Hydrodynamics of a Suspension of Nondilute Stationary Spheres

The linear hydrodynamics of a stationary suspension of randomly distributed, nondilute spheres in an incompressible fluid is rigorously studied with the aid of a scaling expansion method. A space-time coarse graining is carried out in a manner consistent with an expansion in sphere concentration $c$ to obtain a linear macroscopic transport equation, which is local in time but nonlocal in space, to order $c^2$. Fluctuations around the macroscopic motion are also investigated and are shown to be small for dimension $d>\mathrm{}2\mathrm{}$.