Scaling behavior of diffusion and reaction processes in percolating porous media.
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), we recover the classical scaling behavior Phi approximately Lxi(1/2), where Phi is the mass flux of reagent penetrating the pore space and L is the system size. Second, at an intermediate range of xi values, when the process is influenced by the fractal morphology of the percolation cluster, we observe an anomalous diffusion scaling, Phi approximately L(alpha/2)xiB, with an exponent beta approximately 0.34. Third, in the absence of diffusional limitation (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.
Costa
M H A S
MH
Departamento de Física, Universidade Federal do Ceará, Fortaleza, Brazil.
Araújo
A D
AD
da Silva
H F
HF
Andrade
J S
JS