Brownian motion and fluctuating hydrodynamics

Abstract

The generalization of Faxén's theorem to the case of a sphere moving with a time-dependent velocity through a fluid in nonstationary and nonhomogeneous flow, given our first paper, is shown to be also applicable to a fluctuating fluid. This theorem is subsequently used to derive the Langevin equation for a spherical brownian particle from the equations governing fluctuating hydrodynamics. A comparison is made with previous hydrodynamic derivations.