Couette Flow of a Dusty Incompressible Fluid with One of the Horizontal Moving Boundaries Suddenly Stopped

Abstract

The unsteady flow of an incompressible viscous fluid with a uniform distribution of dust particles between two parallel plates when one of which is impulsively stopped from the state of uniform motion is studied. Analytical expressions for velocities of the fluid and dust particles have been obtained. It is found that the dust particles slip on the wall which is brought to rest impulsively instead of sticking to it; on the other hand, they stick to the stationary plate. The slip-velocity of the dust is noticed to be decreasing as the physical time increases and the relaxation time of the dust particles decrease.