Flow Induced by an Oscillating Infinite Flat Plate in a Dusty Gas

The flow induced in an incompressible dusty gas by an infinite flat plate oscillating in its own plane is studied. The differential equation describing this problem is given; its form exhibits the relaxation from a frozen-diffusion process (corresponding to a clean gas) to an equilibrium-diffusion process (corresponding to a single heavier gas). The gas velocity profile, shear stress on the plate, and the particle velocity profile are obtained exactly and are discussed in terms of the parameters of the problem. The essential feature is the inhibition of viscous diffusion in the gas by the particle-gas velocity relaxation. Mechanical energy dissipation is discussed.