Interaction of ballistic particles with irregular pore walls, Knudsen diffusion, and catalytic efficiency

Abstract

The statistical behavior of ballistic trajectories in irregular two-dimensional systems is studied numerically. The geometrical irregularity is modeled by specific prefractal shapes. Many statistical distributions arising from these trajectories are found to obey power laws of the L\'evy type with an exponent of order -2. This is the case for the probability distribution of the collision numbers, collision frequencies, trajectory lengths, and free paths. The results are applied to several physical systems in which these statistics govern the physical properties. The global absorption of light by irregular, partially absorbing surfaces is found to be weakly dependent on the geometrical irregularity. In contrast, the mean interaction of a gas with an irregular surface increases strongly with the irregularity of the surface. Catalytic efficiency is also found to increase strongly with irregularity. However, surface irregularity has only weak effects on the macroscopic Knudsen diffusion. These conclusions are not modified when the partially random character of the interaction on the pore wall is taken into account.