Droplet levitation over a moving wall with a steady air film

Abstract

In isothermal non-coalescence behaviours of a droplet against a wall, an air film of micrometre thickness plays a crucial role. We experimentally study this phenomenon by letting a droplet levitate over a moving glass wall. The three-dimensional shape of the air film is measured using an interferometric method. The mean curvature distribution of the deformed free surface and the distributions of the lubrication pressure are derived from the experimental measurements. We vary experimental parameters, namely wall velocity, droplet diameter and viscosity of the droplets, over a wide range; for example, the droplet viscosity is varied over two orders of magnitude. For the same wall velocity, the air film of low-viscosity droplets shows little shape oscillation with constant film thickness (defined as the steady state), while that of highly viscous droplets shows a significant shape oscillation with varying film thickness (defined as the unsteady state). The droplet viscosity also affects the surface velocity of a droplet. Under our experimental conditions, where the air film shape can be assumed to be steady, we present experimental evidence showing that the lift force generated inside the air film balances with the droplet’s weight. We also verify that the lubrication pressure locally balances with the surface tension and hydrostatic pressures. This indicates that lubrication pressure and the shape of the free surface are mutually determined. Based on the local pressure balance, we discuss a process of determining the steady shape of an air film that has two areas of minimum thickness in the vicinity of the downstream rim.