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

本文采用三维、高分辨率的数值模拟方法，研究了离子交换膜(平界面)中的纳米孔和固定床(曲面界面)中的多孔颗粒之间的电动力学输运过程。通过对三维多孔介质中Poisson-Nernst-Planck和电流体动力学耦合问题的求解实施新颖的、先进的数值格式(格子-Boltzmann方法和基于格子的算法)，可以将固-液界面的微观细节(表面电荷密度；局部pH和离子强度；表面几何形状)和实际的孔空间形态(孔形状、连通性和尺寸分布；平均孔隙率)与介观长度尺度上的电动力学和流体动力学以及宏观输运理论相关联。将特别关注浓度极化和扩展的电场诱导的空间电荷区的时空动力学，这些空间电荷区可能是由于在外加电场的影响下垂直于电荷选择界面的耦合质量和电荷传输而发展的。诱导电荷电渗透(一类尚未发现的非线性电动现象的一部分)可以解释电渗析中电导超限或球形填料中电动不稳定性的发生。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传输的限制。

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.