Porendiffusion

Porendiffusion is the transport of chemical species through porous materials driven by concentration gradients. It encompasses molecular diffusion within pore bodies, Knudsen diffusion when pore sizes are comparable to the molecular mean free path, and surface diffusion along pore walls. The diffusion process is strongly influenced by the pore network’s porosity, tortuosity, connectivity, pore-size distribution, and surface chemistry.

In porous media, diffusion is often described using an effective diffusion coefficient Deff that combines the intrinsic diffusivity of the species with geometric hindrances from the solid matrix. A common form is Deff ≈ ε/τ × D, where ε is porosity and τ is tortuosity; more detailed models incorporate pore-size corrections, adsorption effects, and, for gases, transitions between molecular and Knudsen regimes. The concentration field C evolves according to the equation ∂C/∂t = ∇·(Deff ∇C) plus terms for sorption or chemical reactions. When multiple diffusion mechanisms operate, composite or multi-regime formulations are used to capture the combined behavior.

Porendiffusion has wide applications in catalysis, gas separation membranes, and energy storage, including diffusion of reactants in porous catalysts, transport in fuel cell and battery electrodes, and species migration in porous polymers. It also plays a key role in soil science and environmental engineering, where the movement of gases, nutrients, or contaminants occurs through soil pores.

Measurement and modeling of porendiffusion face challenges such as heterogeneity, anisotropy, scale dependence, and coupling with adsorption and chemical reactions. Techniques include tracer experiments, pulse-field gradient NMR, sorption isotherms, and numerical simulations to bridge pore-scale processes with macroscopic transport.