Scaling approach to study diffusion and reaction processes on fractal catalysts

Abstract

We use simple scaling arguments to predict the behaviour of diffusion and reaction processes taking place in porous fractal object, modelled by fractal surface, or over isolated catalyst crysallite, using a fractal subset to represent the distribution of active sites. These scalings are tested then by exact numerical simulations. The analysed processes and scaling are: (a) In a process of reaction and diffusion inside a catalyst with fractal external surface exposed to a fixed reactant concentration the overall reaction rate scales as k( D/ k) ( d− D f )/2 , where D is the diffusion coefficient, k is the rate constant of a first-order reaction and d is the dimension of the embedding Euclidean space. (b) In a process of diffusion from the bulk, through a stagnant film, towards a fractal surface over which an instantaneous reaction occurs, the overall rate scales as δ − D f , where D f is the surface fractal dimension and δ is the film thickness. This holds for a fractal rough surface as modelled by the Koch curve ( D f >1) or for a fractal subset as modelled by the Cantor set (CS). (c) In a process of adsorption on the gaps of a Cantor set (CS) and surface diffusion towards the CS points where instantaneous reaction occurs the rate scales as k a ( D s / k a ) (1− D f )/2 , where D s is the surface diffusion coefficient and k a is the adsorption constant.