# Curvature affects electrolyte relaxation: studies of spherical and cylindrical electrodes

## TL;DR

This paper investigates how electrode curvature influences electrolyte relaxation times using minimal models for spherical and cylindrical electrodes, revealing that relaxation times depend on both electrode radii rather than just their difference.

## Contribution

It extends existing models to curved electrodes, demonstrating that ionic relaxation times are affected by electrode radii, not only electrode separation.

## Key findings

- Relaxation times depend on both electrode radii.
- Equivalent circuit models accurately predict ionic relaxation times.
- Curvature significantly influences electrolyte response.

## Abstract

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 $\lambda_{\textrm{D}} L/D$, with $\lambda_{\textrm{D}}$ 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.