Anomalous Diffusion and Electrical Response of Ionic Solutions


We analyze the electrical response obtained in the framework of a model in which the diffusion of mobile ions in the bulk is governed by a fractional diffusion equation of distributed order subjected to integro-differential boundary conditions. The analysis is carried out by supposing that the positive and negative ions have different mobility and that the electric potential profile across the sample satisfies the Poisson’s equation. In addition, we also compare the analytical results with experimental data obtained from ionic solutions of a salt dissolved in water, reveling a good agreement and evidencing that the dynamics of the ions can be related to different diffusive processes and, consequently, to anomalous diffusion.