Direct verification of the lubrication force on a sphere travelling through a viscous film upon approach to a solid wall

Abstract

Experiments were performed to observe the motion of a solid sphere approaching a solid wall through a thin layer of a viscous liquid. We focus mainly on cases where the ratio of the film thickness, ℘, to the sphere diameter, D, is in the range 0.03 ℘</D < 0.09 and the Stokes number, St, a measure of the sphere inertia to viscous forces, is below a critical level Stc so that the spheres do not rebound and escape from the liquid layer. This provides us with the scope to verify the force acting on the sphere, derived from lubrication theory. Using high-speed video imaging we show, for the first time, that the equations of motion based on the lubrication approximation correctly describe the deceleration of the sphere when St < Stc. Furthermore, we show that the penetration depth at which the sphere motion is first arrested by the viscous force, which decreases with increasing Stokes number, matches well with theoretical predictions. An example for a shear-thinning liquid is also presented, showing that this simple set-up may be used to deduce the short-time dynamical behaviour of non-Newtonian liquids. © 2010 Cambridge University Press.