We investigate through molecular dynamics the transition from Knudsen to molecular diffusion transport towards two-dimensional absorbing interfaces with irregular geometry. Our results indicate that the length of the active zone decreases continuously with density from the Knudsen to the molecular diffusion regime. In the limit where molecular diffusion dominates, we find that this length approaches a constant value of the order of the system size, in agreement with theoretical predictions for Laplacian transport in irregular geometries. Finally, we show that all these features can be qualitatively described in terms of a simple random-walk model of the diffusion process.

We investigate the diffusion-reaction behavior of two-dimensional pore networks at the critical percolation point. Our results indicate the existence of three distinct regimes of reactivity, determined by parameter xi[triple bond]D/(Kl2), where D is the molecular diffusivity of the reagent, K is its chemical reaction coefficient, and l is the length scale of the pore. First, when the diffusion transport is strongly limited by chemical reaction (i.e., D<>K), the flux of reagent reaches a saturation limit Phi(sat) that scales with the system size as Phi(sat) approximately L(alpha), with an exponent alpha approximately 1.89, corresponding to the fractal dimension of the sample-spanning cluster. We then show that the variation of flux Phi calculated for different network sizes at the second and third regimes can be adequately described in terms of the scaling relation, Phi approximately L(alpha)f(xi/L(z)), where the crossover exponent z approximately 2.69 is consistent with the predicted scaling law alpha=2betaz.