Charging dynamics of electrical double layers in a pore with an axially varying radius: Impact of pore shape and roughness

Electric double-layer capacitors (EDLCs) are devices that provide high power density and fast charging times, offering a unique advantage over batteries in high-power density applications. Previous studies have used direct numerical simulations to explore ionic transport inside porous electrodes. However, these simulations are computationally expensive and limited to single pores. To enhance EDLCs, it is essential to simulate ionic transport in pore networks containing thousands or millions of pores.

In our prior work, we linearized the Poisson-Nernst–Planck equations to develop an equivalent model of ionic transport in a network of straight cylindrical pores. In this study, we expand the model and derive effective equations for a pore where the radius varies along the axial direction. We investigate linearly converging or diverging pores and find that convergence allows for faster charge times. Additionally, we focus on a geometry with cyclic variation to model a "rough pore" and thoroughly examine the impact of phase variation of sinusoidal functions on charging times. Our work opens opportunities to study networks of shape-changing pores, which will more accurately capture the performance of EDLCs and aid in their future design.