Creeping couette flow over an undulated plate

Summary

Under creeping flow conditions, we consider the steady Couette flow of a newtonian fluid between two plates, one of them a plane, the other one with a sinusoidal profile. The streamlines of the flow are obtained from an exact analytical treatment of the Stokes equations by making use of complex function theory. This nonconventional approach, which has been recently developed for film flows, [16, 17], allows for a reduction of the problem to the solving of ordinary differential and integral equations for functions of one variable. Based on our calculations, we visualize the formation and evolution of vortices in the flow. The influence of the plate undulations and vortex structure on the drag force and flow rate is shown by parameter studies. We also discuss the classical lubrication approximation and its limitations. Taking the drag flow as a simple model for lubricant friction, we also discuss resulting friction coefficients and material transport of the lubricant.