Numerical modelling of nonequilibrium electrokinetic phenomena in porous media containing ion-permselective spatial domains

这项工作涉及一个三维，高分辨率的数值模拟的电动力学传输通过多孔介质包含离散离子-超选择性，即电荷选择的空间域，覆盖耦合质量和电荷传输通过离子交换膜的纳米孔（平面界面）和固定床的多孔颗粒（弯曲界面）。通过实施新颖、先进的数值方案（晶格-玻尔兹曼方法和基于晶格的算法）来解决三维多孔介质中的耦合泊松-能斯特-普朗克和电流体动力学问题，可以将固液界面的微观细节（表面电荷密度、局部pH值和离子强度、表面几何形状）和实际孔隙空间形态(孔隙形状、互联性和尺寸分布；在介观长度尺度上演化的电动力学和流体动力学，以及宏观输运理论。将特别关注浓度极化的时空动力学和扩展，电场诱导的空间电荷区域，这些区域可能是由于在外部施加电场的影响下，质量和电荷的耦合传输正常到电荷选择界面而形成的。诱导电荷电渗透（一类尚未被发现的非线性电动力学现象的一部分）可以解释电渗析中过限电导的发生，或球体填料中电动力学的不稳定性。对这些现象进行了分析和调整，以减少由浓度极化引起的多孔介质中耦合质量和电荷输运的限制。

This work is concerned with a three-dimensional, high-resolution numerical simulation of electrokinetic transport through porous media containing discrete ion-permselective, i.e., charge-selective spatial domains, covering coupled mass and charge transport through nanopores in ion-exchange membranes (flat interface) and porous particles in fixed beds (curved interfaces). By implementing novel, advanced numerical schemes (lattice-Boltzmann method and lattice-based algorithms) for a solution of the coupled Poisson-Nernst-Planck and electrohydrodynamic problems in three-dimensional porous media, it is possible to correlate microscopic details of a solid-liquid interface (surface charge density; local pH and ionic strength; surface geometry) and actual pore space morphology (pore shape, interconnectivity, and size distribution; average porosity) with the electrokinetics and hydrodynamics evolving on mesoscopic length scales, as well as with the macrotransport theory. Particular attention will be devoted to the spatio-temporal dynamics of concentration polarisation and extended, electrical field-induced space charge regions which may develop due to coupled mass and charge transport normal to a charge-selective interface under the influence of externally applied electrical fields. The induced-charge electroosmosis (part of a yet hardly discovered class of nonlinear electrokinetic phenomena) can explain the occurence of overlimiting conductance in electrodialysis, or electrokinetic instability in sphere packings. These phenomena are analysed and tailored for reducing limitations to coupled mass and charge transport in porous media arising from concentration polarisation.