A 2-D model of electrodialysis stacks including the effects of membrane deformation

Membrane-based processes have gained a relevant role in many engineering applications. Much effort has been devoted to thoroughly understand the fundamental phenomena behind them. However, membrane deformation has been taken into consideration only recently, although much evidence has shown its impacts in many applications. This work presents a novel 2-D, multi-scale, semi-empirical process model able to predict the behavior and the performance of Electrodialysis (ED) systems in cross-flow configurations in the presence and absence of local membrane deformations. The model exploits the results and the simulation approaches of previous fluid-structure investigations performed by the authors. Low-scale numerical simulations are coupled with a high-scale model to predict the redistribution of channel height, flow rate, friction coefficient and Sherwood number in ED stacks caused by local membrane deformations. Finally, salt and water fluxes, mass balances and electrochemical quantities are computed to assess the performances of cross-flow ED stacks. Different test cases have been simulated for the desalination of seawater by two-stage ED. Interestingly, membrane deformation is found to reduce, albeit slightly, the energy consumption. More pronounced effects are expected if thinner or less stiff membranes are used.