Chemical Engineering Communications, Vol.197, No.1, 76-91, 2010
RHEOLOGY OF SUSPENSIONS OF MASS-POLARIZED PARTICLES IN A GRAVITATIONAL FIELD
We derive the complete set of equations of motion for a suspension of mass-polarized rigid particles in a gravity field. The particles are acted upon by forces and couples exerted by the surrounding fluid and by the external gravity field. Besides their mass, momentum, and energy, the particles are characterized by their angular momentum and their (mass) polarization. We discuss the many cross-effects that involve their translational and angular velocities. The balance equations for the fluid phase are obtained from the ensemble average of the local Navier-Stokes equations, while the equations of motion for the particulate phase are obtained by ensemble-averaging the equations for a single particle, much like that in the kinetic theory of gases. We explain why this approach leads to a nonsymmetric stress tensor for the whole suspension, in contrast with the two-fluid approach in which the suspension stress tensor is perfectly symmetric for a suspension of this kind.