Aplicações da equação de difusão : vínculo geométrico e difusão iônica

Abstract

In this work we studied two models that have applications in physical contexts. One is characterized by a diffusive process in a geometric constraint medium, commonly called comb-model, and the other consists in ionic diffusion under action of an external potential. For this study it was necessary a general view about diffusion, ranging from Brownian motion to anomalous diffusion, and a brief introduction of fractional calculus. Comb model was studied in a semi-infinite medium in the axis x with an adsorbing surface in x = 0. It was obtained the temporal evolution of particles density for any position of system in terms of the initial conditions along with mean squared displacement, survival probability and first passage time. These quantities showed the existence of traps in the ramification of comb when considered derivatives of not integer order. The second model studied consists in charge diffusion under influence of external potentials in a one dimentional system formed by a slab d with electrodes in ±d=2. It was considered a general boundary condition on surface of electrode with any odd potential applied, in other words, an electrolytic cell. For this case it was obtained the temporal evolution of potential for any position z of system, considering both the external electric potential and the boundary condition generic. It was realized an analogy with a current measure system in nematic liquid-crystals through with potential applied in the measure process, thus finding similar results to the observed in the lab.