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

TL;DR

This paper investigates how a trapped rigid sphere's fluctuation amplitude is affected by a near-critical binary fluid mixture, considering adsorption effects and hydrodynamic interactions within a Gaussian model framework.

Contribution

It provides a theoretical analysis of the fluctuation amplitude of a sphere in a near-critical binary fluid, incorporating adsorption layer effects and hydrodynamic influences.

Findings

Fluctuation amplitude is reduced by additional stress from the adsorption layer.

Hydrodynamic interactions influence the mean square displacement of the particle.

The model accounts for weak surface attraction and near-critical conditions.

Abstract

The position of a colloidal particle trapped in an external field thermally fluctuates at equilibrium. As is well known, the ambient fluid is not a simple heat bath and the particle mass appears to increase, which influences the mean square velocity of the particle. In this study, we suppose that the particle is surrounded by a binary fluid mixture in the homogeneous phase near, but not too close to, the critical point. Usually, one component is preferably attracted by the particle surface, and the resultant adsorption layer becomes significant because of the near-criticality. When the particle fluctuates in this situation, its mean square displacement should also be influenced by the ambient fluid because the adsorption layer does not follow the particle motion totally. We calculate the influence in a simple case, where a rigid spherical particle fluctuates with a small amplitude and its surface attracts one component weakly. We utilize the hydrodynamics in the limit of no dissipation to examine the contribution from the ambient mixture to the equal-time correlation, which is shown to be reduced by an additional stress, including osmotic pressure.