Diffusion controlled reaction rate, survival probability, and molecular trajectory characteristics in the bulk, transition and Knudsen regime

Abstract

Random walk simulation results are presented for the diffusion controlled reaction rate coefficient, molecular survival probability, average track length and relative collision frequency in the bulk, transition and Knudsen diffusion regime, in porous media formed by randomly oriented cylindrical fibers. The survival probability and mean survival distance are found to increase with the porosity in all diffusion regimes. The diffusion controlled reaction rate coefficient attains higher values at lower porosities, obeying an upper bound of the literature and approaching its value in the bulk regime. The values computed for all three parameters in the transition regime depend strongly on the Knudsen number, whereas in the Knudsen regime they are in line with analytical predictions based on the chord length distribution of the fiber structures. A harmonic average approximation based on Bosanquet's equation for the effective diffusivities is found to link successfully the values of the diffusion controlled reaction rate coefficient in the three diffusion regimes. The simulation results for the average molecular track length and relative collision frequency deviate in the biggest part of the transition regime from earlier analytical and numerical results obtained from long diffusion time random walks, in agreement with an analysis centered on the basic differences of molecular trajectories in diffusion controlled reaction systems from those involving molecular reflection from the pore surface.