Influence of Particle Size on the Dynamic Non-Equilibrium Effect (DNE) of Pore Fluid in Sandy Media

Round 1

Reviewer 1 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

1. In the introduction section, the author made significant revisions by summarizing the content into four aspects, resulting in a clearer structure, stronger logic, and improved readability.

2. The basic parameters of the samples, the TDR and T5tensiometer probes during the experiment were presented in tabular form, allowing for clear observation of the experimental process.

3. X-CT scanning images of different samples were used to show the pores and water distribution features. The imaging results directly reveal the water distribution around particles and the DNE effect. It is recommended to incorporate quantitative comparisons of these images by creating a contrast table.

Comments on the Quality of English Language

There are some English expressions and grammar errors in the paper.

Author Response

1. In the introduction section, the author made significant revisions by summarizing the content into four aspects, resulting in a clearer structure, stronger logic, and improved readability.

Answer: We would like to express our sincere gratitude to the reviewer for the valuable suggestions provided in our previous submission. We have revised the manuscript accordingly. Furthermore, we have engaged MDPI's Author Services for polishing and refined the manuscript accordingly.

2. The basic parameters of the samples, the TDR and T5tensiometer probes during the experiment were presented in tabular form, allowing for clear observation of the experimental process.

Answer: We would like to express our sincere gratitude to the reviewer for the valuable suggestions.

3. X-CT scanning images of different samples were used to show the pores and water distribution features. The imaging results directly reveal the water distribution around particles and the DNE effect. It is recommended to incorporate quantitative comparisons of these images by creating a contrast table.

Answer: We would like to express our sincere gratitude to the reviewer for the valuable suggestions.  We have established a contrast table for quantitative comparison in lines 405-407, lines 417-419.

Author Response File: Author Response.pdf

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

“Influence of the particle size on the Dynamics Non-Equilibrium Effect (DNE) of pore fluid in sandy media” titled manuscript tries to develop basic Richards equation and soil hydraulic properties. Then, the results are evaluated by DNE metrics. The topic is interesting in terms of development of multiphase flow models. Some comments and suggestions to the authors are presented below:

 

1. There is no detailed information about dynamic non-equilibrium effect and numerical results in Abstract.
2. Used data characteristics should be explained in detail. To assess the usability of this method in similar studies, what are the range, outliers, etc. of dataset. Then, previous studies based on basic Richards equation and soil hydraulic properties can be compared by the results.
3. Results and discussion and Conclusions parts are very well and meticulously prepared. There are some limitations about applications. However, some clues can be explained to overcome these limitations. Then, what are the initial and boundary conditions of experimental setup?
4. Why is the dashed blue line not horizontal after t3 in Figure 6? Add legends on Figures 4, 6 …
5. There are no equations in the paper. At least, basic Richards equation and equations of DNE should be presented.
6. L142-145: The authors explained no statistically significant linkage between τ extreme values (maximum/minimum) and peak DNE manifestations during drainage events. The correlation results should be explained here.
7. In Figure 1, data visualization skills are not good and the colors cannot be followed on the graph. Vertical axis can be physically maximum as 100%. It can be improved.
8. Latest studies about water saturation and drainage should be discussed well. Then, the authors can explain easily the differences between this study and previous ones.
9. Calibration stage is explained under a subtitle. However, there is no information about the validation stage.

Comments on the Quality of English Language

1. Use passive sentences. Check the sentences started by “we”.
2. Check the tenses in the paragraphs. For example, there present and past tenses in the first paragraph under Introduction.
3. One sentence can’t be a paragraph. See lines 146-149.
4. More keywords can be added to keywords.

Author Response

Responses to Review2:

Comments and Suggestions for Authors

“Influence of the particle size on the Dynamics Non-Equilibrium Effect (DNE) of pore fluid in sandy media” titled manuscript tries to develop basic Richards equation and soil hydraulic properties. Then, the results are evaluated by DNE metrics. The topic is interesting in terms of development of multiphase flow models. Some comments and suggestions to the authors are presented below:

 

1. There is no detailed information about dynamic non-equilibrium effect and numerical results in Abstract.

Answer:  Thank you for your valuable suggestions. Based on your feedback, we have expanded the abstract to include the concept and origin of DNE, added relevant data, and revised the text (lines 11-31).

2. Used data characteristics should be explained in detail. To assess the usability of this method in similar studies, what are the range, outliers, etc. of dataset. Then, previous studies based on basic Richards equation and soil hydraulic properties can be compared by the results.

Answer: We sincerely appreciate the reviewer's valuable suggestions. In response, we have systematically quantified the temporal differences between peak capillary pressure (PMAX) and minimum water saturation (SMIN) across all four experimental sets. These data were rigorously compared against predictions from traditional soil water characteristic curve theory. Subsequently, we have comprehensively rewritten the relevant section to incorporate these analyses (lines 349-362).

3. Results and discussion and Conclusions parts are very well and meticulously prepared. There are some limitations about applications. However, some clues can be explained to overcome these limitations. Then, what are the initial and boundary conditions of experimental setup?

Answer:  We sincerely appreciate the reviewer's valuable suggestions. We have augmented the description of initial and boundary conditions for the experimental apparatus (lines 191-197).

 

4. Why is the dashed blue line not horizontal after t3 in Figure 6? Add legends on Figures 4, 6 …

Answer: Following time T3 in Figure 6, gravitational drainage induced minor downward water migration after each drying-stage pause, resulting in small capillary pressure increasing. We have supplemented Figures 4 and 6 with corresponding legends to clarify this phenomenon.

5. There are no equations in the paper. At least, basic Richards equation and equations of DNE should be presented.

Answer: We sincerely appreciate your valuable suggestions. Regarding the reference to Richards' equation in our manuscript, we confirm it appeared solely in the abstract. We have comprehensively revised the abstract to remove all mentions of Richards' equation. The presentation of dynamic non-equilibrium effects (DNE) in the abstract now focuses exclusively on three experimentally derived signatures: (1) the temporal lag between peak capillary pressure and minimum water saturation, (2) the pressure gap between transient and equilibrium states, and (3) residual water saturation. The equation of DNE proposed by Hassanizadeh and Gray is given in lines 138-141.

6. L142-145: The authors explained no statistically significant linkage between τ extreme values (maximum/minimum) and peak DNE manifestations during drainage events. The correlation results should be explained here.

Answer: We sincerely appreciate your valuable suggestions. DNE fundamentally represents the dynamic non-uniqueness of hydraulic characteristics under varied flow regimes and media textures. Its signatures in a drainage include PMAX-SMIN temporal decoupling, disequilibrium pressure gaps, saturation-rate dependencies etc.. While Hassanizadeh & Gray's model (Eq. 1) proposes τ-calibration and ΔP (the pressure gap between transient and equilibrium states)∝∂S/∂t relationships, these may remain theoretically contested and empirically unverified across heterogeneous media (lines 146-152).

7. In Figure 1, data visualization skills are not good and the colors cannot be followed on the graph. Vertical axis can be physically maximum as 100%. It can be improved.

Answer: We sincerely appreciate your valuable suggestions. We have recreated the chart. 

8. Latest studies about water saturation and drainage should be discussed well. Then, the authors can explain easily the differences between this study and previous ones.

Answer: We sincerely appreciate your insightful feedback. DNE research continues to occupy a specialized niche with incremental advancements. Macroscale challenges include delayed development of multi-scale dynamic monitoring technologies, while microscale limitations involve real-time observation of pore-scale fluid dynamics and fluid-particle interactions. Our revision prioritizes inclusion of the most recent references (within 5 years) to the fullest extent feasible.

9. Calibration stage is explained under a subtitle. However, there is no information about the validation stage.

Answer: Thank you for your valuable suggestions; We have incorporated the relevant content (lines 237-242).

 

Comments on the Quality of English Language

1. Use passive sentences. Check the sentences started by “we”.

Answer: We sincerely appreciate your insightful feedback. While our initial approach followed traditional writing conventions, current norms favor active voice. Since editing services like Sees-editing also recommend this approach, we have maintained active voice throughout the article. We have engaged MDPI's Author Services for polishing and refined the manuscript accordingly (English-edited-97284).

2. Check the tenses in the paragraphs. For example, there present and past tenses in the first paragraph under Introduction.

Answer: We have engaged MDPI's Author Services for polishing and refined the manuscript accordingly.

3. One sentence can’t be a paragraph. See lines 146-149.

Answer: We sincerely appreciate your insightful feedback. We have corrected it.

4. More keywords can be added to keywords.

Answer: We sincerely appreciate your insightful feedback. We have added another two. 

 

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

Thanks authors for their efforts on the revision of the manuscript. Many of the suggestions & comments were replied properly. Only some minor suggestions are below:

 

1) One more keyword as “coarse media” can be added to keywords. Then, keywords should be ordered A to Z.

2) Use passive sentences. Check the sentences started by “we”.

3) More explanations about initial and boundary conditions supported by numerical data are required.

4) A basic table can be used to detailed explanation of data characteristics.

Author Response

1) One more keyword as “coarse media” can be added to keywords. Then, keywords should be ordered A to Z.

Answer: We would like to express our sincere gratitude to the reviewer for the valuable suggestions. We have added “coarse media” and sorted all keywords alphabetically.

2) Use passive sentences. Check the sentences started by “we”.

Answer: We would like to express our sincere gratitude to the reviewer for the valuable suggestions. All sentences beginning with "we" have been converted to passive voice.

3) More explanations about initial and boundary conditions supported by numerical data are required.

Answer: We would like to express our sincere gratitude to the reviewer for the valuable suggestions. In the manuscript, we have added the initial water table and initial saturation parameters, along with descriptions of initial and final boundary conditions at both top and bottom interfaces. The experimental initiation and termination procedures (lines 191-203) were comprehensively rewritten to enhance clarity.

4) A basic table can be used to detailed explanation of data characteristics.

Answer: We would like to express our sincere gratitude to the reviewer for the valuable suggestions. The tables have been incorporated into the manuscript (Lines 345-351). All the explanations are presented in Chapter 3.3.

Author Response File: Author Response.pdf

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. Abstract. It is not usual to use symbols at the beginning of results places again, especially symbols that have no stated meaning. For example, ΔT and ΔP.
2. In line 25, you say “dynamic non-equilibrium effects (DNE)”. Line 37, you say “The dynamic non-equilibrium effects (DNEs)”. So, what is the abbreviation for dynamic non-equilibrium effects?
3. The reviewer felt that the first section, “Introduction”, was very long, but did not have a clear theme to summarize the existing research, and thus summarize the shortcomings and the need for the current research. After reviewing the paper 3 times, I still have nothing. In addition, abbreviations should be widely used from the first time they are presented, rather than repeating the full name of the abbreviation, e.g., line 37, line 60, line 66, line 79, line 94, and line 101, so I would recommend that the authors make significant and effective changes to this section. Although translation software is permitted, authors should proofread the translated text carefully.
4. Lines 148 - 158. this paragraph does not make any sense because the detailed grain size grading parameters of the sand can be clearly and simply compared in a table instead of a redundant textual narrative. Also, where does the sand come from? What is its mineral composition? Is it easy to break? Here, what do you mean by “particle density”? Density in general would be related to the volume of the sample and the number of particles, but it's clearly not a fundamental property of particles. Also, for Figure 1, quite a few data points are unnecessary. For example, sand 1 is larger than the portion of the particle size of 310 μm.
5. Is equation (1) necessary?
6. A clear test plan form and test procedure is encouraged. Currently, reviewers are confused.
7. Equations (2)-(9) are recommended to be put into a table to show what they represent and compare.
8. In line 242, you say “D50”, what is “d50” in line 149?
9. Figure 3, what kind of sand do you mean by test 1 and test 4? Or do you mean sand 1 and sand 4, I'm very confused. Also, the horizontal coordinate (time) doesn't seem to start at 0. Is this by any special design? At the moment, I'm having a hard time clearly understanding what the author is trying to say.
10. The coordinates are different in each of the graphs, Figure 4 and Figure 5, which leads me to not notice any pattern, I think each graph is the same. Also, the font size of “step” is different in the graphs, and it is bigger in Figure 5. This makes me uncomfortable.
11. Line 313-320, is this a note to figure 6? Because the font size in this paragraph matches the font size in the figure notes.
12. Figure 7, do you mean “stand 4” or “sand 4”?

After reviewing the entire paper, the reviewers felt that they did not gain anything new. So, what is the innovation of the study? Is there any particular finding or new framework proposed? Strictly speaking, this is like an undergraduate course report, with nothing new, just a pure presentation of results, and with a large number of irregular formatting errors. A significant and effective revision is a must. Where possible, I would recommend that the author spend considerable time meticulously working on improving the quality of the article for resubmission. Happy Children's Day to you, if applicable.

Reviewer 2 Report

Comments and Suggestions for Authors

1. The improvement of English would strengthen the manuscript. There are some English expressions and grammar errors in the paper.
2. The author needs to further synthesize and refine the research findings from the references, analyzing the influencing factors and dynamic processes of water migration in soils.
3. While the study investigated particle size effects on capillary pressure, it should be noted that pore-scale phenomena are fundamentally governed by pore tortuosity (τ) and packing geometry (φ). We recommend supplementary microstructural characterization of the samples, particularly quantitative analysis of pore-throat size distribution and connectivity, to better elucidate the underlying mechanisms.
4. The authors are encouraged to include photographs of the samples (both pre- and post-experiment) as well as the experimental setup to enhance the reproducibility and visualization of the study.
5. Previous studies have reported similar experimental results. We recommend that the authors incorporate comparative analysis with existing research findings to better position their work within the current scientific context.

Comments for author File: Comments.pdf