A generalized multi-dimensional mathematical model for charging and discharging processes in a supercapacitor

A generalized three dimensional computational model based on unified formulation of electrode-electrolyte system of an electric double layer supercapacitor has been developed. This model accounts for charge transport across the electrode-electrolyte system. It is based on volume averaging, a widely used technique in multiphase flow modeling ([1], [2]) and is analogous to porous media theory employed for electrochemical systems [3], [4], [5]. A single-domain approach is considered in the formulation where there is no need to model the interfacial boundary conditions explicitly as done in prior literature ([6]). Spatio-temporal variations, anisotropic physical properties, and upscaled parameters from lower length-scale simulations and experiments can be easily introduced in the formulation. Model complexities like irregular geometric configuration, porous electrodes, charge transport and related performance characteristics of the supercapacitor can be effectively captured in higher dimensions. This generalized model also provides insight into the applicability of 1D models ([6]) and where multidimensional effects need to be considered. A sensitivity analysis is presented to ascertain the dependence of the charge and discharge processes on key model parameters. Finally, application of the formulation to non-planar supercapacitors is presented.