Environmental Science and Pollution Research

, Volume 26, Issue 32, pp 33621–33630 | Cite as

Random walk particle tracking simulation on scalar diffusion with irreversible first-order absorption boundaries

  • Yu-Fei Wang
  • Wen-Xin HuaiEmail author
Research Article


Scalar transport in an open channel with irreversible first-order absorption boundaries is investigated through random walk particle tracking method (RWPT). We provide the pre-asymptotic behavior of scalar transport as well as a comparison with existing asymptotic formulations. The RWPT method is based on the development of the probability that a particle is absorbed at the boundary. The random walk model is applied to simulate three main parameters of the scalar transport in the laminar flow with sorption boundaries. The three parameters are (1) the attenuation coefficient reflecting the depletion rate of the total mass; (2) the effective velocity coefficient representing the effective advection of the total mass; and (3) the effective longitudinal dispersion coefficient expressing the effective spreading rate of the solute plume. When the Peclet number is large, numerical results agree well with previous theoretical solutions. Results show that (1) the three coefficients reach their asymptotic values when the dimensionless time τ (= Dt/H2) is about 0.5, where t is the time, H is the water depth, and D is the molecular diffusion coefficient and (2) when the Damkohler number reaches a value around 100, the boundary can be treated as a totally absorptive boundary.


Absorption boundaries Random walk particle tracking Taylor dispersion 



We appreciate insightful suggestions from two anonymous reviewers, assistance from Dr. Daniel Fernàndez-Garcia in preparing the draft, discussions with Dr. Piotr Szymczak, and help from the editor Marcus Schulz.

Funding information

This work received support from the National Natural Science Foundation of China (Nos. 11672213, 11872285, and 51439007). Y.F.W. also appreciates the fellowship from FI-AGAUR.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Water Resources and Hydropower Engineering ScienceWuhan UniversityWuhanChina
  2. 2.Department of Civil and Environmental EngineeringUniversitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.Associated Unit: Hydrogeology Group (UPC-CSIC)BarcelonaSpain

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