Kinetic-Theory Derivation of the Stokes-Einstein Law

Abstract

We employed repeated-ring kinetic theory incorporating the equilibrium correlations in a dense fluid to study Brownian motion. It is demonstrated that the theory predicts the Stokes-Einstein law relating the diffusion coefficient of a Brownian particle to its radius and the fluid shear viscosity. In addition, the correct long-time behavior ($t^{-\frac{3}{2}}$) of the velocity autocorrelation function is obtained.