The modelling of electrokinetic flows is a critical aspect spanning many industrial applications and research fields. This has introduced great demand in flexible numerical solvers to describe these flows. The underlying phenomena are microscopic, non-linear, and often involve multiple domains. Therefore often model assumptions and several numerical approximations are introduced to simplify the solution. In this work, we present a multi-domain multi-species electrokinetic flow model including complex interface and bulk reactions. After a dimensional analysis and an overview of some limiting regimes, we present a set of general purpose finite-volume solvers, based on \of, capable of describing an arbitrary number of electrochemical species over multiple interacting (solid or fluid) domains \cite{spnpfoam}. We provide verification of the computational approach for several cases involving electrokinetic flows, reactions between species, and complex geometries. We first present three one-dimensional verification test cases, and then show the capability of the solver to tackle two- and three-dimensional electrically driven flows and ionic transport in random porous structures. The purpose of this work is to lay the foundation for a general-purpose open-source flexible modelling tool for problems in electrochemistry and electrokinetics at different scales.

翻译：电动力学流体的建模是跨越众多工业应用和研究领域的关键问题。这催生了对描述此类流动的灵活数值求解器的巨大需求。其潜在现象是微观、非线性的，且通常涉及多个域。因此，常常引入模型假设和若干数值近似来简化求解。在本工作中，我们提出了一种包含复杂界面和本体反应的多域多物种电动力学流体模型。在进行了量纲分析并概述了一些极限状态后，我们展示了一套基于OpenFOAM的通用有限体积求解器，能够描述任意数量的电化学物种在多个相互作用的（固体或流体）域上的输运。我们针对涉及电动力学流动、物种间反应以及复杂几何形状的若干案例，验证了该计算方法的有效性。我们首先展示了三个一维验证测试案例，随后展示了该求解器在二维和三维电驱流动以及随机多孔结构中离子输运问题的处理能力。本工作旨在为不同尺度的电化学与电动力学问题奠定一个通用、灵活的开源建模工具的基础。