Mathematical Modeling of the Effect of Pulsed Electric Field on the Specific Permselectivity of Ion-Exchange Membranes

Abstract

The application of pulsed electric field (PEF) in electrodialysis has been proven to be efficient for a number of effects: increasing mass transfer rate, mitigation of scaling and fouling, reducing water splitting. Recently, the improvement of the membrane permselectivity for specific counterions was discovered experimentally by the group of Laurent Bazinet (N. Lemay et al. J. Memb. Sci. 604, 117878 (2020)). To better understanding the effect of PEF in electrodialysis, simulations were performed using a non-stationary mathematical model based on the Nernst–Planck and Poisson equations. For the first time, it was not only the condition used when the current density is specified but also the condition when the voltage is set. A membrane and two adjacent diffusion layers are considered. It is shown that when applying the regime used by Lemay et al. (the same current density in conventional continuous current (CC) mode and during the pulses in PEF mode), there is a significant gain in specific permselectivity. It is explained by a reduction in the membrane concentration polarization in PEF mode. In the CC mode of electrodialysis, increasing current density leads to a loss in specific permselectivity: concentration profiles in the diffusion layers and membrane are formed in such a way that ion diffusion reduces the migration flux of the preferentially transferred ion and increases that of the poorly transferred ion. In PEF mode, the concentration profiles are partially restored during the pauses when the current is zero. However, if a different condition is used than the condition applied by Lemay et al., that is, when the same average current density is applied in both the PEF and CC modes, there is no gain in specific permeability. It is shown that within the framework of the applied mathematical model, the specific selectivity depends only on the average current density and does not depend on the mode of its application (CC or PEF mode).

A model-based analysis of electrodialysis fouling during pulsed electric field operation

“…Assuming local electroneutrality and no water flux, the electric potential is computed as follows [27],…”

“…Since the active period decreases with the frequency (Eq. ( 19)), the concentration polarisation and relaxation occurs during shorter periods and becomes less extreme [27] leading to smaller fluctuations of the electrical potential during the galvanostatic operation of the stack.…”

“…In literature, the suppression of fouling during PEF is attributed to a combination of concentration relaxation in the diffusion boundary layer, the suppression of water splitting and the promotion of electroconvection along with potentially other unknown factors [27,60]. The mechanisms of fouling suppression due to electroconvection or a decrease of water splitting is notoriously challenging to simulate [27]. This research focuses on the effect of SDS boundary layer relaxation as a fouling suppression mechanism.…”

“…Such an advanced fouling model does not exist yet and the energy consumption is studied separately from the fouling behaviour. The energy consumption computed by (27) expressed as energy per ion removed as a function of the pulse frequency and the duty cycle is depicted in Fig. 8.…”

“…This current mode is known as PEF ED. Many studies report advantages of PEF compared to the continuous current (CC) operation including an increase in mass transfer rate [23][24][25], an increase in selectivity towards certain ions [26][27][28][29], an increase in the limiting current density [12] and a reduction of fouling and scaling [21,28]. There are also disadvantages to operating ED in PEF mode since only the active cycle leads to desalination and PEF thus reduces the overall desalination rate and a higher electrical potential or current density has to be applied to maintain the CC desalination rate [30].…”