Motion of a massive particle attached to a spherical interface: statistical properties of the particle path

Abstract

We have studied the motion of a Brownian particle on a spherical interface under gravity, with the aim of setting up a protocol to measure the friction (f) felt by such a particle in experimental conditions. Our analysis is based on the Schmoluchowski equation for particle motion. Essentially we derive a practical criterion to find f from the average particle path. Our statements are illustrated by a few experimental and numerical examples. Numerical paths are obtained by computer simulation and experimental paths are those of micrometre-sized latex or glass particles attached to spherical giant lipid (SOPC) vesicles. From experimental values of f, we estimate the surface shear viscosity of SOPC bilayers to be in the range 3-8×10^(-6) Poise