The average stress in incompresible disperse flow

An analysis of the average stress in a disperse flow consisting of equal spherical particles suspended in a fluid is presented. Other than incompressibility, no assumptions are made on the rheological nature of the fluid. In particular, the Reynolds number of the particle motion relative to the fluid is arbitrary. The use of ensemble averages permits the consideration of spatially non-uniform systems, which reveals features not identified before. In particular, it is shown that, in general, the average stress is not symmetric, even when there are no external couples acting on the particles. A quantity to be identified with the mixture pressure (including the particle contribution) is identified. The structure of the momentum equations for the fluid and particle phases is systematically derived. As an example, the case of particles suspended in a locally Stokes flow is considered.