The stress in a non-uniform suspension of heavy particles

The ensemble averaged stress system in a non-uniform suspension of equal spheres subject to external forces or torques is considered. It is found that, as a consequence of the spatial non-uniformity of the system, new terms arise both in the symmetric and antisymmetric parts of the bulk stress. In particular, a new antisymmetric contribution is found even in the absence of external torques. All these terms depend on the particle volume fraction but are independent of the particle size. At low concentrations these results are established by a new formulation of the renormalization technique while, at finite concentrations, a combination of ensemble averaging and numerical simulation is used.