New Insights into Computational Fluid Dynamic (CFD) Modeling of Concentration Overpotential
Authors: Jalili Zohreh , Burheim Odne Stokke , Einarsrud Kristian Etienne 
Published: February 2020

Salinity gradient power (SGP) is a promising source of sustainable energy production involving technologies such as pressure retarded osmosis (PRO), reverse electrodialysis (RED) and capacitive mixing (CAPMIX). Coupling these technologies to their counterparts used for desalination, salinity gradient batteries can in principle be developed [1], as recently demonstrated for RED/ED [2].
Electrode and membrane processes typically involve an accumulation or depletion of specific ions compared the bulk solution, resulting in so called concentration polarization. Concentration polarization is a considerable challenge in RED/ED, effectively reducing the driving force across the membrane, hence reducing the performance of the process [3]. In addition to concentration polarization, the presence of concentration gradients will result in both Ohmic and non-Ohmic contributions to the electrical potential [3], further influencing the characteristics of the system.
Different strategies have been proposed in order to mitigate the influence of concentration gradients, specifically increasing the flow velocity and introducing flow promoters – typically by optimizing the spacer geometry [3, 4] – in order to alter momentum and concentration boundary layers. The interaction between ionic species and fluid flow can be achieved by solving the coupled Navier-Stokes (NS) and Nernst-Planck (NP) equations [5,6], allowing for simultaneous prediction of flow and pressure fields, concentration and electrical potential, all of which of interest for the overall performance of the system.
The current work describes a simulation framework for simulation of the NS-NP system based on the open source CFD platform OpenFOAM [7], aiming to predict the influence of flow conditions and geometry on concentration and electrical potential. Figure 1 (left) shows constant, linear and parabolic concentration profiles, corresponding to the extreme conditions of plug and Poiseuille flow in a flat channel, with the corresponding results for electrical potential in Figure 1 (right), clearly demonstrating the strong coupling between the two. The suggested framework is applied to spacer filled channels aiming to describe pros and cons of different configurations such as height and pitch of spacers.
The presented approach sheds light on future concentration polarization modeling, providing better descriptions of the mass transfer and electric potential and highlighting the role of spacer-filled channel in membrane based processes.
References
1. Yip, N.Y., Brogioli, D., Hamelers, H.V.M., Nijmeijer, K., 2016. Salinity Gradients for Sustainable Energy: Primer, Progress, and Prospects. Environmental Science & Technology 50, 12072–12094.
2. Kingsbury, R.S., Chu, K., Coronell, O., 2015. Energy storage by reversible electrodialysis: The concentration battery. Journal of Membrane Science 495, 502–516.
3. Gurreri, L., Tamburini, A., Cipollina, A., Micale, G., Ciofalo, M., 2014. CFD prediction of concentration polarization phenomena in spacer-filled channels for reverse electrodialysis. Journal of Membrane Science, 468, 133-148.
4. Ahmad, A. L., Lau, K. K., Bakar, M. A., 2005. Impact of different spacer filament geometries on concentration polarization control in narrow membrane channel. Journal of Membrane Science, 262(1), 138-152.
5. Tadimeti, J.G.D., Kurian, V., Chandra, A., Chattopadhyay, S., 2016. Corrugated membrane surfaces for effective ion transport in electrodialysis. Journal of Membrane Science, 499, 418-428.
6. Pawlowski, S., Geraldes, V., Crespo, J.G., Velizarov, S., 2016. Computational fluid dynamics (CFD) assisted analysis of profiled membranes performance in reverse electrodialysis. Journal of Membrane Science 502, 179–190.
7. https://www.openfoam.com/

Figure 1