Journal of Statistical Physics

, Volume 174, Issue 3, pp 548–561 | Cite as

Fluid Reactive Anomalous Transport with Random Waiting Time Depending on the Preceding Jump Length

  • Hong ZhangEmail author
  • Guo-Hua Li


Anomalous (or non-Fickian) diffusion has been widely found in fluid reactive transport and the traditional advection–diffusion–reaction equation (ADRE) based on Fickian diffusion is proved to be inadequate to predict this anomalous transport of the reactive particle in flows. To capture the complex coupling 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 generalized master equations in Fourier–Laplace space for the distribution of A and B particles in continuous time random walks scheme. As examples, the generalized ADREs for the jump length of Gaussian distribution and L\({\acute{\mathrm{e}}}\)vy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived generalized master equations.


Anomalous (or non-Fickian) diffusion Continuous time random walk Advection–diffusion–reaction equation 



The authors wish to thank the anonymous referees for their valuable suggestions leading to the improvement of the work. Project supported by the National Natural Science Foundation of China (Grant No. 11626047) and the Foundation for Young Key Teachers of Chengdu University of Technology, China (Grant No. KYGG201414).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics TeachingChengdu University of TechnologyChengduChina

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