The 3D version of this simulator tracks individual electrons and holes random-walking to discrete surface sites. This 2D companion instead solves the actual reaction-diffusion PDE for the electron and hole density fields ne(x,y,t), nh(x,y,t) over the particle's cross-section on a finite-difference grid, every frame — carrier transport, recombination and surface capture all emerge from integrating a continuum field, not from sampling per-particle probabilities:
∂n_e/∂t = D_e·∇²n_e − k_rec·n_e·n_h + G − S_e(x,y)·n_e [surface shell, active Pt sites]
∂n_h/∂t = D_h·∇²n_h − k_rec·n_e·n_h + G − S_h·n_h [surface shell, everywhere]
G = G0 if hν ≥ E_g, else 0 (uniform generation, thin-particle limit)
De > Dh reflects the higher electron mobility typical of oxide photocatalysts. The bimolecular term k_rec·n_e·n_h is the same Langevin-type recombination used in semiconductor photophysics — both fields lose population at an equal rate wherever electrons and holes overlap, exactly like real electron-hole annihilation. Surface capture only removes carriers in the thin shell ring at the particle's edge, and — like the 3D version — is gated by the electron surface being trapped (Pt loading sets what fraction of the shell is an active capture site) versus whether the resulting carrier can actually do chemistry once trapped (the same thermodynamic straddling condition against H⁺/H₂ and O₂/H₂O).
- Wavelength — sets photon energy E = 1240/λ(nm) eV; below Eg the generation term G is zero everywhere and the fields simply decay to zero (no absorption, no chemistry).
- Photocatalyst / custom band edges — same real band-edge data as the 3D model (TiO₂ anatase/rutile, WO₃, CdS), deciding whether captured carriers can complete both half-reactions.
- Defect recombination — scales k_rec directly; watch the overlap glow (white, where cyan electron and orange hole densities coincide) intensify and the surface rings starve as more carriers die in the bulk before diffusing out.
- Pt co-catalyst loading — widens the active fraction of the electron-capture shell and boosts its capture rate, exactly mirroring the 3D slider's effect on site count and hazard rate.
Apparent quantum yield here is measured the same way as the literature figure of merit: productive surface captures (weighted by the same thermodynamic drive factors) divided by the total electron-hole pairs the generation term has produced — an emergent PDE output, not a lookup.