Fluctuation amplitudes of a trapped particle in a near-critical binary fluid mixture

We assume that a binary fluid mixture, lying in the one-phase region near the demixing critical point, contains a Brownian particle trapped by a harmonic potential. A mixture component, preferred by the particle surface via a short-range interaction, concentrates near the surface to generate a thick adsorption layer. This layer, deformed by particle motion, increases the effective mass and restoring force, thereby reducing the equal-time correlation of the fluctuations of the particle position and that of the particle velocity. We calculate these fluctuation amplitudes using the reversible part of hydrodynamics on the basis of the free-energy density of a local functional theory, which is known to describe the critical properties well. The effects of the preferential adsorption are negligible when the stiffness of the trapping potential is sufficiently large. A typical stiffness below which the effects emerge is largely determined by the strength of preferential adsorption and shifts toward larger stiffness as the adsorption is stronger. Plots of the fluctuation amplitudes against the stiffness are approximately independent of the deviation of the temperature from the critical temperature. These properties should facilitate future experimental studies on this phenomenon.