Eur. Phys. J. Plus (2019) 134: 492
https://doi.org/10.1140/epjp/i2019-12867-7

Regular Article

Diffusion in a heterogeneous system, fractional dynamics and anomalous diffusion

¹ Departamento de Física, Universidade Estadual de Ponta Grossa, Av. Gen. Carlos Cavalcanti 4748, 84030 - 900, Ponta Grossa, PR, Brazil
² National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas Físicas, 22290-180, Rio de Janeiro, RJ, Brazil
³ Departamento de Engenharia Química, Universidade Federal do Paraná, Av. Cel. Francisco H. dos Santos, 210 - Jardim das Americas, 81531 - 980, Curitiba, PR, Brazil
⁴ Departamento de Física, Universidade Tecnológica Federal do Paraná, Avenida Marcilio Dias 635, Apucarana, Paraná, Brazil
⁵ National Institute of Science and Technology on Complex Fluids, Instituto de Física-USP, 05508-090, São Paulo, SP, Brazil

^* e-mail: eklenzi@uepg.br

Received: 12 March 2019
Accepted: 27 June 2019
Published online: 7 October 2019

Abstract

We investigate the diffusion phenomenon in a heterogeneous system composed by two different media in contact. We consider the dynamics of the particles for each medium governed by generalized diffusion equations, which can be related to fractional diffusion equations. The interface separating the different media defines the boundary conditions to be satisfied by the bulk equations. In particular, we analyze the situation for which one medium offers resistance to the passage of particles to the other. The results obtained in this scenario exhibit a rich variety of behaviors which may be connected to anomalous diffusion.