles in the framework of the suspension balance model (SBM). The consistency of both approaches indicates that the SBM describes the steady state properly. The results are in agreement with some earlier empirical expressions of the normal viscosity coefficients in limited ranges of particle volume fractions, but they appear to overestimate the stresses in the semi-dilute regime (solid fraction in the range 25-35\%). New expressions are proposed for. We show that these discrepancies can be due to inertial effects which appear at rather low particle Reynolds number. The results also highlight that the normal stress anisotropy depends on the volume fraction.