INERTIAL OSCILLATIONS IN THE IMPULSIVELY STARTED FLOW BETWEEN A POROUS INJECTOR AND AN IMPERMEABLE SUBSTRATE

The dynamic behaviour of impulsively started axisymmetric flow between a porous injector and an impermeable substrate is considered for the case where fluid is injected at a constant rate. Flow in the separate boundary layer regions near each disk are matched with the evolving in viscid core flow to provide approximate analytical solutions to the sh ort-time dynamics of the flow held. The short-time analytical solution s are valid for all Reynolds numbers where the flow remains laminar. T he intermediate and long-time dynamics of the fluid motion are analyse d using numerical methods. It is shown that this simple injection how can exhibit a wide range of interesting dynamic behaviours, the nature of which depend upon the size of the Reynolds number. In the vicinity of the impermeable substrate, under-damped inertial oscillations are present in large Reynolds number hows, whereas over-damped inertial os cillations are present in low Reynolds number hows. Critical-damping o f how near the impermeable substrate occurs at Re approximate to 9. Th e implications of inertial oscillation for electrochemical materials p rocessing are discussed.