Brownian motion in a fluid close to its' critical point

The frequency dependent friction coefficient of a spherical Brownian particle of radius a in a compressible fluid close to its critical point is evaluated taking into account the large correlation length ζ of the density fluctuations in the fluid. The expression found depends for finite frequencies on the ratio a/Gx. It is furthermore shown that a negative contribution to the amplitude of the usual t−3/2 long time tail of the velocity autocorrelation function of the particle appears very close to the critical point when ζ ⪢ a.