The Nernst-Planck model has long served as a foundational framework for understanding the behavior of electrolyte systems. However, inherent deficiencies in this model have spurred the exploration of alternative approaches. In this context, this study presents simulation in multidimensional contexts for a new, fully-coupled, non-linear, thermodynamically consistent electrolyte model introduced by Dreyer et al. We present a robust mathematical formulation and employ a conforming finite element approximation to comprehensively explore both compressible and incompressible variants of the electrolyte mixture. Our investigation extends across diverse spatial dimensions, facilitating an in-depth analysis of parametric dependencies governing space-charge layer formation at boundaries under external voltage influence. Furthermore, meticulous consideration is given to finite ion size effects, which play a critical role in electrolyte flow dynamics. Insights from annular battery designs are also incorporated, which introduce unique dynamics to ion transport phenomena. Through rigorous simulations, we validate the accuracy and reliability of our numerical scheme, thereby laying the groundwork for an enhanced understanding and optimization of electrolyte system behaviors across various applications, notably in semiconductor devices and electrochemistry.

翻译：长期以来，Nernst-Planck 模型一直是理解电解质系统行为的基础框架。然而，该模型固有的缺陷促使人们探索替代方法。在此背景下，本研究针对 Dreyer 等人提出的新型全耦合、非线性、热力学一致电解质模型，开展了多维情境下的仿真。我们提出了稳健的数学表述，并采用保形有限元逼近方法，全面探究了电解质混合物的可压缩与不可压缩变体。我们的研究涵盖了多种空间维度，从而能够深入分析在外加电压影响下边界处空间电荷层形成的参数依赖性。此外，研究还细致考虑了有限离子尺寸效应，该效应对电解质流动动力学起着关键作用。同时，我们还借鉴了环形电池设计中的见解，这些设计为离子传输现象引入了独特的动力学特性。通过严格的仿真，我们验证了数值方案的准确性与可靠性，从而为深入理解和优化各类应用（特别是在半导体器件与电化学领域）中的电解质系统行为奠定了基础。