A study of the transport of ions against their concentration gradient across ion-exchange membranes using the network method

The network method has been used to analyze the conditions that favour the uphill transport across ion-exchange membranes. A model for the Nernst-Planck-Poisson equations describing the ionic transport in such system is proposed, including the Donnan equilibrium relations at the membrane/solution interfaces. With this model and the electric circuit simulation program PSPICE, the transient response of the system under open circuit conditions (I=0) and the response of the system subject to an applied potential difference are simulated. The ionic concentrations and electric potential profiles, as well as the electric current density, the ionic fluxes and the charge density, have been obtained as a function of time.