Linear dynamics of dilute hard-sphere suspensions

We study the linear dynamics of a dilute dispersion of solid spherical particles in an incompressible viscous fluid. We start from a rest situation, in which the spheres are assumed to be distributed at random. The rest situation is perturbed linearly by small oscillatory applied forces and torques acting on the solute particles, and by an oscillatory force density acting on the fluid. By averaging over an ensemble of rest configurations we obtain linear average equations of motion for the two-phase system with well-defined transport coefficients. We evaluate the transport coefficients as a function of wavenumber and frequency to first order in the volume fraction.