Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94703.
Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94703;
Proc Natl Acad Sci U S A. 2017 Oct 10;114(41):10829-10833. doi: 10.1073/pnas.1714464114. Epub 2017 Sep 26.
We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson-Nernst-Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation-anion diffusion coefficient. Specifically, we predict a nonzero cation-anion Maxwell-Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye-Huckel-Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced "giant" velocity fluctuations and reduced fluctuations of salt concentration.
我们分析了外电场对二元电解质流体热涨落的影响。结果表明，带电多组分扩散的涨落泊松-纳斯特-普朗克（PNP）方程与涨落流体动量方程相结合，导致电荷输运增强，其机制与伴随巨涨落的质量输运增强机制不同。尽管质量和电荷输运是通过热速度涨落的平流来实现的，但可以宏观上表示为电扩散，具有修正后的电导率和非零阳离子-阴离子扩散系数。具体而言，我们预测非零阳离子-阴离子麦克斯韦-斯蒂芬系数与盐浓度的平方根成正比，这一预测与实验测量结果定量一致。修正后的或有效宏观方程与起始 PNP 方程不同，即使对于相当稀的二元电解质，它们也不含交叉扩散项。同时，对于无限稀的溶液，修正后的电导率和修正后的扩散系数是一致的，并且恢复了具有修正系数的经典 PNP 方程，证明了涨落流体力学方程的自洽性。我们的计算表明，涨落流体力学方法恢复了德拜-休克尔-昂萨格理论得到的电泳和弛豫修正，同时阐明了这些修正的物理起源，并直接推广到更复杂的多组分电解质。最后，我们表明强外电场导致各向异性增强的“巨大”速度涨落和盐浓度涨落减小。
