the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 26 May 2026
Quantitative Analysis of the Effect of Flow Velocity on the Size Exclusion Transport of Colloids in Saturated Porous Media
Abstract. Despite extensive studies on colloid transport in porous media, the influence of flow velocity on the size exclusion effect (SEE) remains poorly understood. In this study, nuclear magnetic resonance (NMR) and micro-computed tomography (μ-CT) were employed to characterize the pore structures, and column experiments combined with HYDRUS-1D modeling were conducted to quantitatively analyze colloid transport under varying flow velocities. NMR and μ-CT results indicated that coarser sand possesses a larger average pore diameter. Colloids consistently broke through earlier than the conservative tracer, confirming SEE. Both (ΔTb) and the relative peak arrival time (ΔTpeak) decreased with increasing flow velocity, indicating that SEE weakened as flow increased. Across all media, γ declined from about 0.09–0.14 at low velocity (~0.004 cm s−1) to about 0.03–0.04 at high velocity (~0.03 cm s−1). In addition, γ was generally higher in 10 cm columns than in 30 cm columns, especially at low velocity. Flow simulations further suggested that increasing velocity reduced the dominance of low-velocity regions and enhanced the continuity of active flow pathways. These results indicate that γ is not a fixed geometric constant, but a flow-dependent effective parameter governed by pore accessibility and transport conditions.
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Status: open (until 08 Aug 2026)
- RC1: 'Comment on egusphere-2026-2442', William Johnson, 19 Jun 2026 reply
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RC2: 'Comment on egusphere-2026-2442', Atefeh Vafaie, 08 Jul 2026
reply
The manuscript presents a useful experimental and modeling study on the influence of flow velocity on size-exclusion transport of colloids in saturated porous media. The combination of column experiments, conservative tracer tests, silica colloid breakthrough curves, NMR/μ-CT pore characterization, HYDRUS-1D modeling, and pore-scale flow simulations is valuable. The main conclusion that the size-exclusion coefficient γ behaves as a flow-dependent effective parameter rather than a fixed geometric constant is interesting and potentially important. But,
1- The mechanistic interpretation requires careful consideration. While the manuscript suggests that increased flow velocity enhances pore accessibility and activates more flow pathways, the pore-scale simulations offer only indirect evidence. Because the μ-CT resolution is 11 μm and the colloids are just 0.5 μm in diameter, the simulations cannot directly visualize the pore regions most critical for colloid exclusion.
2- The authors should better separate the effects of size exclusion from retention/deposition. Colloid recovery changes with flow rate, suggesting that attachment and detachment processes also influence the breakthrough curves. The fitted γ values may therefore partly reflect parameter covariance with retention and dispersion parameters in HYDRUS-1D. Sensitivity analysis, confidence intervals, or parameter-correlation analysis would strengthen the conclusions.
3-The breakthrough-time differences ΔTb and ΔTpeak should be reported not only in dimensional time but also in pore volumes or dimensionless time. Otherwise, the decrease in time difference with increasing velocity may partly reflect the shorter residence time at higher flow rates rather than a true weakening of size exclusion.
4-The pore-scale flow simulations should be presented in greater detail. The velocity fields appear to be compared using absolute velocity magnitudes; therefore, high-flow cases will naturally show higher velocities. Normalized velocity fields, streamline statistics, particle tracking, or quantification of accessible pore volume would provide stronger support for the proposed mechanism.
5-Please check the consistency between the γ values reported in the text, figures, and tables.
6- The figures are generally useful, but some are dense and difficult to read.
7-The English is understandable, but the manuscript would benefit from careful language editing. In particular, terms such as flow rate, Darcy velocity, pore-water velocity, accessible porosity, and size-exclusion coefficient should be used consistently throughout.
Citation: https://doi.org/10.5194/egusphere-2026-2442-RC2
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The manuscript concerns analysis of colloid transport experiments across five flow rates spanning an order of magnitude to discern the relationship of flow rate on the size exclusion effect. The manuscript is well organized and clearly written with effective figures. Before publication however, the reproducibility of the breakthrough curves needs to be addressed, the relevance of the high-porosity media to environmental porous media needs to be addressed, and an apparent misunderstanding among the authors needs to be addressed regarding the sequential steps of colloid interception (entry to the near surface fluid domain, secondary minimum) versus contact (entry to primary minimum) versus attachment (torque balance in contact).
Lines 80-81, 85, 323-325. The authors suggest that the torque balance is a primary impact on colloid retention. This is likely not true for the fluid velocities examined here. Under the unfavorable deposition conditions examined here (both colloid and grain surfaces being negatively charged), colloid retention concerns entry to the near surface fluid domain corresponding to the secondary minimum in xDLVO profiles. If nanoscale heterogeneity exists (which it always seems to do) then the electric double layer barrier will be locally eliminated and the colloid may enter the primary minimum (contact). If contact is made, then the colloid may arrest if the torque balance allows, which is the case under the fluid velocities of most colloid transport experiments (see VanNess et al., 2019, Ron et al., 2019). So, depending on the range of fluid velocities in the authors’ experiments (the authors should provide these), retention in the experiments is likely far less about torque balance and far more about whether the colloid can come into contact in the first place.
VanNess Kurt, Anna Rasmuson, Cesar A. Ron, William P. Johnson, 2019, A Unified Theory for Colloid Transport: Predicting Attachment and Mobilization under Favorable and Unfavorable Conditions, Langmuir, 35 (27), 9061-9070, 10.1021/acs.langmuir.9b00911.
Ron Cesar, Kurt VanNess, Anna Rasmuson, William P. Johnson, 2019, How Nanoscale Surface Heterogeneity Impacts Transport of Nano- to Micro-Particles on Surfaces under Unfavorable Attachment Conditions, Environmental Science: Nano, 6, 1921 - 1931, 10.1039/C9EN00306A.
This issue of contact and attachment is actually somewhat problematic for the authors’ purposes. The authors need to be clearer about the conditions under which deposition versus SEE impacts the early breakthrough. It should be noted that irreversible deposition (which colloid deposition almost always is in the absence of perturbations in flow or chemistry) does not impact timing of breakthrough.
Line 114: The 0.434 porosity is very high, suggesting a very open structure presumably because the grains are angular and uniform. Most uniform sands have a porosity of 0.35-ish. The porosity of non-uniform sands trends toward 0.3. The authors should address the relationship of the authors’ media to environmental porous media, and how the breakthrough (SEE) results shown for the authors’ media might relate to colloid breakthrough in environmental porous media.
Lines 126-128: UV absorbance quantification is typically coarse. I've never before seen (Figure 4) such fine-scale changes in breakthrough using UV absorbance. The authors should demonstrate that the range across triplicate experiments under a single condition is significantly smaller than the range associated with changing the flow rate.
Line 303: The authors state that the BTC shapes “are strongly dependent on flow velocity”. The fact is that the apparent dependence is not strong, the breakthrough curves only modestly change with flow rate (or fluid velocity). But the curves show a surprising implied reproducibility via consistent minor changes in the timing and magnitude of breakthrough with changes in velocity. I’ve already brought up the need to demonstrate reproducibility of the trend. The figure would be clearer if the authors used a consistent color ramp, e.g., cool to warm colors across lower to higher flow rates. BTW, "flow velocity" is an oxymoron. It's either flow rate or fluid velocity. The authors create redundant and misstated observations by also stating on line 315: “Additionally, the BTCs of the colloids exhibit a strong dependence on the flow rate”.
Line 99: Is particle “size” the diameter or radius?