Brownian motion of non-wetting droplets held on a flat solid by gravity

Department of Mathematics, University of Arizona - Tucson, AZ 85721-0089, USA

Received: 16 August 2013
Accepted: 12 December 2013

Abstract

At equilibrium a small liquid droplet standing on a solid (dry) horizontal surface it does not wet rests on this surface on a small disc. As predicted and observed if such a droplet is in a low-viscosity vapor the main source of drag for a motion along the surface is the viscous dissipation in the liquid near the disc of contact. This dissipation is minimized by a Huygens-like motion coupling rolling and translation in such a way that the fluid near the disc of contact is almost motionless with respect to the solid. Because of this reduced drag and the associated large mobility the coefficient of Brownian diffusion is much larger than its standard Stokes-Enstein value. This is correct if the weight of the droplet is sufficient to keep it on the solid, instead of being lifted by thermal noise. The coupling between translation along the surface and rotation could be measured by correlated random angular deviations and horizontal displacement in this Brownian motion.