Fluctuating hydrodynamics of electrolytes at electroneutral scales
Fluctuating hydrodynamics of electrolytes at electroneutral scales
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DOI：
10.1103/physrevfluids.4.043701
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发表时间：
2019-04-05
影响因子：
2.7
通讯作者：
Bell, John B.
中科院分区：
文献类型：
--
作者：
Donev, Aleksandar;Nonaka, Andrew J.;Bell, John B.
在介观尺度上，电解液溶液由波动的广义Poisson-Nernst-Planck(PNP)方程模拟[J.-P.Peraud等，Phys.流体修订版1,074103(2016年)]。然而，在长度和时间尺度大于德拜尺度的情况下，电解液实际上是电中性的，带电流体PNP方程变得太僵硬，无法数值求解。在这里，我们建立了含有带电物种的反应性多组分混合物涨落流体动力学的等温不可压缩方程，并设计了一个数值算法来求解这些方程。我们的模型没有假设一个稀电解质溶液，而是平等地对待所有物种，使用Maxwell-Stefan理论解释了交叉扩散和非理想性。通过强制局域电中性作为约束，我们得到了一个关于电势的椭圆型方程，它取代了涨落PNP方程中的泊松方程。我们发展了一种二阶中点预测-校正算法，只需改变椭圆型求解器，即可求解带电流体方程或电中和方程。我们使用电中和算法来研究重力指进不稳定性，这种不稳定性是由热波动引发的，在界面上，酸和碱发生反应，相互中和。我们的结果表明，由于这四个离子的扩散系数非常不同，所以必须将每个离子作为一个单独的物种对待，而不能将酸、碱和盐作为中性物种对待。这强调了电扩散和经典费克扩散之间的区别，甚至在电中和尺度上也是如此。
At mesoscopic scales electrolyte solutions are modeled by the fluctuating generalized Poisson-Nernst-Planck (PNP) equations [J.-P. Peraud et al., Phys. Rev. Fluids 1, 074103 (2016)]. However, at length and time scales larger than the Debye scales, electrolytes are effectively electroneutral and the charged-fluid PNP equations become too stiff to solve numerically. Here we formulate the isothermal incompressible equations of fluctuating hydrodynamics for reactive multispecies mixtures involving charged species in the electroneutral limit and design a numerical algorithm to solve these equations. Our model does not assume a dilute electrolyte solution but rather treats all species on an equal footing, accounting for cross diffusion and nonideality using Maxwell-Stefan theory. By enforcing local electroneutrality as a constraint, we obtain an elliptic equation for the electric potential that replaces the Poisson equation in the fluctuating PNP equations. We develop a second-order midpoint predictor-corrector algorithm to solve either the charged-fluid or electroneutral equations with only a change of the elliptic solver. We use the electroneutral algorithm to study a gravitational fingering instability, triggered by thermal fluctuations, at an interface where an acid and base react to neutralize each other. Our results demonstrate that, because the four ions diffuse with very different coefficients, one must treat each ion as an individual species and cannot treat the acid, base, and salt as neutral species. This emphasizes the differences between electrodiffusion and classical Fickian diffusion, even at electroneutral scales.