Estudo do Fenômeno de Difusão Anômala em Sistemas de Engenharia

Abstract

In last years, numerous efforts have been devoted to the understanding of certain phenomena that do not perfectly follow classical theories presented in the literature. Among these, the particle diffusion process, which can be mathematically modeled by Fick's law, may not be able to represent some phenomena occurring in nature. These include phenomena of time delay and retention effects, which occur due to adsorption, mechanical entrapment, chemical reactions and mechanical interactions with the support medium. In general, the literature deals with these cases through the inclusion of retention effects in the diffusion equation through fractional derivatives; or via modeling of the diffusion coefficient variant with time and/or concentration or from a discrete approach in population dynamics. In view of the foregoing, the present contribution aims to review the phenomena of anomalous diffusion in engineering systems. Thus, a study on the model proposed by BEVILACQUA et al. (2011a, 2011b) was done, which it was evaluated the influence of the parameters of the model on the process, using the Method of Lines as alternative numerical methodology to solve the problem. The anomalous diffusion process was analyzed considering a symmetrical and asymmetric distribution, then these models were studied separately and each parameter had its influence detailed. The results indicated that the adopted methodology obtained satisfactory results and it can be observed that the anomalous diffusion process presents a delay in relation to the time when compared to the classic process.