Continuous-time random-walk approach to normal and anomalous reaction-diffusion processes

TL;DR

This paper models the transport of radioactive particles in heterogeneous porous media using a continuous-time random walk framework, focusing on decay coupled with anomalous diffusion to understand particle displacement and spread.

Contribution

It introduces a novel approach to analyze radioactive decay coupled with anomalous diffusion in heterogeneous media within the CTRW framework.

Findings

Derived the distribution of the number of jumps before decay.

Computed moments of particle distribution to quantify displacement.

Provided insights into contaminant spread in complex media.

Abstract

We study the dynamics of a radioactive species flowing through a porous material, within the Continuous-Time Random Walk (CTRW) approach to the modelling of stochastic transport processes. Emphasis is given to the case where radioactive decay is coupled to anomalous diffusion in locally heterogeneous media, such as porous sediments or fractured rocks. In this framework, we derive the distribution of the number of jumps each particle can perform before a decay event. On the basis of the obtained results, we compute the moments of the cumulative particle distribution, which can be then used to quantify the overall displacement and spread of the contaminant species.