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The drag coefficient of a rigid spherical particle deviates from the Stokeslaw when it is put into a near-critical fluid mixture in the homogeneous phasewith the critical composition. The deviation ($\Delta\gamma_{\rm d}$) isexperimentally shown to depend approximately linearly on the correlation lengthfar from the particle ($\xi_\infty$), and is suggested to be caused by thepreferential attraction between one component and the particle surface. Incontrast, the dependence was shown to be much steeper in the previoustheoretical studies based on the Gaussian free-energy density. In the vicinityof the particle, especially when the adsorption of the preferred componentmakes the composition strongly off-critical, the correlation length becomesvery small as compared with $\xi_\infty$. This spacial inhomogeneity, notconsidered in the previous theoretical studies, can influence the dependence of$\Delta\gamma_{\rm d}$ on $\xi_\infty$. To examine this possibility, we hereapply the local renormalized functional theory, which was previously proposedto explain the interaction of walls immersed in a (near-)critical binary fluidmixture, describing the preferential attraction in terms of the surface field.The free-energy density in this theory, coarse-grained up to the localcorrelation length, has much complicated dependence on the order parameter, ascompared with the Gaussian free-energy density. Still, a concise expression ofthe drag coefficient, which was derived in one of the previous theoreticalstudies, turns out to be available in the present formulation. We show that, as$\xi_{\infty}$ becomes larger, the dependence of $\Delta\gamma_{\rm d}$ on$\xi_\infty$ becomes distinctly gradual and close to the linear dependence.

Drag Coefficient of a Rigid Spherical Particle in a Near-Critical Binary Fluid Mixture beyond the Regime of the Gaussian Model