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

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 frictio n (zeta) felt by such a particle in experimental conditions. Our analysis i s based on the Schmoluchowski equation for particle motion. Essentially we derive a practical criterion to find zeta from the average particle path. O ur 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 spheric al giant lipid (SOPC) vesicles. From experimental values of zeta, we estima te the surface shear viscosity of SOPC bilayers to be in the range 3-8 x 10 (-6) Poise. (C) 1999 Elsevier Science B.V. All rights reserved.