Correlated Brownian motions and the depletion effect in colloids

Abstract

We briefly review the derivation of a system ofN correlated Brownian motions as a kinematic mesoscopic limitfor a system of nonlinear deterministic oscillators consisting ofN large (solute) particles and infinitely many small (solvent) particles by Kotelenez.We then sketch the qualitative analysis of correlated Brownian motions and thedepletion effect in colloids by Kotelenez, Leitman and Mann. For space dimensiond≥2 they showed that two correlated Brownian particles, when sufficiently close, have an initialtendency to attract each other further. For large times (and for large separations) they performindependent Brownian motions. The key to their short-time result is a generalization tod≥2 dimensions of the one-dimensional probability flux, as defined by van Kampen. Weconclude with a discussion of three unresolved problems.