Dynamics of a suspension of a random array of spheres in a Navier–Stokes fluid

An effective medium theory of the screening of hydrodynamic interactions in a suspension of randomly distributed immobile spheres in a Navier–Stokes fluid is presented. We consider the shear viscosity for a stationary suspension of penetrable spheres, where the fluid flow is generated by the motion of a single labeled sphere with uniform velocity. We also derive the tracer friction coefficient at arbitrary filling fractions (φ) of the immobile spheres. By a self-consistent calculation, the shear velocity (η) of the suspension is found to diverge nonexponentially at a filling fraction of 0.49, much lower than the closest random packing filling fraction: η∼[(1/φ)−(1/0.49)]−2.12⋅⋅⋅. The friction coefficient of the labeled mobile sphere is also found to diverge similar to η.