On the validity of ion selective membrane simplification in concentration polarization

Ion selective membrane (ISM) is widely used in electrochemical engineering and micro-fluidic processes, yet accurate modeling of the ISM is still challenging due to many scientific issues. So far, assumptions on the "ideal ISM" have been used in most simulation studies involving ion transport and electrokinetic flow in ion concentration polarization systems, but the validity or accuracy of those assumptions has never been investigated. In this paper, using a two-dimensional nanochannel system with practical significance, we verify the validity of the ideal ISM model by making comparisons between the idealized ISM system and a more realistic permselective nanochannel system in terms of simplifications over the electrical potential, counter-ion concentration, and zero co-ion flux. Our results show that the simplifications of fixed voltage and fixed counter-ion concentration in the ideal ISM model are largely accurate in most situations, especially under high applied voltage and/or with high charge density inside the ISM. However, zero co-ion flux simplification is not exactly accurate in most occasions. Significant errors may be incurred by the zero co-ion flux assumption when steady state solutions are sought using the ISM model. Some discussions over the influences of structures of the nanochannel system are also added. The obtained results will help in obtaining detailed understanding of the transport features inside the nanoporous ISM, especially when the comparison between simulation and experimental data is necessary.