论文标题
稀释电解质溶液的流体动力学波动：有效运输系数的系统扰动计算，这些系数管理大规模动力学
Fluctuating hydrodynamics of dilute electrolyte solutions: systematic perturbation calculation of effective transport coefficients governing large-scale dynamics
论文作者
论文摘要
我们根据波动的流体动力方程研究稀释电解质溶液的转运性能，该方程是一个非线性兰格文鸟方程，用于离子密度和流速。 Langevin方程的非线性通常会导致平均离子密度和流速的确定性动力学的有效动力学系数；有效系数通常与Langevin方程中的对应物不同，并且依赖频率。使用涉及辅助场的路径综合形式主义，我们对离子扩散，剪切粘度和电导率的有效动力学系数进行系统的扰动计算，该系数控制了大长度尺度上的动力学。作为新颖的贡献，我们研究了一环近似中粘度和电导率的频率依赖性。关于有限频率的电导率，除了放松部分之外，我们还得出了所谓的电泳部分，在该部分中，Debye和Falkenhagen获得了后者。可以预测，这两个部分的组合产生频率$ω_ {\ rm max} $与盐密度成比例的频率，在该盐密度中，电导率的实际部分表现出最大值。电导率和剪切粘度的零频率限制与稀释溶液的经典限制定律相吻合，该定律是由Debye，Falkenhagen和Onsager以不同方式得出的。至于在较大长度尺度的慢离子扩散的有效动力学系数中，我们的直接计算产生了阳离子和阴离子之间的横际动力学系数。此外，我们讨论了将本研究扩展到更集中的解决方案的可能性。
We study the transport properties of dilute electrolyte solutions on the basis of the fluctuating hydrodynamic equation, which is a set of nonlinear Langevin equations for the ion densities and flow velocity. The nonlinearity of the Langevin equations generally leads to effective kinetic coefficients for the deterministic dynamics of the average ion densities and flow velocity; the effective coefficients generally differ from the counterparts in the Langevin equations and are frequency-dependent. Using the path-integral formalism involving auxiliary fields, we perform systematic perturbation calculations of the effective kinetic coefficients for ion diffusion, shear viscosity, and electrical conductivity, which govern the dynamics on the large length scales. As novel contributions, we study the frequency dependence of the viscosity and conductivity in the one-loop approximation. Regarding the conductivity at finite frequencies, we derive the so-called electrophoretic part in addition to the relaxation part, where the latter has been obtained by Debye and Falkenhagen; it is predicted that the combination of these two parts gives rise to the frequency $ω_{\rm max}$ proportional to the salt density, at which the real part of the conductivity exhibits a maximum. The zero-frequency limits of the conductivity and shear viscosity coincide with the classical limiting laws for dilute solutions, derived in different means by Debye, Falkenhagen, and Onsager. As for the effective kinetic coefficients for slow ion diffusions in large length scales, our straightforward calculation yields the cross kinetic coefficient between cations and anions. Further, we discuss the possibility of extending the present study to more concentrated solutions.
