TY - JOUR

T1 - Fluctuating hydrodynamics of dilute electrolyte solutions

T2 - systematic perturbation calculation of effective transport coefficients governing large-scale dynamics

AU - Okamoto, Ryuichi

N1 - Funding Information:
The author would like to thank Hirofumi Wada and Tsuyoshi Yamaguchi for informative discussions. This work was supported by JSPS KAKENHI (Grant Nos. 18K03562 and 18KK0151).
Publisher Copyright:
© 2022 IOP Publishing Ltd and SISSA Medialab srl.

PY - 2022/9/1

Y1 - 2022/9/1

N2 - 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 originally been obtained by Debye and Falkenhagen; it is predicted that the combination of these two parts gives rise to the frequency ω 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.

AB - 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 originally been obtained by Debye and Falkenhagen; it is predicted that the combination of these two parts gives rise to the frequency ω 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.

KW - charged fluids

KW - current fluctuations

KW - diffusion

KW - fluctuating hydrodynamics

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U2 - 10.1088/1742-5468/ac8c8d

DO - 10.1088/1742-5468/ac8c8d

M3 - Article

AN - SCOPUS:85139422995

SN - 1742-5468

VL - 2022

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

IS - 9

M1 - 093203

ER -