Convection can enhance the capacitive charging of porous electrodes

Charge transport in porous electrodes is foundational for modern energy storage technologies like supercapacitors, fuel cells, and batteries. Supercapacitors in particular rely solely on storing energy in charged pores. Here, we simulate the charging of a single electrolyte-filled pore using the modified Poisson-Nernst-Planck and Navier-Stokes equations. We find that electroconvection can substantially speed up the charging dynamics. We uncover the fundamental mechanism of electroconvection during pore charging through an analytical model that predicts the induced flow field and the electric current arising due to convection. Our findings suggest that convection is especially important in the limit of slender pores with thin electric double layers, and becomes significant beyond a certain threshold voltage that is an inherent electrolyte property.

💡 Research Summary

This paper investigates how electroconvection influences the charging dynamics of a single electrolyte‑filled nanopore, a fundamental element of porous electrodes used in supercapacitors, batteries, and fuel cells. The authors couple a modified Poisson‑Nernst‑Planck (PNP) model, which accounts for ion crowding at high potentials, with the incompressible Navier‑Stokes (NS) equations to capture fluid motion driven by electric body forces. Finite‑element simulations are performed for cylindrical dead‑end pores with radii ranging from 1 nm to 50 nm and lengths from 5 nm to 2.5 µm, filled with a symmetric 1:1 KCl solution (Debye length ≈ 1 nm, diffusion coefficient 1 × 10⁻⁹ m² s⁻¹).

When a step voltage is applied to the pore walls, an axial electric field (Ez) appears near the pore entrance. Initially, no space charge exists, so the electric body force ρv Ez is negligible. As the electric double layers (EDLs) develop along the pore walls, a net space charge ρv forms. The product ρv Ez then drives an electro‑osmotic flow (wE) into the pore. Because the pore is dead‑ended, a pressure gradient builds up, generating a compensating pressure‑driven backflow (wP) out of the pore. The total axial flow w = wE + wP is transient, existing primarily between two characteristic timescales: a short diffusion‑migration time τs = λ rp/D (formation of the diffuse charge layer at the entrance) and a long access‑resistance‑limited time τl = 8π²λ rp Lp²/D ·