Exact Solution of the Equations of Axisymmetric Viscous Fluid Flow between Parallel Plates Approaching and Moving Apart from One Another

Abstract

The exact solutions of the Navier-Stokes equations in a fluid layer in between parallel plates moving so that the distance varies in accordance with an arbitrary-power law are investigated. The no-slip condition is imposed on the plate boundary. The exact solutions of the Navier-Stokes equations are constructed as series in powers of the Reynolds number. The cases of the decelerated motion in accordance with the time-square-root law, the uniform motion, and the uniformly accelerated motion of the plates are studied in detail. In the first of the cases mentioned above the series converge and in the other cases the solution is determined by means of asymptotic series. The critical Reynolds number which corresponds to the development of backflow is determined.