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Reaction-Diffusion Problems

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An Introduction to Anomalous Diffusion and Relaxation

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Abstract

In this chapter, we start by investigating the adsorption-desorption phenomenon followed by a reaction process that may occur on a surface in contact with a system composed of two different kinds of particles, 1 and 2. We consider that generalized diffusion equations govern the diffusion of particles of the system in the bulk. Depending on the conditions required to describe the bulk dynamics, these generalized equations may also be related to the fractional diffusion equations. The processes on the surface are also assumed to be related to linear kinetic equations with memory effects, which may be connected to an unusual (or non-Debye) relaxation. In this approach, we may obtain the behavior of the quantities on the surface, where the processes are present, and in the bulk. Subsequently, we consider the diffusion and reaction processes when surfaces do not limit the system as in the first case, thus obtaining a rich class of behaviors and connecting the processes with the continuous time random walk approach. Furthermore, we also consider the diffusion and reaction processes by incorporating a finite phase velocity into the bulk equations.

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Authors and Affiliations

  1. Departamento de Física, Universidade Estadual de Maringá, Maringá, Paraná, Brazil

    Luiz Roberto Evangelista

  2. Departamento de Física, Universidade Estadual de Ponta Grossa, Ponta Grossa, Paraná, Brazil

    Ervin Kaminski Lenzi

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  1. Luiz Roberto Evangelista
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  2. Ervin Kaminski Lenzi
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Correspondence to Luiz Roberto Evangelista .

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Evangelista, L.R., Lenzi, E.K. (2023). Reaction-Diffusion Problems. In: An Introduction to Anomalous Diffusion and Relaxation. PoliTO Springer Series. Springer, Cham. https://doi.org/10.1007/978-3-031-18150-4_7

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