A predictive dimensionless framework for optimization of reaction localization in transport-limited porous silicon micro-battery electrodes

Electrochemical performance in porous electrodes is governed by coupled transport and nonlinear reaction kinetics, yet spatial reaction heterogeneity is rarely condensed into a design-oriented quantitative metric. Here, a dimensionless Reaction Localization Number (RLN), defined as the peak-to-average magnitude of the Faradaic reaction-current distribution, is introduced for transport-limited porous silicon micro-battery electrodes. A physics-based continuum model first maps RLN across electrolyte ionic conductivity (κₑ) and diffusivity (Dₑ), showing that ionic conduction is the dominant control: RLN decreases from 8.77 to 1.52 as κₑ increases from 0.05 to 1.2 S m⁻¹, an 82.7% reduction, whereas Dₑ produces comparatively minor changes over the investigated range. Robustness is then tested using an expanded 54-case matrix spanning κₑ = 0.05–1.2 S m⁻¹, applied current density iapp = 35–105 A m⁻², and negative-electrode thickness Lneg = 125–375 µm. Across this matrix, RLN spans 1.12–13.35 and populates low (RLN < 3), moderate (3 ≤ RLN < 6), and high (RLN ≥ 6) localization regimes. At κₑ = 0.20 S m⁻¹ and iapp = 70 A m⁻², increasing Lneg from 125 to 250–375 µm drives RLN from 2.64 to 4.60–6.73, traversing all three regimes. Conversely, every tested current–thickness combination at κₑ ≥ 0.8 S m⁻¹ remains in the low-localization regime. The RLN = 3 and 6 boundaries are therefore interpreted as operational peak-amplification thresholds rather than universal constants. The results establish RLN as a compact descriptor linking transport demand, electrode geometry, and reaction heterogeneity for screening porous-electrode designs against localization risk.