the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Aug 2026
Transient electroosmotic transport under evolving pH and contrasting background electrolyte concentrations: coupled controls of interfacial charge and pore structure
Abstract. Electroosmotic flow (EOF) can transport porewater and dissolved neutral solutes through fine-grained porous media, but its magnitude may evolve as electrode reactions alter pH and electrolyte conditions at mineral–water interfaces. Here, we use 24 two-dimensional pore-scale simulations to quantify how interfacial-charge parameterization, background electrolyte concentration, and pore architecture regulate transient electroosmotic displacement. The model couples incompressible flow, multicomponent Nernst–Planck–Poisson transport, time-dependent electrolysis boundary forcing, and chemistry-dependent electroosmotic slip. Zeta potential is calculated from the local aqueous chemistry using either a one-pK electric-double-layer (EDL) parameterization or a two-pK extended triple-layer (ETL) parameterization. The simulations were conducted in four uniformly oriented packings and two composite pore geometries. Under a matched background electrolyte concentration of 10 mM, the geometry-averaged fraction of tracer depleted from the contaminated medium zone after 30 min was 0.998 for the EDL cases and 0.918 for the ETL cases, while the corresponding late-time tailing indices were 0.002 and 0.094. Within the ETL cases, increasing the background electrolyte concentration from 1 to 100 mM reduced the mean 30 min depletion fraction from 0.963 to 0.613 and increased the tailing index from 0.037 to 0.465. None of the 100 mM cases reached 90 % depletion within 30 min. Pore architecture did not alter this group-level ordering but systematically reorganized directional transport and plume geometry within each electrochemical regime. In the uniformly oriented packings, rotation redistributed flow between the gradient-aligned and transverse directions and produced systematic plume reorientation, although fixed-time depletion varied non-monotonically with angle. In the composite geometries, the heterogeneous directional geometry maintained stronger domain-scale directional organization and reached its case-specific early and intermediate progress levels earlier than the non-directional geometry, whereas their fixed-window depletion ranking depended on the electrochemical setting. Comparisons at case-specific relative progress levels separated plume reorganization from differences in transport timescale. These results reveal a two-level control on transient electroosmotic transport: interfacial-charge representation and background electrolyte concentration determine transport magnitude and timescale, whereas pore structure redistributes flow pathways and plume geometry within the resulting regime.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Hydrology and Earth System Sciences.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: open (until 15 Sep 2026)
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RC1: 'Comment on egusphere-2026-4386', Anonymous Referee #1, 23 Aug 2026
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AC1: 'Reply on RC1', Ping Yang, 09 Sep 2026
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On behalf of all co-authors, we sincerely thank Anonymous Referee #1 for the constructive comments. Our preliminary point-by-point response is provided in the attached supplement. Detailed revisions will be incorporated into the manuscript after the post-discussion decision.
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AC1: 'Reply on RC1', Ping Yang, 09 Sep 2026
reply
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RC2: 'Comment on egusphere-2026-4386', Anonymous Referee #2, 25 Aug 2026
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Wu et al. use pore-scale simulations to investigate how evolving aqueous chemistry, interfacial charge, electrolyte concentration, and pore architecture regulate transient electroosmotic transport in low-permeability porous media. The topic is interesting, the manuscript is generally well organized, and the figures clearly present the main results. However, several minor issues require further clarification before publication. My comments are listed below and I hope they will help the authors improve the manuscript.
Major comments
- The model imposes a potential difference of 0.25 V across the computational domain while water electrolysis is treated as the only electrode reaction. Please clarify how the electrolysis flux is related to the imposed electrical potential and whether the 0.25 V represents only the transport domain voltage drop rather than the full electrode potential difference, particularly considering the thermodynamic potential required for water electrolysis.
- The model solves the Poisson equation for porewater charge density while the interfacial electric double layer is not explicitly resolved and electroosmosis is represented by a slip condition. The authors should clarify the consistency between these two treatments and demonstrate that the numerical resolution is sufficient for the charge-density and electric-potential fields under the tested electrolyte concentrations.
- Group-level means and standard deviations are calculated across six deterministic pore geometries that include structurally different SROE, HD, and ND configurations. Please clarify the physical meaning of pooling these geometries and ensure that the resulting statistics are interpreted as descriptive summaries rather than measures of statistical uncertainty or ensemble behavior.
- The Discussion could better emphasize the broader implications and limitations of the pore-scale findings. A stronger discussion of how the identified controls on transport magnitude, timescale, and plume organization may influence larger-scale electrokinetic transport and remediation systems would improve the significance of the manuscript.
Minor comments
- Lines 135-145: Please report representative Reynolds numbers to support the stated low-Reynolds-number flow regime.
- Lines 255-260: Please explain why the molecular diffusivity of Org was set equal to that of Cl-1, and provide supporting references if available.
- Line 264: Please provide a brief physical justification or supporting references for selecting 30 min as the common simulation window.
- Lines 265-270: Numerical convergence is mainly demonstrated using TT30; please clarify whether similar numerical behavior is expected for the more extreme TH cases.
- Lines 278-285: Please discuss whether the periodic upper and lower boundaries affect transverse flow and plume displacement in the rotated geometries.
- Lines 320-329: The 15-30 min interval used to define the tailing index requires further justification, and a brief justification or sensitivity statement would be useful.
- Lines 345-350: Please indicate whether this temporal mismatch has a measurable effect on the plume descriptors.
- Lines 370-379: Please clarify the sensitivity of the concentration-ridge results to the selected smoothing, peak-height, prominence, and separation criteria.
- Lines 540 to 548: HD reaches the 90 percent depletion threshold earlier than ND under TO and TT but shows lower depletion after 30 min. A brief explanation of this apparent difference between threshold attainment time and end window depletion would help readers interpret these metrics.
Citation: https://doi.org/10.5194/egusphere-2026-4386-RC2 -
AC2: 'Reply on RC2', Ping Yang, 09 Sep 2026
reply
On behalf of all co-authors, we sincerely thank Anonymous Referee #2 for the constructive comments. Our preliminary point-by-point response is provided in the attached supplement. Detailed revisions will be incorporated into the manuscript after the post-discussion decision.
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General Assessment
This manuscript presents a coherent pore-scale numerical investigation of transient electroosmotic transport in low-permeability porous media. The coupled treatment of aqueous chemistry, interfacial charge, electroosmotic slip, and pore structure is scientifically meaningful, and the comparison between the one-pK EDL and two-pK ETL formulations is particularly useful. The 24-case simulation matrix is well designed, and the mesh, time-step, and solver-sensitivity tests support the numerical robustness of the results.
The main conceptual contribution is clear: the interfacial electrochemical setting primarily controls transport magnitude and timescale, whereas pore architecture mainly redistributes flow pathways and plume geometry. The manuscript is publishable in principle. I recommend minor revision, mainly to sharpen the interpretation of the metrics, clarify model limitations, and avoid over-generalization.
Main Comments
1.Clarify the meaning of CMZ depletion.
The main bulk metrics are defined with respect to the contaminated medium zone (CMZ). Depletion from the CMZ does not necessarily mean removal from the whole computational domain, because tracer transferred into the buffer zones is already counted as depleted from the CMZ. Please state this distinction more explicitly in the Abstract, Results, and Conclusions. If convenient, a whole-domain mass or cumulative outflux metric could be added as a complementary measure.
2.Qualify the EDL–ETL comparison more clearly.
The large difference between EDL and ETL is an important result, but it reflects both model-form and parameter-set differences. The comparison therefore demonstrates sensitivity to the selected interfacial representation rather than proving that one model is universally superior. This point should be emphasized earlier. A limited parameter sensitivity test would strengthen the conclusion, although a clearer discussion may be sufficient.
3.Strengthen the discussion of chemical simplifications.
The model updates zeta potential from local surface speciation but does not include finite surface-site inventories or surface-reaction source/sink terms in the aqueous mass balance. In addition, activity coefficients are set to unity, which is increasingly restrictive at 100 mM. Please explain more explicitly how these assumptions may affect pH propagation, interfacial charge, and the quantitative interpretation of the high-electrolyte cases.
4.Keep the pore-structure conclusions appropriately limited.
The SROE rotation series also introduces modest changes in porosity and local pore geometry, so the results should continue to be described as orientation-associated structural effects rather than pure orientation effects. Likewise, the HD–ND comparison is based on one deterministic realization of each geometry. The authors should avoid implying a universal ranking of directional and non-directional structures.
5.Emphasize the scope of the neutral conservative tracer.
Org is used as a neutral, conservative tracer without electromigration, sorption, degradation, or reaction. This is appropriate for isolating electroosmotic advection–diffusion, but the resulting depletion should not be interpreted directly as remediation efficiency for ionic, sorbing, or reactive contaminants. A concise statement in the Discussion and Conclusions would improve the environmental interpretation.
6.Briefly justify the relative-progress analysis.
The stage-aligned plume comparison is a useful feature because it separates transport-rate differences from plume reorganization. Please add a short rationale for the selected progress levels (0.25, 0.60, and 1.00) and state whether the main structural conclusions are expected to be robust to moderate changes in these thresholds.
Minor Comments
1.“Contaminated medium zone” first appears in the Abstract without introducing the abbreviation CMZ, while “CMZ depletion” is subsequently used in the main text before CMZ is formally defined in Sect. 2.3.2. Please define “contaminated medium zone (CMZ)” at its first occurrence and use the terminology consistently throughout.
2.For the 100 mM cases, emphasize that the results are most reliable for qualitative concentration-dependent trends rather than absolute values.
3.If possible, include the post-processing scripts for CMZ metrics and plume descriptors in the final public repository to improve reproducibility.
Recommendation
The manuscript is scientifically sound and the major conclusions are supported by the simulations. The remaining issues are primarily matters of clarification, scope, and interpretation rather than fundamental methodological flaws. I therefore recommend Minor Revision / Accept after Revision.