The equations of motion of the particles and the interstitial fluid are averaged using a ’soft’ spatial averaging procedure, thus generating equations relating local average values of the fluid pressure, the fluid velocity, and the velocity and angular velocity of the particles. Terms whose form is not related to the above average variables are shown to be expressible as average values of tenser-weighted integrals of the forces exerted on the surface of a particle by the fluid, or by contact with other particles. Other undetermined terms relate to momentum transport by velocity fluctuations about the average values. It is shown that the equations can be reduced to closed forms, entirely in terms of the averaged variables, in the limiting case of Stokesian particles at very low concentration.