Renormalization-group treatment of the critical dynamics of the binary-fluid and gas-liquid transitions
Renormalization-group treatment of the critical dynamics of the binary-fluid and gas-liquid transitions
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二元流体和气液转变临界动力学的重正化群处理
DOI：
10.1103/physrevb.13.2110
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发表时间：
1976
影响因子：
3.7
通讯作者：
P. Hohenberg
中科院分区：
文献类型：
--
作者：
E. Siggia;B. Halperin;P. Hohenberg
本文用重整化群研究了气-液和二元-流体相变动力学的简化模型。一个精确的标度律，发现连接的指数的发散运输系数的静态指数为任意值的维数dl 4 $。Kadanoff和Swift以及川崎根据近似的模式耦合参数，已经预测了这种标度律。扩散率，剪切粘度和相关长度之间的“川崎-斯托克斯”关系被证明是准确的，但具有与其模式耦合值略有不同的普遍振幅。输运系数的临界指数在$\ensuremath{\displaystyle $\ensuremath {-}d$中被评估为二阶，并导致预测三维剪切粘度[$\ensuremath{\eta}（T）\ensuremath{\propto}{（T\ensuremath{-}{T}_{c}）}^{\ensuremath{-} 0. 04}$]的弱发散。这种分歧的弱点反映了理论中存在一个小参数，这解释了川崎对瑞利线宽的评估与实验之间的良好一致性。修正简单的川崎理论进行了各种作者，并提出了一些建议，为完善这些计算。本文所研究的简单模型具有与真实的流体相同的动力学性质，足够接近临界点。
A simplified model for the dynamics of the gas-liquid and binary-fluid transitions is studied with the renormalization group. An exact scaling law is found, connecting the exponents for the diverging transport coefficients to static exponents for arbitrary value of the dimensionality $dl4$. This scaling law had been anticipated by Kadanoff and Swift, and Kawasaki, on the basis of approximate mode-coupling arguments. The "Kawasaki-Stokes" relation between the diffusivity, the shear viscosity, and the correlation length is shown to hold exactly, but with a universal amplitude which differs slightly from its mode-coupling value. Critical exponents for the transport coefficients are evaluated to second order in $\ensuremath{\epsilon}=4\ensuremath{-}d$, and lead to the prediction of a weak divergence of the shear viscosity [$\ensuremath{\eta}(T)\ensuremath{\propto}{(T\ensuremath{-}{T}_{c})}^{\ensuremath{-}0.04}$] in three dimensions. The weakness of this divergence reflects the existence of a small parameter in the theory, which explains the excellent agreement between Kawasaki's evaluation of the Rayleigh linewidth and experiment. Corrections to the simple Kawasaki theory carried out by various authors are reviewed, and a number of suggestions are made for refining these calculations. The simple model studied in this paper is shown to have the same dynamic properties as real fluids, sufficiently close to the critical point.