The skidding of an elliptic plate on a wet surface

Abstract

A viscous fluid separates a massed, sliding, free elliptic plate and a smooth bottom plate. Due to the weight, the gap width between the plates decreases. The increased viscous drag eventually stops the skidding. The Navier-Stokes equations are expanded in terms of a small squeeze number. It is found that the gap width decrease as (time)^−1/2 and the maximum skidding distance depends on five nondimensional groups. An example shows it is easier for the elliptic plate to side longitudinally than laterally.