Difusão em meios desordenados

Abstract

The diffusion process is widely approached in physical systems where matter transport takes place in a medium. In homogeneous media, where there are no barriers, the diffusion is characterized as normal, because the particles have a mean square displacement that grows linearly with time. However, in critically disordered media, when the particles are trapped within a region with fractal contours, the relation of the mean square displacement of the particle ceases to be linear with time, characterizing the process of anomalous diffusion. Several examples of disordered media can be found in nature and, because of this, the study of the anomalous diffusion process has great applicability. There are statistical models capable of simulating both the process of diffusion of particles and the geometry of disordered medium, generating a fractal object. In this work we use the percolation model to obtain a fractal, which represents a critically disordered media, and we use the random walk model to simulate the random motion of particles that diffuse through this medium. Thus, we determine the correlation between the system geometry and the dynamic diffusion process, characterized by the dynamic exponents dw, which represents the fractal dimension of the trajectory of the particle, and µ, which represents the conductivity of the medium. We also obtained the spectral dimension of the system, ds, in a value close to that predicted through the Alexander-Orbach conjecture.