The drag coefficient of a rigid spherical particle deviates from the Stokes law when it is put into a near-critical fluid mixture in the homogeneous phase with the critical composition. The deviation ($\Delta\gamma_{\rm d}$) is experimentally shown to depend approximately linearly on the correlation length far from the particle ($\xi_\infty$), and is suggested to be caused by the preferential attraction between one component and the particle surface. In contrast, the dependence was shown to be much steeper in the previous theoretical studies based on the Gaussian free-energy density. In the vicinity of the particle, especially when the adsorption of the preferred component makes the composition strongly off-critical, the correlation length becomes very small as compared with $\xi_\infty$. This spacial inhomogeneity, not considered in the previous theoretical studies, can influence the dependence of $\Delta\gamma_{\rm d}$ on $\xi_\infty$. To examine this possibility, we here apply the local renormalized functional theory, which was previously proposed to explain the interaction of walls immersed in a (near-)critical binary fluid mixture, describing the preferential attraction in terms of the surface field. The free-energy density in this theory, coarse-grained up to the local correlation length, has much complicated dependence on the order parameter, as compared with the Gaussian free-energy density. Still, a concise expression of the drag coefficient, which was derived in one of the previous theoretical studies, 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.

中文翻译：

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近临界二元流体混合物中刚性球形颗粒的阻力系数，超出了高斯模型的范围

当将刚性球形颗粒放入具有临界组成的均相近临界流体混合物中时，其阻力系数偏离斯托克斯定律。实验表明，偏差 ($\Delta\gamma_{\rm d}$) 与远离粒子的相关长度 ($\xi_\infty$) 近似线性相关，并且被认为是由一种成分和颗粒表面。相比之下，在先前基于高斯自由能密度的理论研究中，这种依赖性被证明要陡峭得多。在粒子附近，特别是当优选组分的吸附使组合物强烈地离临界时，与$\xi_\infty$相比，相关长度变得非常小。这种空间不均匀性，之前的理论研究中没有考虑，可以影响 $\Delta\gamma_{\rm d}$ 对 $\xi_\infty$ 的依赖性。为了检验这种可能性，我们在这里应用了局部重整化泛函理论，该理论先前被提出用来解释浸入（近）临界二元流体混合物中的壁的相互作用，描述了表面场方面的优先吸引力。与高斯自由能密度相比，该理论中的自由能密度粗粒度到局部相关长度，对阶参数的依赖性要复杂得多。尽管如此，在之前的一项理论研究中得出的阻力系数的简明表达在当前公式中仍然可用。我们证明，随着 $\xi_{\infty}$ 变大，