On the microscopic origin of Stokes’ law

Abstract

The microscopic origin of Stokes’ law for a hard sphere system is examined from two points of view. First, we derive a set of hydrodynamic equations with source terms, which account for the presence of a Brownian particle in the fluid, from the generalized Langevin equation. The friction coefficient can be expressed in terms of averages of the hydrodynamic fields over the Brownian particle. The solution of the source hydrodynamic equations for these averaged fields leads to the slip Stokes’ law result. Second, we consider the problem from kinetic theory and show that the same source hydrodynamic equations are obtained when projections onto hydrodynamic states are made.