Transport of electrolytic solutions under influence of electric fields occurs in phenomena ranging from biology to geophysics. Here, we present a continuum model for single-phase electrohydrodynamic flow, which can be derived from fundamental thermodynamic principles. This results in a generalized Navier–Stokes–Poisson–Nernst–Planck system, where fluid properties such as density and permittivity depend on the ion concentration fields. We propose strategies for constructing numerical schemes for this set of equations, where the electrochemical and the hydrodynamic subproblems are decoupled at each time step. We provide time discretizations of the model that suffice to satisfy the same energy dissipation law as the continuous model. In particular, we propose both linear and non-linear discretizations of the electrochemical subproblem, along with a projection scheme for the fluid flow. The efficiency of the approach is demonstrated by numerical simulations using several of the proposed schemes.

电场作用下电解液的传输发生在从生物学到地球物理学的各种现象中。在这里，我们提出了一个单相电动流体流动的连续模型，可以从基本的热力学原理中得出。这导致了一个广义的Navier–Stokes–Poisson–Nernst–Planck系统，其中流体性质（例如密度和介电常数）取决于离子浓度场。我们提出了构建用于该组方程的数值方案的策略，其中在每个时间步上，电化学和流体动力学子问题都将解耦。我们提供模型的时间离散化，足以满足与连续模型相同的能量耗散定律。特别是，我们提出了电化学子问题的线性和非线性离散化，以及流体流动的投影方案。使用几种建议的方案通过数值模拟证明了该方法的有效性。