Electrodialysis and other electromembrane processes have been researched for decades. However, not all fundamental mechanisms of charge-selective membranes and their interfaces have been understood. This thesis aims to increase the understanding of some of the processes happening at and around these interfaces by eliminating the electroneutrality condition from the set of commonly assumed simplifications. Multiple layers, reactions and convection are considered in combination with diffusion and electromigration. The complex set of equationsis shown to be tractable by computational methods. The thesis discusses a computational framework and tackles various problems not easily accessible by commercial software. A fundamental study of the common assumption of the ideal bulk boundary condition with an artificial mixing model reveals a deviation in dynamic settings, demonstrated by an increase in the depletion time of the boundary layer under limiting current density. Layer-by-Layer membrane assemblies are investigated under steady-state conditions and their impedance in asymmetric salt solutions is highlighted, showing that a single systemic capacitance may yield multiple characteristic frequencies. Bipolar membranes are investigated towards their behaviour at the junction in a reactive electrolyte under various conditions. Using the same model, weak dissociating salts are studied. Weak dissociating acids and bases play a major role in biological systems and their purification is a major issue in process engineering. Leveraging the charge mechanics of the computational framework, nanofiltration of Itaconic acid is investigated and the capability to predict complex pH dependent systems is demonstrated
