刚性球形颗粒在近临界二元流体混合物中的阻力系数
Drag Coefficient of a Rigid Spherical Particle in a Near-Critical Binary Fluid Mixture beyond the Regime of the Gaussian Model
摘要：
刚性球形颗粒在临界组成的均相近临界流体混合物中的阻力系数偏离Stokes定律。实验结果表明，偏离（$Δγ_{\rm d}$）近似线性地依赖于远离粒子的关联长度（$ξ_\infty$），并认为是由一种组分与粒子表面之间的优先吸引力引起的.与此相反，在以前的理论研究的基础上的高斯自由能量密度的依赖性被证明是陡峭得多。在颗粒附近，特别是当优选组分的吸附使得组合物强烈地非临界时，与$ξ_\infty$相比，相关长度变得非常小。这种在以前的理论研究中没有考虑的空间不均匀性，可以影响$Δγ_{\rm d}$对$ξ_\infty$的依赖性。为了研究这种可能性，我们在这里应用局部重整化泛函理论，这是以前提出来解释的墙壁沉浸在（近）临界二元流体混合物的相互作用，描述的优先吸引力的表面场。与高斯自由能量密度相比，该理论中的自由能密度，粗粒化到局域关联长度，对序参量的依赖性要复杂得多。尽管如此，一个简洁的表达式的阻力系数，这是在以前的理论研究之一，原来是可用在本配方。我们发现，随着$ξ_{\infty}$变大，$Δγ_{\rm d}$对$ξ_\infty$的依赖性变得明显逐渐接近线性依赖。
英文摘要：
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 ($Δγ_{\rm d}$) is experimentally shown to depend approximately linearly on the correlation length far from the particle ($ξ_\infty$), 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 $ξ_\infty$. This spacial inhomogeneity, not considered in the previous theoretical studies, can influence the dependence of $Δγ_{\rm d}$ on $ξ_\infty$. 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 $ξ_{\infty}$ becomes larger, the dependence of $Δγ_{\rm d}$ on $ξ_\infty$ becomes distinctly gradual and close to the linear dependence.
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