The steady streaming generated by a vibrating plate parallel to a fixed plate in a dusty fluid

A viscous dusty fluid between two parallel plates, when the top plate is performing both normal and lateral small translatory oscillations, is considered. The unsteady Navier-Stokes equations are solved using the perturbation method. It is observed that nonlinear Reynolds stress introduces a secondary steady streaming. Normal oscillations induce a steady lift while the interaction between normal and lateral oscillations causes a directional net flux. The system thus is seen to be operating as a valveness pump with rigid walls. The presence of dust particles has accelerated the rate of increase of the lift forces. Net pumping is computed for both the fluid and the dust, and certain significant conclusions are drawn for the case Re = 1.