SCALING AND SCALING CROSSOVER FOR TRANSPORT ON ANISOTROPIC FRACTAL STRUCTURES

Diffusion into fibrous anisotropic structures can exhibit a variety of crossover phenomena. Scaling of amount adsorbed versus time in such s tructures is studied by standard renormalization methods as a function of anisotropy for several kinds of discrete models. Total mass adsorb ed as a function of time from a reservoir attached at a single point e xhibits different power laws in different logarithmic ranges separated by crossover times. For example, one expects a transition from scalin g characteristic of a one-dimensional channel to that of an effective isotropic medium as adsorbed material spreads out over successively lo nger length scales. In the models studied, there is an easy diffusion pathway imbedded in a medium having a much lower diffusivity. The easy -diffusion subspace can have fractal dimension below that of the backg round. Different types of crossovers are identified. Power-law exponen ts for mass sorption are controlled by inter-play between effective so urce dimension and fractal dimension of the active diffusion space. Ex ponents characterizing scaling of crossover times as a function of ani sotropy an largely independent or the fractal dimension of the easy-di ffusion pathways.