The 3D simulator tracks O₂ concentration and clogging through depth only — every point around its cylindrical cathode ring is forced to behave identically at a given depth. Real porous-carbon cathodes are not that uniform: pore size varies from spot to spot across the electrode surface. This 2D companion is a genuine finite-volume solve of the coupled diffusion-reaction PDE over both depth (z) and lateral position (x), with each lateral column given its own intrinsic pore diffusivity:
∂C/∂t = ∂/∂z(D_eff ∂C/∂z) + ∂/∂x(D_eff ∂C/∂x) − R(x,z,t)
D_eff(x,z) = D0(x) · ε(x,z)^1.5 (Bruggeman, per column)
D0(x) = D0,base · (1 + spread·h(x)) (smoothed pore-heterogeneity field)
Because reaction demand is apportioned to wherever O₂ and open sites both exist, columns with slightly finer pores clog a little faster — and once a column's pore mouth narrows, it starves further, pulling in less current while its neighbours pick up the slack. That local feedback is what makes clogging concentrate into preferential channels ("fingers") instead of an even front, exactly what electron-microscopy cross-sections of spent Li-O₂ cathodes show.
The cell's overpotential is computed from the mean of each column's local penalty, not from the average pore-mouth opening — a convexity effect (Jensen's inequality) that means a patchy cathode always reaches sudden death at least as early as an equally-porous-on-average but uniform one. The "heterogeneity penalty" stat shows exactly how much earlier, in real time, compared to what a 1D-averaged model like the 3D twin would predict.
- Discharge current — higher current raises total reaction demand, so any given column clogs sooner.
- O₂ partial pressure — sets the boundary concentration via Henry's law.
- Pore size — the mean pore diffusivity/capacity across all columns (mesoporous → macroporous).
- Pore-network heterogeneity — how unevenly that pore size is distributed laterally; 0% reproduces the 3D twin's uniform-column behaviour exactly, higher values open up visible clogging fingers in the heatmap.
Verified numerically before shipping: the diffusion stencil matches the analytic erfc profile of 1D Fickian diffusion into a fixed-concentration boundary (max error < 0.01 in the Dirichlet limit), total O₂ mass balances exactly against integrated boundary flux with no reaction, and a heterogeneous pore field reaches sudden death no later than an equal-mean uniform one at every heterogeneity level tested.