This is a genuine 2D field simulation, not a flattened camera view of a tank: instead of animating individual ion particles, it solves Fick's second law — the same diffusion equation the 3D version quotes — directly on a 1D grid of cells running from deep inside the negolyte, through the membrane, to deep inside the posolyte. Two tagged concentration fields (which vanadium ions started on the left vs. the right) diffuse through that grid every frame with an explicit finite-difference scheme, so the crossover you see is a real numerical PDE solve, not a random walk.
Fick's 2nd law on the grid:
∂C/∂t = ∂/∂x( D(x) · ∂C/∂x )
D(x) = D_tank inside each well-mixed tank (fixed, fast)
D(x) = D_m(perm) inside the membrane band (slow, your slider)
Crossover flux at the membrane face:
J = -D_m · ∂C/∂x (Fick's first law, evaluated at the interface)
Because D_tank ≫ D_m, each tank stays nearly uniform while the membrane band acts as the resistive bottleneck — the concentration profile you see is literally the numerical gradient driving the flux. The "purity" bars track how much of each tank's vanadium is still native vs. foreign (crossed) origin; cell capacity fades with the same asymptotic form as the 3D model, because the concentration gradient — and therefore the flux — shrinks as the two tags mix toward equilibrium:
Q(N) ≈ Q₀ · [1 − f_fade·(1 − e^(−crossed / scale))]
- Membrane permeability Dm — sets the membrane band's diffusivity directly; higher values let the grid mix faster and fade capacity sooner.
- Cycling rate — how fast the stack's oxidation-state phase (the color mix drawn on the field) swings; faster cycling accumulates cycle count sooner, independent of the diffusion itself.
- Electrolyte concentration — sets the initial step height of both tagged fields, i.e. the raw size of the gradient the membrane has to relax.
Real-world relevance: crossover-driven capacity fade (not electrode wear) is the dominant long-term degradation mechanism in commercial VRFB installations, which is why utility-scale systems schedule periodic electrolyte rebalancing rather than replacing electrodes.