Fluid reactive anomalous transport with random waiting time depending on the preceding jump length

TL;DR

This paper develops a mathematical framework for fluid reactive anomalous transport, incorporating random waiting times influenced by previous jump lengths, to better model complex reactive particle flows in fluids.

Contribution

It introduces a novel master equation approach for anomalous diffusion with waiting times dependent on prior jump lengths, extending traditional models to include energy-dependent effects.

Findings

Derived generalized advection diffusion reaction equations for Gaussian and Lévy flight jump lengths.

Established a master equation framework in Fourier-Laplace space for reactive anomalous transport.

Provided specific models with quadratic waiting time dependence on jump length.

Abstract

Anomalous (or non-Fickian) diffusion has been widely found in fluid reactive transport and the traditional advection diffusion reaction equation based on Fickian diffusion is proved to be inadequate to predict this anomalous transport of the reactive particle in flows. To capture the complex couple effect among advection, diffusion and reaction, and the energy-dependent characteristics of fluid reactive anomalous transport, in the present paper we analyze $A\rightarrow B$ reaction under anomalous diffusion with waiting time depending on the preceding jump length in linear flows, and derive the corresponding master equations in Fourier-Laplace space for the distribution of A and B particles in continuous time random walks scheme. As examples, the generalized advection diffusion reaction equations for the jump length of Gaussian distribution and l\'evy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equations.