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, δ, to the sphere diameter, D, is in the range 0.03 < δ/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.

We investigate the growth of a mixing zone in the displacement of oil by a solvent. Such a zone usually takes the form of long thin fingers of solvent which protrude into the oil. However, despite the existence of reasonably good empirical models for the evolution of mixing zones, there is limited theoretical understanding of the observed growth. Of particular interest is the rate at which the leading edge of the mixing zone grows. In this paper we establish the structure of the mixing zone, and reveal a critical mechanism that plays a role in the growth of the leading edge of the mixing zone. It turns out that there is a close link between the growth rate of the mixing zone and a shape selection problem for Saffman–Taylor fingers.