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The position of a colloidal particle trapped in an external field thermallyfluctuates at equilibrium. As is well known, the ambient fluid is not a simpleheat bath and the particle mass appears to increase, which influences the meansquare velocity of the particle. In this study, we suppose that the particle issurrounded by a binary fluid mixture in the homogeneous phase near, but not tooclose to, the critical point. Usually, one component is preferably attracted bythe particle surface, and the resultant adsorption layer becomes significantbecause of the near-criticality. When the particle fluctuates in thissituation, its mean square displacement should also be influenced by theambient fluid because the adsorption layer does not follow the particle motiontotally. We calculate the influence in a simple case, where a rigid sphericalparticle fluctuates with a small amplitude and its surface attracts onecomponent weakly. We utilize the hydrodynamics in the limit of no dissipationto examine the contribution from the ambient mixture to the equal-timecorrelation, which is shown to be reduced by an additional stress, includingosmotic pressure.

Fluctuation Amplitude of a Trapped Rigid Sphere Immersed in a Near-Critical Binary Fluid Mixture within the Regime of the Gaussian Model