ANOMALOUS DIFFUSION OF MOMENTUM IN A DILUTE GAS-SOLID SUSPENSION

The velocity variations in a monodisperse suspension of solid particles settling in a gas are studied in the limit 1 << St << phi(-3/4), where phi is the volume fraction, St = mU/(6-pi-mu(f)a2) is the Stokes number, m is the mass of particles, a is their radius, U is their terminal velocity, and mu(f) is the viscosity of the suspending gas. In this limit, the particles' viscous relaxation time is small compared to a time scale for interparticle fluid dynamic interactions. Thus the particles act to enhance the effective density of the suspension. The velocity fluctuations induced by the body forces acting on the particles lead to a Reynolds stress that is described by a wave-number-dependent effective viscosity. This nonlocal viscosity causes a screening of the velocity disturbance of a particle at an O(a St-1/2-phi(-3/4)) radial separation; the screening yields finite O(U2 St-2/3) variances of the velocities of the gas and particles.