A Similarity Principle‐Based Multiscale Electrodialysis Desalination Unification With Multi‐Physical Parameter Sensitivity Analysis

Electrodialysis (ED) is a promising seawater desalination technology using electricity. However, the existing research studies on ED mainly focus on design of electrode materials and device structure. The ED is a multiscale and multi-physical process with multiple influencing parameters. Under these circumstances, the complicated ED process needs to be unified for understanding its physical essence and further optimization. In the current work, a similarity principle-based multiscale model is constructed to analyze ion migration mechanism inside ED device. The multiscale model is developed by correlating cation and anion concentration difference in a mesoscopic nanopore with macroscopic space charge density. On the basis of non-dimensionalization of Poisson-Nernst-Planck equations, the mesoscopic model of ED is unified with three dimensionless variables instead of eight-dimensional input parameters, which can be categorized as representative of ion absorption capability, ion transport characteristic, and nanopore characteristic. Then, the macroscopic model of ED is further unified using 6 dimensionless variables instead of 12-dimensional input parameters, and their physical meaning include ion absorption capability, ion transport characteristic, ion migration driving force, and desalination tank characteristic. The similarity principle of multiscale ED process is verified through nine dimensional different cases with identical dimensionless variables. The dimensionless cation-anion difference in nanopores of mesoscopic model varies within 0.25%, and the dimensionless outlet Na⁺ concentration of macroscopic model changes within 0.05%. Besides, a multi-physical sensitivity analysis is also carried out using the Taguchi method to clarify dominant parameters for ED. The Taguchi sensitivity analysis quantifies parameter contribution to seawater desalination rate in ED as seawater temperature 39.74%, initial ion concentration 15.94%, applied electric potential 15.91%, desalination tank length 11.45%, ion exchange membrane porosity 8.76%, and seawater flow velocity 8.19%. The current work lays a theoretical foundation for developing experimental correlations of ED, and it also contributes to rapid sampling generation in artificial intelligence prediction.