Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306, USA.
Advanced Cooling Technologies, Inc., Lancaster, Pennsylvania 17601, USA.
J Chem Phys. 2017 Sep 28;147(12):124102. doi: 10.1063/1.5003915.
We develop a nonlocal Nernst-Planck model for reaction and diffusion in multicomponent ionic systems. We apply the model to the one-dimensional liquid junction problem, in which two electrolytic solutions of different ionic concentrations are brought into contact via a permeable membrane. Transport of ions through the membrane induces an electric field which is modeled using two separate nonlocal conditions: charge conservation and Gauss' law. We investigate how well they satisfy the criterion of strict electroneutrality which stipulates that the net charge at each point in the domain is zero, by considering four different initial scenarios. Charge conservation and Gauss' law yield similar results for most practical scenarios in which the initial condition satisfies strict electroneutrality. However, Gauss' law has two important advantages over charge conservation: (i) it is numerically more stable and can be applied even when the concentration of all the charged species drops to zero and (ii) computationally, it is significantly cheaper. Further, this study provides insights on the prescription of electroneutrality conditions necessary to handle the physics of evolving charges in nonlocal peridynamic models that are aimed at modeling nonlocal reaction-diffusion or corrosion-type processes.
我们开发了一种用于多组分离子体系反应和扩散的非局部能斯特-普朗克模型。我们将该模型应用于一维液体结问题中，其中两种不同离子浓度的电解质溶液通过可渗透膜接触。离子通过膜的传输会引起电场，我们使用两个独立的非局部条件来模拟电场：电荷守恒和高斯定律。我们通过考虑四种不同的初始情况来研究它们在满足规定各点净电荷为零的严格电中性条件方面的表现。对于大多数初始条件满足严格电中性的实际情况，电荷守恒和高斯定律得出的结果相似。然而，与电荷守恒相比，高斯定律有两个重要优势：（i）它在数值上更稳定，甚至在所有带电物质的浓度都降至零时也可以应用；（ii）在计算方面，它的成本显著降低。此外，本研究还深入探讨了在非局部动理学模型中处理不断变化的电荷物理所需的电中性条件的规定，这些模型旨在模拟非局部反应扩散或腐蚀类过程。
