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Understanding how electrolyte-filled porous electrodes respond to an appliedpotential is important to many electrochemical technologies. Here, we considera model supercapacitor of two blocking cylindrical pores on either side of acylindrical electrolyte reservoir. A stepwise potential difference $2\Phi$between the pores drives ionic fluxes in the setup, which we study through themodified Poisson-Nernst-Planck equations, solved with finite elements. We focusour discussion on the dominant timescales with which the pores charge and howthese timescales depend on three dimensionless numbers. Next to thedimensionless applied potential $\Phi$, we consider the ratio $R/R_b$ of thepore's resistance $R$ to the bulk reservoir resistance $R_b$ and the ratio$r_{p}/\lambda$ of the pore radius $r_p$ to the Debye length $\lambda$. Wecompare our data to theoretical predictions by Aslyamov and Janssen ($\Phi$),Posey and Morozumi ($R/R_b$), and Henrique, Zuk, and Gupta ($r_{p}/\lambda$).Through our numerical approach, we delineate the validity of these theories andthe assumptions on which they were based.

Direct numerical simulations of the modified Poisson-Nernst-Planck equations for the charging dynamics of cylindrical electrolyte-filled pores