From Light Diffusion to Photocatalytic Rates: Compact Scaling Laws for Strongly Scattering Porous Slabs

Abstract

Light transport in strongly scattering porous photocatalytic materials governs the spatial distribution of absorbed photons and therefore the generation of charge carriers driving photocatalytic reactions. Yet translating measured optical properties of such media into intrinsic reaction rate constants remains challenging, as it requires simultaneously accounting for multiple scattering, boundary losses, photochemical efficiency, and surface kinetics. Here we develop a compact analytical framework that unifies these processes for nanoparticle-loaded photocatalytic slabs. Using a finite-slab diffusion model with extrapolated boundaries, we derive closed-form expressions for the fluence field and couple them to a photochemical quantum efficiency and first-order surface kinetics. The resulting predictors yield intrinsic volumetric and areal rate constants whose dependence on the transport mean free path, optical thickness, and surface-to-volume ratio emerges transparently. Validation against Monte-Carlo photon-migration simulations shows that the diffusion approximation reproduces the fluence and generation-rate profiles with a modest multiplicative mismatch, typically within a factor of about 1.20-1.39, depending on the anisotropy and scattering phase function. This level of agreement is consistent with the known limits of the diffusion approximation and is sufficient to enable reliable, design-oriented predictions. The analytical descriptors introduced here, such as l*, S/V and the extrapolation length zb are general, physically interpretable, and directly integrable into data-driven optimisation and geometry-engineered reactor design. The framework thus provides a versatile and physically grounded tool for photocatalytic systems across diverse applications, including VOC photo-degradation, indoor air purification, and solar-fuel production.