Osmotic effects on dynamics of a colloidal rigid sphere in a near-critical binary fluid mixture

When a rigid spherical particle is put in a binary fluid mixture lying in the homogeneous phase near the demixing critical point, one of the fluid components is expected to be significantly concentrated around the particle because it is attracted preferentially by the particle surface. The resultant gradient of the mixture composition causes an additional pressure including osmotic pressure. We study how this pressure changes the particle motion by using the Gaussian free-energy functional for the mixture and assuming a correlation length much smaller than the particle size. The drag coefficient in this situation was calculated in the regime of sufficiently weak preferential attraction in a previous study [R. Okamoto, Y. Fujitani, and S. Komura, J. Phys. Soc. Jpn. 82, 084003 (2013)]. We here devise a new procedure beyond the regime to calculate the drag coefficient and the long-time tail of the velocity correlation of the particle. Our results cannot be explained totally by effective enlargement of the particle due to the layer rich in the preferred component.