Eddy-Driven effects on solute transport in turbulent channel flows in porous media

Li, Zhongxia; Yang, Xianshuo; Yuan, Shuai; Wan, Junwei; Yang, Yun; Feng, Haibo; Kang, Xixian; Huang, Kun; Ma, Chong

doi:10.5194/egusphere-2025-6295

Preprints

https://doi.org/10.5194/egusphere-2025-6295

Preprints

02 Feb 2026

| 02 Feb 2026

Eddy-Driven effects on solute transport in turbulent channel flows in porous media

Zhongxia Li, Xianshuo Yang, Shuai Yuan, Junwei Wan, Yun Yang, Haibo Feng, Xixian Kang, Kun Huang, and Chong Ma

Abstract. Groundwater pollution poses a significant threat to water resource sustainability, yet the role of pore-scale eddies in solute transport remains underexplored. This study investigates the effects of hydrodynamic conditions (flow velocity) and porous media structural parameters (particle size, arrangement) on eddy development and solute transport through laboratory experiments and numerical simulations. A novel three-dimensional (3D) quantitative method for characterizing eddy zones was proposed, revealing the mechanisms of eddy formation and their impact on solute breakthrough curves (BTCs). Results indicate that higher flow velocities and larger particle sizes amplify eddy proportions, leading to pronounced BTC tailing due to delayed solute exchange between main flow stream and eddy zones. The mobile-immobile model (MIM) parameters, particularly the immobile zone ratio (1-β), showed strong alignment with eddy proportions, reducing inversion ambiguity. Smaller particle sizes diminished early solute breakthrough, while random-packed (RP) media exhibited the slowest solute penetration compared to structured arrangements (SC, FCC, BCC). The study establishes exponential relationships between dilution index and eddy-dominated solute heterogeneity, highlighting structural controls on diffusion coefficients. These findings enhance theoretical frameworks for groundwater solute transport and provide practical insights for optimizing pollution remediation strategies in porous media systems.

Received: 17 Dec 2025 – Discussion started: 02 Feb 2026

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Zhongxia Li, Xianshuo Yang, Shuai Yuan, Junwei Wan, Yun Yang, Haibo Feng, Xixian Kang, Kun Huang, and Chong Ma

Status: final response (author comments only)

RC1:
'Comment on egusphere-2025-6295', Anonymous Referee #1, 24 Feb 2026
The authors present a novel 3D quantitative method for characterizing eddy zones and successfully link these physical characteristics to the Mobile-Immobile Model (MIM) parameters. The methodology is sound, and the results are clearly presented. Here are a few questions and suggestions, particularly the simplification and deepening of the introduction section, to help further refine the manuscript:
Terminology Consistency (Turbulence vs. Laminar Flow): The title of the manuscript uses the phrase "turbulent channel flows". However, in Section 3.2, the authors note that the Reynolds numbers range from 113 to 1697 and explicitly clarify that the observed eddy formation is a result of "inertial effects within the laminar flow regime, rather than full turbulence". The authors should clarify this terminology choice, whichwould be helpful to either adjust the title or add a brief explanation in the introduction to ensure consistency with the described flow regime.

Optical Measurement Uncertainty: The authors accurately acknowledge the "increased uncertainty in low-concentration estimation" which is an inherent limitation of the optical calibration method. Given that late-time tailing (e.g., t₉₈) relies heavily on these low-concentration readings to quantify eddy-driven retention, the authors should briefly discuss in the text how this specific limitation might affect the precision of the fitted MIM parameters, particularly the immobile zone ratio (1-β)?

Inert Tracer Assumption: The numerical simulation and the governing equations of the MIM model assume that Brilliant Blue acts as a perfectly inert solute without adsorption or degradation. While this is a reasonable assumption for the experimental setup, is there any possibility of very slight physical sorption onto the artificial spheres? A brief comment on whether minor sorption could have any compounding effect on the observed non-Fickian tailing would strengthen the discussion.

Robustness of the v_cThreshold Method: The determination of the critical velocity threshold (v_c) using the PDF/CDF inflection point is an elegant approach for quantifying the 3D eddy volume in these specific structural packings. How robust do the authors expect this threshold identification method to be if applied to more natural, highly heterogeneous porous media with a wide particle size distribution (unlike the uniform spheres used here)? Adding a short perspective on this in the discussion would highlight the broader applicability of your method.

The first paragraph of the introduction contains a significant amount of textbook knowledge or general background information, such as the current state of contamination and classification of aquifer media. While such content is necessary, it has not yet established a strong connection with the core keyword "Eddy effects" and therefore requires substantial condensation. Similarly, lines 73–83 are overly verbose in setting the stage for introducing "Eddy."

The entire introduction section contains only lines 84–107 that offer an in-depth literature review of the core topic. While the latter part of this section talks about the advantages of the MIM model in characterization from a technical perspective, the first half still fails to clearly articulate the significance of this study. For example, line 93 mentions that current research rarely considers the impact of eddies on solute transport at the pore scale, even though the preceding text has already discussed their influence on pore-scale water flow. However, why bridging the understanding from water flow to solute transport presents such a major challenge or gap remains unclear to the reader. Thus, further elaboration is needed.

Line 92 mentions that previous studies have not directly observed the eddy region. This raises the question: are there any potential experimental methods or techniques that could address this gap? Given that the authors subsequently conducted detailed laboratory experiments, it is recommended that they provide some background on the current state of research regarding such methods. This would help underscore the necessity and significance of the experimental work presented later.

Typos in this manuscript such as the figure caption in Fig. 4 (“comparison between”) should be checked.

Figure 4 is significant for the validation of this proposed method, there the authors should better try best to analyze why there are larger fitting errors in the case of “D=5mm”than those in other cases.
Citation: https://doi.org/10.5194/egusphere-2025-6295-RC1
RC2: 'Comment on egusphere-2025-6295', Anonymous Referee #2, 03 Mar 2026

This manuscript presents a pore-scale experimental and numerical investigation of eddy-driven non-Fickian solute transport in porous media. A three-dimensional numerical method is developed to quantify eddy-zone proportion under varying flow velocities, particle sizes, and packing structures. The relationship between eddy proportion and the immobile fraction of the Mobile–Immobile Model (MIM) is also examined.

The study is scientifically interesting and technically well executed. The topic is relevant, and the attempt to provide a quantitative pore-scale basis for conceptual MIM parameters is valuable. However, several weaknesses need to be addressed before the manuscript can be considered for publication.

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Major Concern

My primary concern relates to the validation strategy. The experimental validation is currently limited to comparison of hydraulic behavior (v–J curves). While this confirms the accuracy of the simulated flow field, it does not sufficiently validate the solute transport model.

The breakthrough curve (BTC) behavior—particularly early arrival and tailing—is central to the study's conclusions regarding eddy-driven non-Fickian transport. Therefore, the solute transport results should be validated directly against experimental BTC data.

I strongly recommend including a comparison between experimental and simulated outlet BTCs under representative flow conditions. Even if limited to a subset of cases, such a comparison would significantly strengthen the robustness of the numerical model and the credibility of the conclusions.

Flow validation alone is not sufficient to validate transport behavior.

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Additional Comments

Line 24

The statement that pore-scale eddies in solute transport “remain underexplored” is not entirely accurate. Several previous studies have investigated this topic. Please revise the wording to reflect that, although eddies have been studied, their quantitative linkage to upscaled transport parameters remains insufficiently established.

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Line 213

The manuscript mentions a mesh sensitivity analysis but does not present the results. Please include the independent mesh convergence analysis, either in the main text or as supplementary material.

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Line 224

The authors state that validation is based on previous experimental data. Why was the current experimental setup not used directly for model validation? Please clarify.

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Lines 244–260

I disagree with the statement that validation of the flow field alone ensures the reliability of the solute transport simulation. Solute transport models must be validated using experimental transport data. At minimum, the simulated and observed outlet BTCs should be compared.

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Line 262

Subsection 3.1 (Identification of eddy zone in 3D scale) describes methodology rather than results. It would be more appropriate to include this section in the Methods.

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Lines 327–328

Please clarify how the Reynolds number was calculated. Specify the characteristic velocity and length scale used.

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Line 357

Why were the numerical BTCs not compared with the experimental BTCs? This comparison would substantially strengthen the study.

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Line 687

The manuscript states that DMIM increases with eddy proportion. What is the physical interpretation of DMIM? Does it represent mechanical dispersion, enhanced mixing, or an effective fitting parameter? This should be clearly explained.

Citation: https://doi.org/10.5194/egusphere-2025-6295-RC2

Zhongxia Li, Xianshuo Yang, Shuai Yuan, Junwei Wan, Yun Yang, Haibo Feng, Xixian Kang, Kun Huang, and Chong Ma

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Short summary

This research investigates how water flows through porous media, focusing on tiny swirling currents called eddies that form around particles. Using experiments and computer, we found that faster flow and larger particles create more eddies, which trap pollutants and slow down their cleanup. A new method is developed to measure these eddies and showed how they can be accurately represented in standard transport models. This study provides a clearer physical basis for predicting pollutant spread.


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