Galvanostatic dynamic response of ion-exchange membrane systems emphasizing energy consumption in electrodialysis for desalination under chronopotentiometry and pulsed electric field

Abstract

The galvanostatic dynamic response of ion-exchange membrane (IEM) systems, has been studied. It emphasizes a key topic in desalination: energy consumption in electrodialysis under chronopotentiometry and pulsed electric field (PEF). From the Warburg-type impedance function, the chronoamperometric dynamic response is obtained on the basis of its expansion into partial fractions. The limit time at which the Cottrell-type transient response, which corresponds to a semi-infinite diffusion process, reaches the steady-state voltage of the system is π/4 the diffusion time, and it is interpreted in the chronopotentiogram. Energy consumption is analytically evaluated during the application time of a current step. Concepts such as effective inductance, accumulated charge, effective capacitance, effective charge time, or average open-circuit voltage, are novelty introduced in order to interpret the saved energy in PEF electrodialysis with respect to that consumed under direct current performance. Analytical expressions based on the Laplace transformation method are also derived for the time evolution of the voltage and energy waves obtained in response to a square wave current. Finally, energy consumption in electrodialysis for desalination under chronopotentiometry and PEF mode is novelty related to reactive power and average stored energy in the dynamic response of IEM systems to external sinusoidal currents.