Curvature affects electrolyte relaxation: studies of spherical and cylindrical electrodes

With two minimal models, I study how electrode curvature affects the response of electrolytes to applied electrostatic potentials. For flat electrodes, Bazant et al. [Phys. Rev. E. 70, 021506 (2004)] popularized the “RC” timescale ${\lambda }_{\text{D}}L\mathrm{/}D$, with ${\lambda }_{\text{D}}$ being the Debye length, $2L$ the electrode separation, and $D$ the ionic diffusivity. For thin electric double layers near concentric spherical and coaxial cylindrical electrodes, I show here that equivalent circuit models again predict the correct ionic relaxation timescales. Importantly, these timescales explicitly depend on both electrode radii, not simply on their difference.