A molecular theory of Stokes-Einstein behavior. III. Translational Brownian motion in a compressible fluid

The expressions for the friction coefficient of a diffusing particle, obtained from a completely molecular theory in a previous paper, are solved for a Brownian particle in a compressible fluid. In appropriate limits the exact forms of the hydrodynamic friction coefficients in the slip and stick limits are reproduced. The use of the hydrodynamic results in describing the velocity autocorrelation function (VACF) of a molecule is discussed.