Effect of pulsations on two-layer channel flow

The effect of vertical wall vibrations on two-phase channel flow is examined. The basic flow consists of two superposed fluid layers in a channel whose walls oscillate perpendicular to themselves in a prescribed, time-periodic manner. The solution for the basic flow is presented in closed form for Stokes flow, and its stability to small periodic perturbations is assessed by means of a Floquet analysis. It is found that the pulsations have a generally destabilizing influence on the flow. They tend to worsen the Rayleigh-Taylor instability present for unstably stratified fluids; the larger the amplitude of the pulsations, the greater the range of unstable wave numbers. For stably stratified fluids, the pulsations raise the growth rate of small perturbations, but are not sufficient to destabilize the flow. In the latter part of the paper, the basic flow for arbitrary Reynolds number is computed numerically assuming a flat interface, and the motion of the interface in time is predicted. The existence of a time-periodic flow is demonstrated in which the ratio of the layer thicknesses remains constant throughout the motion.