Vanadium Crossover — Fick's-Law Diffusion Field

Vanadium redox flow batteries store charge in two electrolyte tanks separated by an ion-exchange membrane, but that membrane is never a perfect barrier: vanadium ions constantly leak across it, driven by the concentration gradient between the negolyte (V²⁺/V³⁺) and posolyte (V⁴⁺/V⁵⁺). This simulator solves Fick's second law directly on a 1D spatial grid spanning both tanks and the membrane between them, so the concentration profile, the crossover flux, and the resulting capacity fade are all genuine outputs of a numerical diffusion solve — not animated particles — cycling the stack through charge/discharge swings at your chosen C-rate exactly as real utility-scale VRFB installations experience between scheduled electrolyte remixing.