Newtonian plane Couette flow with dynamic wall slip

Abstract

The occurrence of slip complicates the estimation of the viscosity in rheometric flows. Thus, special analyses and experimental protocols are needed in order to obtain reliable estimates of the viscosity and other rheological parameters. In the present work, the plane Couette flow of a Newtonian fluid is considered allowing the possibility of dynamic wall slip, i.e. slip with a slip-relaxation parameter, along the fixed plate. For comparison purposes, the analytical solution corresponding to static slip, i.e. to the Navier slip condition, is derived first. Then, the dynamic-slip solution is obtained using separation of variables as well as the one-sided Fourier transform method. Both methods give essentially the same results. The effects of the slip and slip-relaxation parameters on the solution are discussed. It is demonstrated that flow dynamics becomes slower in the presence of slip and decelerates further as the value of the slip-relaxation parameter is increased.