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Non-Fickian transport of sodium chloride in inter-river land: experiment validation and fractional derivative modeling

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Abstract

River–groundwater interactions, accompanied by solute transport, are one of the most important contemporary challenges. Non-Fickian diffusion behavior has been extensively documented for solute transport in groundwater or river, but less in river–groundwater system. This paper confirms the existence of anomalous diffusion in the river–groundwater system by experiments and then accurately describes the solute transport process by fractional derivative model, especially for the long-time power law tailing characteristic. Laboratory experiment in inter-river land sample shows that the time fractional advection–dispersion equation, which has a parameter (time index \(\alpha\)) defining memory function and other basic transport parameters (velocity v and dispersion coefficient D) with the different hydrogeologic significances, provides a prominent improvement in simulating non-Fickian diffusion behavior compared with the classical advection–dispersion equation. Analysis results indicate that low flow rates reduce mass exchange between the mobile and immobile domains, resulting in late-time heavy tailing phenomenon. In a word, this study provides a new approach to improve our understanding on solute transport in the interfluve with river–groundwater interactions.

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Data Availability Statement

This manuscript has associated data in a data repository. [Authors’ comment: All experimental data were conducted in Hefei University of Technology (China). Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.]

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Acknowledgements

This research was funded by the National Natural Science Foundation of China, grant numbers U2267218, 11972148 and 41831289, the Natural Science Foundation of Jiangsu Province, Grant Number BK20190024, Key R &D Program of Anhui Province, Grant Number 201904a07020071.

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Authors and Affiliations

  1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu, 210098, China

    Yi Xu & HongGuang Sun

  2. School of Resources and Environmental Engineering, Hefei University of Technology, Hefei, 230009, China

    Chuantai Qiao & Jiazhong Qian

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  1. Yi Xu
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Correspondence to HongGuang Sun.

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Xu, Y., Sun, H., Qiao, C. et al. Non-Fickian transport of sodium chloride in inter-river land: experiment validation and fractional derivative modeling. Eur. Phys. J. Plus 137, 1275 (2022). https://doi.org/10.1140/epjp/s13360-022-03498-6

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