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