Motion Control of Gallium-Based Liquid Metal Droplets in Abrasive Suspensions Within a Flow Channel

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper develops a hybrid control framework for precise motion control of liquid metal droplets in abrasive-laden 1-D channels. A dynamic model incorporating particle-dependent damping is established, coupled with vision-guided voltage actuation. Experiments and simulations demonstrate that the proposed dynamic damping strategy enhances stability, minimizes fluctuations, and accelerates positioning in polymethyl methacrylates channels, enabling high-precision control in complex fluidic environments. However, this paper still contains many unclear and non-standard explanations. Therefore, I recommend the article for publication in symmetry after major revising the following issues:

1. The paper mentions that “the research seeks to elucidate the influence of abrasive particles on the behavior of liquid metals under electric field conditions and to propose methods for achieving precise control of liquid metals in complex fluid environments” the expression lacks specificity. The authors should consider refining the focus to more specific aspects of abrasive particle-liquid metal interactions under electric fields.
2. The model presented in Figure 1 lacks proper validation.
3. The paper contains erroneous characters in lines 210-214 that require correction. Correct the duplicate numbering: two 2.3 subsections and Figure 10.
4. The description of Figure 8 seems inconsistent with the presented data. While the text states that larger droplets show higher peak velocities and accelerations, the figure actually suggests the opposite trend where smaller droplets demonstrate greater peak velocities and accelerations.
5. The experimental validation in section 3.2 would be more appropriately presented as a separate section rather than being incorporated into the Results and Discussion.
6. The experimental setup section should explicitly specify the surface properties of the PMMA channel's inner walls (e.g., hydrophilicity/hydrophobicity, contact angle, etc.).

Author Response

Comment 1:

The paper mentions that “the research seeks to elucidate the influence of abrasive particles on the behavior of liquid metals under electric field conditions and to propose methods for achieving precise control of liquid metals in complex fluid environments.” the expression lacks specificity. The authors should consider refining the focus to more specific aspects of abrasive particle-liquid metal interactions under electric fields.

Response:

We sincerely appreciate the reviewer’s valuable feedback regarding the lack of specificity in the statement “the study aims to clarify the influence of abrasive particles on the behavior of liquid metal under electric field conditions and propose a method for precise control of liquid metal in complex fluid environments.” In response, we have revised this section, now found between lines 105 and 113 of the revised manuscript, and highlighted the changes in red for the reviewer’s convenience. This revision serves to enhance clarity and specificity.

The core of this study lies in exploring how abrasive particles with varying sizes and concentrations affect the viscosity of the mixed electrolyte, and further analyzing how this change influences the damping term in the liquid metal dynamics equation. Specifically, this study focuses on the methods for achieving precise motion control of liquid metal droplets within the mixed electrolyte under the influence of an electric field. By analyzing the behavior of liquid metal droplets, the study proposes a precise control strategy for liquid metals in complex fluid environments, aiming to optimize the motion response of liquid metals and provide theoretical support for efficient control in surface treatment processes.

We believe this revision more clearly articulates the objectives and methods of the study, ensuring that the focus of the research is accurately conveyed, while enhancing the scientific rigor and readability of the manuscript.

 

Comment 2:

The model presented in Figure 1 lacks proper validation.

Response:

We sincerely thank the reviewer for their valuable feedback regarding the model presented in Figure 1. As per the reviewer's suggestion, we would like to clarify that the model in Figure 1 is an original illustration, based on the conceptual framework and graphical structure from the published work, "Alternating Electric Field Actuated Oscillating Behavior of Liquid Metal and Its Application." Since this reference has already been published, we have appropriately cited it in both the text (lines 447–448) and the figure A1 legend(lines 474–475). The citation is highlighted in red text for the reviewer's convenience, ensuring that the original work is properly acknowledged.

We believe this clarification resolves the reviewer's concern, providing transparency and enhancing the academic rigor of the manuscript.

 

Comment 3:

The paper contains erroneous characters in lines 210-214 that require correction. Correct the duplicate numbering: two 2.3 subsections and Figure 10.

Response:

We sincerely thank the reviewer for identifying the issues related to character errors, repeated section numbering in lines 210–214, and the concerns regarding Figure 10. In response to these valuable comments, we have made the following revisions:

Correction of Character Errors: In accordance with the reviewer’s suggestion, we have corrected the erroneous characters in lines 505–507 of the revised manuscript. Additionally, regarding the repeated section “2.3” that previously appeared on page 11, line 352, due to adjustments in the manuscript structure, this section has now been moved to the Materials and Methods section (lines 132–172 of the revised manuscript). The modifications have been highlighted in red for the reviewer’s convenience.

Clarification Regarding Figure 10: Upon careful re-examination, we confirm that there is no repetition of Figure 8 (renumbered in the revised manuscript). We have thoroughly checked all figure references in the text to ensure that Figure 8 is cited correctly throughout the manuscript.

We believe these revisions have fully addressed the reviewer’s concerns. We greatly appreciate your meticulous feedback, which has helped us further improve the accuracy of our manuscript. Thank you again for your valuable suggestions.

 

Comment 4:

The description of Figure 8 seems inconsistent with the presented data. While the text states that larger droplets show higher peak velocities and accelerations, the figure actually suggests the opposite trend where smaller droplets demonstrate greater peak velocities and accelerations.

Response:

We sincerely thank you for your valuable comment regarding the inconsistency between the description of Figure 8 and the displayed data. Upon reviewing the manuscript, we acknowledge that the statement in the text, "Large droplets exhibit higher peak velocities and accelerations," was incorrect. As you correctly pointed out, the data in Figure 9(renumbered in the revised manuscript) actually shows that smaller droplets exhibit higher peak velocities and accelerations.

In response to your feedback, we have revised the text accordingly. Specifically, we have corrected the description in lines 335 to 337 of the revised manuscript, where we now clarify that smaller droplets indeed exhibit higher peak velocities and accelerations, as demonstrated in the figure. These revisions are highlighted in red for your convenience.

We believe this correction improves the accuracy and clarity of the manuscript. Once again, thank you for your insightful feedback, which has greatly contributed to enhancing the quality of our work.

 

Comment 5:

The experimental validation in section 3.2 would be more appropriately presented as a separate section rather than being incorporated into the Results and Discussion.

Response:

We sincerely appreciate your valuable suggestion regarding the chapter structure of Section 3.2 in the original manuscript. In accordance with your recommendation, we have revised the manuscript to enhance the clarity and scientific rigor of the results presentation.

Specifically, the experimental validation section—originally embedded within the results and discussion—has now been reorganized. We emphasize the alignment between experimental observations and model predictions in terms of dynamic response trends, further substantiating the accuracy and effectiveness of the proposed control model. For greater clarity and ease of comparison, we have grouped each set of experimental trajectory curves together with their corresponding simulation results within the Results and Discussion section of the revised manuscript.

We believe these changes not only streamline the manuscript structure, but also facilitate a more direct and comprehensive understanding of the agreement between experimental data and theoretical predictions. All relevant modifications have been clearly marked in the revised version for your convenience.

Thank you again for your constructive feedback, which has greatly contributed to the improvement of our manuscript.

 

Comment 6:

The experimental setup section should explicitly specify the surface properties of the PMMA channel's inner walls (e.g., hydrophilicity/hydrophobicity, contact angle, etc.).

Response:

We sincerely appreciate your insightful suggestion regarding the explicit specification of the surface properties (e.g., hydrophilicity/hydrophobicity, contact angle, etc.) of the PMMA channel walls in the experimental setup. In response to your valuable feedback, we have supplemented the manuscript with detailed descriptions of the surface characteristics of the PMMA channel inner walls, as these parameters are indeed critical for the repeatability and accuracy of the experiments. The relevant information has been added in lines 165 to 172 of the revised manuscript and is highlighted in red text for your convenience.

We believe that this addition enhances the transparency and reproducibility of the experimental methodology. Thank you once again for your constructive feedback, which has greatly improved the quality and rigor of our study.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

 

This work presents a method for the precise motion control of liquid metal (EGaIn) droplets in abrasive suspensions, integrating electric-field actuation, dynamic damping modeling, and closed-loop control, with validation through both simulation and experiment. However, the manuscript still requires several clarifications and improvements:

1. Figure 10 appears twice.
2. On page 4, “The paper establish...” should be revised to “The paper establishes...”.
3. The main focus of the study is the precise motion control of liquid metal (EGaIn) droplets. While the manuscript includes extensive simulations, no actual images of the liquid metal droplets are presented throughout the paper. I believe this is critical and should be emphasized rather than relying solely on simulations.
4. The manuscript claims to propose a closed-loop control strategy based on a PID controller, yet this part is not sufficiently highlighted. This should be one of the main contributions of the paper.
5. The overall quality of the figures is low. Additionally, it is unclear whether the experimental data were repeated multiple times. If so, why are error bars not shown?

Major revision. The manuscript should place stronger emphasis on demonstrating the phenomena of precise motion control of liquid metal (EGaIn) droplets and provide a clearer, more detailed description of the control strategy.

Author Response

Comment 1:

Figure 10 appears twice.

Response:

We sincerely thank the reviewer for pointing out the potential issue regarding the repetition of Figure 8(revised version). After a thorough and careful review of the entire manuscript, we would like to clarify that there is no repetition of Figure 8(revised version) in the current version of the manuscript. All references to Figure 8(revised version) have been double-checked, and we have ensured that the figure is used and cited correctly in the text. If the reviewer has identified a specific location that appears to be problematic, we would greatly appreciate further clarification so that we can address it accordingly.

Thank you again for your careful review and valuable feedback.

 

Comment 2:

On page 4, “The paper establish...” should be revised to “The paper establishes...”.

Response:

We sincerely thank the reviewer for identifying this language error. In accordance with your suggestion, we have revised “The paper establish...” to “The paper establishes...” in line 465 of the revised manuscript. The correction has been highlighted in red for your convenience. Thank you again for your careful review, which has helped improve the accuracy and clarity of the manuscript.

Comment 3:

The main focus of the study is the precise motion control of liquid metal (EGaIn) droplets. While the manuscript includes extensive simulations, no actual images of the liquid metal droplets are presented throughout the paper. I believe this is critical and should be emphasized rather than relying solely on simulations.

Response:

We sincerely appreciate the reviewer’s constructive feedback regarding the inclusion of actual liquid metal (EGaIn) droplet images to enhance the visualization and credibility of our experimental results. In response to this valuable suggestion, we have revised the structure of the manuscript and incorporated a new figure (Figure 11 on page 13 in the revised manuscript), which presents a sequential image series capturing the real-time motion of the liquid metal droplet during the control experiment. A detailed description of this figure has also been provided in lines 364 to 371, with the corresponding modifications highlighted in red for your convenience.

We believe that the inclusion of actual experimental images, alongside the simulation results, significantly improves the clarity and practical relevance of the study. These visualizations provide direct evidence of the liquid metal droplet dynamics and serve to further validate the effectiveness of the proposed motion control strategy. Once again, we thank the reviewer for this insightful suggestion, which has substantially enhanced the overall quality and impact of our manuscript.

Comment 4:

The manuscript claims to propose a closed-loop control strategy based on a PID controller, yet this part is not sufficiently highlighted. This should be one of the main contributions of the paper.

Response:

Thank you very much for your valuable suggestion regarding the emphasis on the proposed closed-loop PID control strategy. In response to your comment, we have carefully revised the manuscript structure to ensure that the closed-loop control framework-one of the core contributions of this study-is clearly highlighted.

Specifically, we have substantially expanded the relevant content in the revised manuscript (lines 180–219) and provided a detailed schematic in the new Figure 4, both of which comprehensively illustrate the design, implementation, and significance of the closed-loop PID controller. These sections, now highlighted in red, describe the control logic, feedback mechanism, and the role of vision-based real-time feedback in enabling precise manipulation of the gallium-based liquid metal droplet.

We believe these revisions more clearly communicate the novelty and importance of the closed-loop PID control strategy as a central contribution of our work, and further strengthen the manuscript’s technical depth and clarity.

Thank you again for your insightful feedback, which has greatly improved the quality and focus of our study.

 

Comment 5:

The overall quality of the figures is low. Additionally, it is unclear whether the experimental data were repeated multiple times. If so, why are error bars not shown?

Response:

Thank you very much for your constructive suggestions regarding the overall quality of the figures and the issue of data reproducibility. In response to your comments, we have taken the following actions:

Figure Quality Improvement:
All previously unclear or low-resolution images have been replaced with high-resolution versions in the revised manuscript. This ensures that all axes, labels, and data lines are clear and easily readable at publication scale.

Clarification of Experimental Reproducibility:
As suggested, we have added a statement in lines 239–241 of the revised manuscript (marked in red) explicitly clarifying that each experimental condition was performed in multiple repeated trials to ensure the reliability and reproducibility of the data.

Regarding Error Bars:

We sincerely appreciate your suggestion regarding the presentation of error bars. In this study, the primary objective was to focus on the comparative analysis and pattern recognition of motion control methods for liquid metal droplets. Therefore, the figures primarily present the mean values of multiple repeated measurements for each experimental group, offering a clear visualization of system performance trends under different parameters. We ensured that all key variable conditions were subjected to multiple independent and repeated experiments, following a consistent experimental protocol to guarantee the representativeness and repeatability of the data. The use of averaged values effectively highlights the influence of different variables on control performance while avoiding the potential impact of individual outliers or minor fluctuations on the overall trend.

We believe that these changes have significantly improved the manuscript’s clarity and transparency. Thank you again for your valuable feedback, which has contributed to the enhancement of both the visual quality and the scientific rigor of our work.

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

In this manuscript, the authors investigate the motion control of liquid metal droplets in an abrasive suspension within a flow channel. The research topic is relevant, and the amount of work carried out is considerable. However, significant improvements are required to strengthen the manuscript. Below are several comments and suggestions aimed at enhancing its overall quality:

1. In the abstract, what do the authors mean by "MATLAB simulation"? Was a specific Simulink toolbox employed?

2. The introduction is generally well written. However, the state of the art is not sufficiently presented, making it difficult for the reader to appreciate the originality of the present study.

3. Line 37: Please provide citations of different gallium-based alloys.

4. Line 139: The authors state that the Lippmann model follows a quadratic form, yet Eq. (1) is not quadratic. Please clarify.

5. Lines 144–145: A supporting reference should be added to the statement.

6. Lines 210 and 213: There appear to be errors in the equations and references. Please correct them.

7. How were the empirical parameters in Eq. (17) determined? Please specify.

8. Section 2 lacks clarity. It seems more like a theoretical background or modeling section. Furthermore, some parts are unclear and require references. This section should be rewritten for better readability.

9. The legends in Fig. 4 are not clear and should be improved.

10. The obtained results must be compared with previous findings in the literature. Such a comparison is necessary both to validate the study and to highlight its originality.

11. The conclusion is overly long, and the perspectives are too generic. Please shorten and rephrase this section to make it more concise and specific.

Author Response

Comment 1:

In the abstract, what do the authors mean by "MATLAB simulation"? Was a specific Simulink toolbox employed?

Response:

We sincerely thank the reviewer for the thoughtful comment regarding the use of the term “MATLAB simulation” in the abstract. To clarify, our study is centered on a vision feedback closed-loop control system for real-time position tracking and motion regulation of liquid metal droplets. The entire control framework was developed in MATLAB and integrates multiple functional modules, including image acquisition, image processing, moving target recognition, serial/USB power communication, PID control algorithms, data visualization, and experimental data recording.

Specifically, the following MATLAB toolboxes were employed in this work:

Image Acquisition Toolbox; Image Processing Toolbox; Instrument Control Toolbox.

No specific Simulink toolbox was used in the present study.

To enhance clarity and technical accuracy, this explanation has been added to the main text (lines 148-154), with the relevant revisions highlighted in red for the reviewer’s convenience. We appreciate the reviewer’s insightful suggestion, which has helped improve the precision and completeness of our manuscript.

Comment 2:

The introduction is generally well written. However, the state of the art is not sufficiently presented, making it difficult for the reader to appreciate the originality of the present study.

Response:

We sincerely appreciate the reviewer’s positive assessment of our introduction, as well as the constructive suggestion regarding the presentation of previous research progress. According to your recommendation, we have revised the introduction to more clearly position our study within the context of current research.

Specifically, in the revised manuscript (lines 84, 85, and 94), we have supplemented the introduction with two key references ([33] and [34]). Reference [33] focuses exclusively on the motion control of liquid metal droplets in pure NaOH solutions, while reference [34] investigates, from an experimental perspective, the driving voltage of liquid metal droplets in NaOH solutions mixed with different abrasives (SiC and B₄C). However, neither of these studies addresses the systematic motion control of liquid metal droplets in NaOH-based abrasive fluids containing SiC particles, as explored in our work.

These additions highlight the originality and uniqueness of our research, as our study is the first to systematically investigate the dynamic control of liquid metal droplets in NaOH solutions containing abrasive SiC particles. All relevant modifications have been highlighted in red in the revised manuscript for your convenience.

We believe these updates provide a more comprehensive overview of the state-of-the-art and better clarify the novelty of our approach. Thank you again for your insightful feedback, which has greatly strengthened the context and contribution of our study.

 

Comment 3:

Line 37: Please provide citations of different gallium-based alloys.

Response:

Thank you very much for your valuable suggestion regarding the literature citation for gallium-based alloys in line 37 of the original manuscript. In response to your comment, we have supplemented the manuscript by adding appropriate references that discuss the properties, applications, and significance of gallium-based alloys. These references have been incorporated in the revised manuscript at line 28 and highlighted in red for your convenience.

We believe that these additions enhance the academic rigor and context of the manuscript, providing readers with a more comprehensive background on gallium-based liquid metals. Thank you again for your constructive feedback, which has significantly contributed to improving the quality of our work.

 

Comment 4:

Line 139: The authors state that the Lippmann model follows a quadratic form, yet Eq. (1) is not quadratic. Please clarify.

Response:

We sincerely thank the reviewer for pointing out the apparent inconsistency regarding Eq. (1). We would like to clarify that the Lippmann equation indeed represents a quadratic relationship between the interfacial tension  and the applied voltage (V). Specifically, Eq. (1):

shows that the interfacial tension decreases proportionally to the square of the applied voltage, while other terms remain constant. Thus, although the equation itself is expressed in a linear form with respect to , the dependency of  on  is quadratic, consistent with our statement in the manuscript.

To improve clarity, we have revised the relevant sentence in the manuscript (lines 431-436) and highlighted it in red for the reviewer's convenience.

 

Comment 5:

Lines 144–145: A supporting reference should be added to the statement.

Response:

We sincerely thank the reviewer for the valuable suggestion regarding the need for supporting references in this section. In accordance with the reviewer’s comment, we have carefully revised the manuscript and added the relevant citations to strengthen the scientific basis of our statements. Specifically, the supporting references have been incorporated in the revised manuscript at lines 440–442, and the additions have been highlighted in red for the reviewer’s convenience.

 

Comment 6:

Lines 210 and 213: There appear to be errors in the equations and references. Please correct them.

Response:

We sincerely thank the reviewer for highlighting the issue regarding the incorrect equation and missing citation. According to the reviewer’s valuable suggestion, we have carefully revised the manuscript to ensure both the correctness of the equation and the accuracy of the corresponding citation. Specifically, the necessary citation has been added in the revised manuscript at lines 505–507 to properly support the equation, and the modification has been highlighted in red for the reviewer’s convenience.

 

Comment 7:

How were the empirical parameters in Eq. (17) determined? Please specify.

Response:

We sincerely thank the reviewer for raising this valuable question regarding the empirical coefficients in Equation (17). In response to the reviewer’s suggestion on the determination of empirical parameters, we have added a new section in the Methods part, which provides a detailed description of the regression modeling process for experimental data using the MATLAB nonlinear curve fitting function (lsqcurvefit). The final fitted parameter values and their physical meanings are also presented (see the revised manuscript, lines 560–575), and the modification has been highlighted in red for the reviewer’s convenience.These revisions enhance the transparency of the model and further support the theoretical foundation of Equation (17).

 

Comment 8:

Section 2 lacks clarity. It seems more like a theoretical background or modeling section. Furthermore, some parts are unclear and require references. This section should be rewritten for better readability.

Response:

We sincerely appreciate your valuable suggestions regarding the clarity of Section 2. In accordance with your recommendations, we have made the following adjustments and improvements to the manuscript:

Structural Optimization
The original Section 2 contained extensive theoretical background and modeling content, which has now been moved entirely to Appendix A. This adjustment enables the main text to focus specifically on the experimental methods, avoids confusion with theoretical derivations, and significantly improves the logical flow and readability of the methodology section.

Rewriting of Experimental Methods
In the revised manuscript (lines 132–172), we have comprehensively rewritten the experimental methods section to ensure clear, concise, and direct descriptions. The revised section emphasizes experimental procedures, key parameters, and operational details, enabling readers to easily reproduce the experiments.

Additional References
As per your suggestion, we have added necessary literature references in the relevant descriptions to ensure that all key technologies and methods are appropriately cited. This enhances the academic rigor and completeness of the manuscript.

All changes have been highlighted in red for your convenience. We believe these modifications have greatly improved the structure and clarity of the methodology section. Thank you again for your detailed comments, which have been instrumental in further enhancing the academic quality of our work.

 

Comment 9:

The legends in Fig. 4 are not clear and should be improved.

Response:

We sincerely thank the reviewer for highlighting the issue of unclear legends in Figure 4. Upon reviewing the manuscript, we identified that the issue arose due to automatic compression during the image insertion process, which resulted in a reduction in image quality. In response to this, we have corrected the problem by re-inserting the high-resolution version of the image. As a result, all the components and legends in Figure 1 (revised version) are now clearly visible. The updated figure has been included to ensure better clarity and readability. We hope this revision addresses the concern raised and makes the figure more comprehensible for the readers.

Thank you again for your insightful feedback, which greatly helped improve the presentation of our work.

 

Comment 10:

The obtained results must be compared with previous findings in the literature. Such a comparison is necessary both to validate the study and to highlight its originality.

Response:

We greatly appreciate your constructive suggestion regarding the comparison of our results with previous literature. As you pointed out, such a comparative analysis is crucial for both validating our findings and highlighting the originality of our work. In our revised manuscript, we would like to clarify that the current study represents an important extension of ongoing research funded by the National Natural Science Foundation of China. Recent literature, including references [34] and [35], has primarily focused on the motion behavior of liquid metal droplets in pure NaOH or other conventional electrolyte solutions. However, there are currently no reports investigating the dynamic behavior of liquid metal droplets in NaOH solutions suspended with SiC particles—i.e., in complex multiphase fluids. Given this gap, our study presents the first exploration of the motion control and dynamic response of gallium-based liquid metal droplets in NaOH-based abrasive fluids containing SiC particles. To the best of our knowledge, no comparable results have been published in this specific research area. Therefore, our work is an original contribution to the field, advancing the understanding of liquid metal dynamics in multiphase microfluidic environments. We respectfully invite the reviewer to recognize the novelty and pioneering nature of this research, as well as the value it adds to the existing body of knowledge.

Comment 11:

The conclusion is overly long, and the perspectives are too generic. Please shorten and rephrase this section to make it more concise and specific.

Response:

We sincerely thank the reviewer for their valuable comments regarding the length of the conclusion and the general nature of the future outlook.
In response to this feedback, we have made the following modifications in the conclusion section:

Simplified Conclusion: As per the reviewer's suggestion, the conclusion has been streamlined to focus on the key findings and methods, making it more concise and clear.

Specific Future Outlook: The future research directions have been made more specific, highlighting the practical applications of the research and its potential future developments. We also discuss how the control framework could be expanded.

The revised conclusion section is located between lines 381 and 403 in the manuscript, with changes marked in red for the reviewer's convenience.

We believe these changes significantly improve the clarity and readability of the conclusion and ensure that the future outlook is more targeted and forward-looking. We appreciate the reviewer’s insightful feedback, which has been invaluable in enhancing the manuscript.

 

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The authors have studied the movement of LM droplet in abrasive suspensions with a channel. At the current stage, the manuscript is lacking critical data and needs significant improvement. Certain claims that the authors make are not justified in the manuscript. I would request the authors to go over the comments and revise this manuscript, after which I can give my final opinion.

Major questions/comments:

1. I would suggest the authors to include Gallium based liquid metal droplet in the paper title as they specifically use gallium. Similarly include it in the abstract wherever liquid metal is mentioned.
2. Lines 99-106 can be combined together; currently it reads as 2 different studies.
3. Materials and Methods section should be reworked on: I would recommend starting with Materials first (where xyz was purchased from) which in the current manuscript is section 2.5 (but labelled as 2.3), and then talk about these models (electrocapillarity, abrasive fluids etc.) which are technically state of the art/theory.
4. Line 126: the authors do use NaOH, thus the sentence should read as: an alkaline solution such as NaOH was used (and not will be employed).
5. Equation should be labelled as equation and not eqn. Moreover, please rectify the equation citations (lines 210-213).
6. Section 2.1 is essentially theory, I am not sure if this has any importance in this manuscript, all of the figures and equations are well-known and can be directly referred, as nothing new is introduced here. What is important is section 2.2; I would recommend to move section 2.1 in the appendix and cite appropriate references who have already shown this before.
7. Please improve the quality of the schematics, some of the text is barely readable which can be improved by increasing the font text size (fig 2), also directly include NaOH instead of electrolyte as this is often misguiding throughout the manuscript.
8. What exactly is section 2.3 talking about? The abrasives used in the experiments or a theoretical model? I would also move this to appendix as so far it doesn’t make any sense especially for the materials and methods section.
9. Same for section 2.4, just talk about the setpoint controller, maybe show an image or schematic and not about the theory part which can be moved to appendix.
10. Quality of all figures and schematics should be improved, the labels arent readable, plot lines are super pixelated (figure 6,7,8).

11 Figure 5 shows for the first time the actual work done in this manuscript; I believe this should be rather earlier if the theoretical figures are moved in the appendix.

12. Section 2.3 lines 354-355, which particles are the authors talking about here? This is totally unclear.
13. Line 366: displacement of liquid metal is mentioned many times, the authors should mentioned LM droplet instead
14. Including table 1 doesn’t make much difference since its just a single row, I would rather include it directly as a sentence.
15. Results 3.1: The first and second paragraph is part of the theory and materials. Directly start with the results.
16. Lines 461-469: why is the experimental part in the results section? Please move this.
17. Section 3.2.1 line 482: these are experimental plots, why the mention of simulation plots? What is causing the droplet to slightly fluctuate from its targeted position over time? Perhaps the authors can include some videos to show this.

Minor suggestions/comments:

1) The word limit of abstract is exceeding 200 words. Please rectify this and make it more concise.

2) Introduction lines 37-40: Would be better to directly include some values of conductivities, surface tension etc. Also nice to mention which alloys of gallium (galinstan, EGain etc.).

3) Lines 44-45. LMs have been successfully used for soft robot applications, the authors can cite them here. For eg: Chen, S., Wang, H., Liu, T. and Liu, J. (2023), Liquid Metal Smart Materials toward Soft Robotics. Adv. Intell. Syst., 5: 2200375. https://doi.org/10.1002/aisy.202200375

4) Lines 50-51: What do the authors mean by NaOH maintains the chemical stability of LM? Its basically used to reduce/dissolve the oxide and form an EDL to actuate it; please also include appropriate citations in this paragraph, also for the silicon carbide section.

5) Lines 59-64: please add appropriate citations to support these statements.

6) Line 86: Galinstan components – missing wt.%

7) Lines 95-98 could use citations.

8) Please separate the entire paragraph into 2-3 individual sentences (lines 117-121).

9) Line 136, unit of angstrom is incorrect, please rectify.

Comments on the Quality of English Language

I would urge the authors to carefully read the manuscript before re-submitting. Some units are wrong, some spaces are missing or are in excess, citations for some equations have this error message, and once check for grammatical mistakes. 

Author Response

Major questions/comments and responses:

Comment 1:

I would suggest the authors to include Gallium based liquid metal droplet in the paper title as they specifically use gallium. Similarly include it in the abstract wherever liquid metal is mentioned.

Response:

We sincerely appreciate the reviewer’s suggestion regarding the inclusion of "gallium-based liquid metal droplet" in the paper title and abstract. In response to this feedback, we have revised both the title and abstract to explicitly mention "gallium-based liquid metal" wherever liquid metal is referenced. This modification clarifies the specific material used in our study and emphasizes the unique properties of gallium-based liquid metal droplets. The relevant changes have been made in the title and from lines 10 to 23 in the abstract, with all revisions highlighted in red for the reviewer’s convenience.

Thank you again for your valuable input, which has significantly enhanced the clarity and focus of our manuscript.

 

Comment 2:

Lines 99-106 can be combined together; currently it reads as 2 different studies.

Response:

We sincerely thank the reviewer for the helpful suggestion regarding the merging of lines 99 to 106. In response to this feedback, we have revised the manuscript by consolidating the previously separate research directions into a coherent and focused paragraph. This revision improves the logical flow of the content and emphasizes the key aspects of the study, ensuring that the research objectives and methodology are conveyed more clearly. The revised content can be found on lines 97 to 104 in the manuscript, with the changes highlighted in red for the reviewer’s convenience.

Thank you again for your valuable input, which has significantly enhanced the clarity and readability of our manuscript.

 

Comment 3:

Materials and Methods section should be reworked on: I would recommend starting with Materials first (where xyz was purchased from) which in the current manuscript is section 2.5 (but labelled as 2.3), and then talk about these models (electrocapillarity, abrasive fluids etc.) which are technically state of the art/theory.

Response:

Thank you very much for your constructive suggestion regarding the restructuring of the Materials and Methods section. In accordance with your recommendation, we have made significant adjustments to the manuscript structure.

Specifically, we have moved the original Section 2.5 to the beginning of the Materials and Methods section to provide a clear introduction to all materials and instruments used in this study. Additionally, we have supplemented detailed information on the sources and suppliers of key materials and equipment, as now described in lines 132 to 147 of the revised manuscript (with changes highlighted in red for your convenience). This adjustment enhances the clarity and logical flow of the section, making it easier for readers to understand the experimental setup and ensuring reproducibility.

We believe that this revision significantly improves the organization and scientific rigor of the Materials and Methods section. Thank you again for your valuable feedback, which has contributed greatly to the overall quality of our manuscript.

 

Comment 4:

Line 126: the authors do use NaOH, thus the sentence should read as: an alkaline solution such as NaOH was used (and not will be employed).

Response:

Thank you for your valuable comment regarding the expression in line 126 of the manuscript. In response to your suggestion, we have revised the sentence as follows:

"An alkaline solution, such as NaOH, was employed to remove the oxide layer."

This revision has been made in the manuscript between lines 419 and 420, and the changes are highlighted in red for your convenience. By using the past tense, we have ensured consistency with the solution actually used in the study, while maintaining clarity and conciseness in the language.

We believe this modification improves the accuracy and clarity of the manuscript. Thank you again for your insightful feedback, which has played a crucial role in enhancing the quality of our work.

 

Comment 5:

Equation should be labelled as equation and not eqn. Moreover, please rectify the equation citations (lines 210-213).

Response:

Thank you for your constructive comment regarding the terminology used for equations and the citation issues. In response to your suggestion, we have made the following revisions in the manuscript:

The term "eqn" has been replaced with "Equation" to ensure consistency with standard scientific writing practices.

The equation citations in lines 210-213 have been corrected to properly reference the equations in the manuscript.

These revisions have been made between lines 505 and 507, and the changes are highlighted in red for your convenience.

We believe these changes improve the clarity and accuracy of the manuscript. Thank you again for your valuable feedback, which has greatly enhanced the quality of our work.

 

Comment 6:

Section 2.1 is essentially theory, I am not sure if this has any importance in this manuscript, all of the figures and equations are well-known and can be directly referred, as nothing new is introduced here. What is important is section 2.2; I would recommend to move section 2.1 in the appendix and cite appropriate references who have already shown this before.

Response:

We sincerely appreciate your valuable suggestion regarding the theoretical content in Section 2.1. In accordance with your advice, we have made comprehensive adjustments to the structure of the manuscript. Specifically, the detailed mathematical derivations related to the dynamic modeling of liquid metal droplets and controller design (original Sections 2.1–2.4), as well as the associated theoretical diagrams, have all been moved to Appendix A (A.1–A.4). In addition, we have supplemented the references to classical models and methods as recommended.

This adjustment enables the main body of the manuscript to better focus on the innovative experimental methods, results, and engineering significance, while the theoretical derivations remain in the appendix for interested readers.

We believe that this change will greatly enhance the organization, focus, and readability of the manuscript. Once again, thank you for your valuable feedback, which has helped us further improve the scientific rigor and quality of our paper.

 

Comment 7:

Please improve the quality of the schematics, some of the text is barely readable which can be improved by increasing the font text size (fig 2), also directly include NaOH instead of electrolyte as this is often misguiding throughout the manuscript.

Response:

Thank you very much for your insightful comments on improving the quality of the figures and the clarity of terminology. In response to your suggestions, we have carefully revised the manuscript as follows:

Figure Quality Improvement:
All figures with insufficient clarity or nearly unreadable text, including the figure highlighted by the reviewer (original Figure 2), have been replaced with high-resolution versions. Font sizes and label clarity have been enhanced to ensure that all elements are clearly legible at publication scale.

Terminology Clarification:
Throughout the manuscript, all instances of “electrolyte” have been revised to “NaOH solution” to avoid ambiguity and to accurately reflect the experimental conditions. This correction eliminates potential misunderstandings regarding the chemical environment used in the study.

We believe these changes have significantly improved the visual quality and scientific rigor of the manuscript. Thank you again for your valuable feedback, which has helped to further enhance the quality and readability of our work.

 

Comment 8:

What exactly is section 2.3 talking about? The abrasives used in the experiments or a theoretical model? I would also move this to appendix as so far it doesn’t make any sense especially for the materials and methods section.

Response:

Thank you for your valuable feedback regarding the clarity and placement of Section 2.3. As pointed out, the original Section 2.3 primarily discusses the theoretical model describing the influence of SiC abrasive particles with varying sizes and concentrations on the viscosity of NaOH-based suspensions. This modeling forms the theoretical basis for the subsequent development of the dynamic model and controller design.

In accordance with your suggestion, we have restructured the manuscript by moving this content from the main “Materials and Methods” section to Appendix A (now labeled as Section A.3). This adjustment ensures that the main text remains focused on the experimental procedures and methodologies, while the supporting theoretical framework is presented in the appendix for interested readers.

We believe that this restructuring enhances the clarity, coherence, and readability of the manuscript. Thank you again for your insightful comments, which have helped us further improve the organization and quality of our work.

 

Comment 9:

Same for section 2.4, just talk about the setpoint controller, maybe show an image or schematic and not about the theory part which can be moved to appendix.

Response:

We sincerely thank the reviewer for the valuable comment regarding Section 2.4. In response to your suggestion, we have made the following revisions to the manuscript:

We have restructured the paper as per the reviewer's recommendation, and have now included a discussion of the controller's operating principles in the Materials and Methods section. Additionally, we have provided a schematic in this section to illustrate the working mechanism of the controller. The revised Figure 4, corresponding to the updated content, is included. The theoretical content, as per your suggestion, has been moved to Appendix A.

These changes are reflected in the Materials and Methods section, specifically between lines 180 and 219 of the manuscript, and are highlighted in red for the reviewer's convenience.

We believe these revisions enhance the clarity of the paper and focus on the key aspects of the controller's working principle, while the theoretical content is still available in the appendix for further reference.

Thank you again for your insightful feedback, which has greatly improved the structure and clarity of the manuscript.

 

Comment 10:

Quality of all figures and schematics should be improved, the labels arent readable, plot lines are super pixelated (figure 6,7,8).

Response:

We sincerely appreciate the reviewer’s valuable suggestion regarding the improvement of the quality of all figures and diagrams. In response to your comments about unclear plot lines and illegible labels-especially in Figures 5, 7, and 9（revised version）-we have carefully revised the manuscript. Specifically, we have re-inserted high-resolution versions of all relevant figures to ensure that axis labels, legends, and curves remain clear and legible at publication size. For the figures you specifically mentioned, we have increased the resolution, which has significantly enhanced the overall quality and clarity of the visualizations.

We believe these improvements have greatly enhanced the quality and readability of the figures, helping readers to more accurately understand the content of the manuscript. All updated images now meet the publication standards and provide a much better experience for both reviewers and readers. Once again, thank you for your constructive comments, which have helped us further improve the professionalism and overall quality of our manuscript.

 

Comment 11:

Figure 5 shows for the first time the actual work done in this manuscript; I believe this should be rather earlier if the theoretical figures are moved in the appendix.

Response:

We sincerely thank the reviewer for the valuable suggestion regarding the placement of Figure 5. In response to your recommendation, we have adjusted the structure of the manuscript. Specifically, we have moved the practical work shown in Figure 5 earlier in the paper, now placed in the Materials and Methods section, as Figure 2, and relocated the theoretical figure to the appendix A. This change ensures that the core experimental content is presented earlier, as suggested.

We believe this adjustment enhances the logical flow and readability of the manuscript. Thank you once again for your constructive feedback, which has greatly contributed to the clarity and structure of our paper.

 

Comment 12:

Section 2.3 lines 354-355, which particles are the authors talking about here? This is totally unclear.

Response:

Thank you very much for pointing out the lack of clarity regarding the term "particles" in the original manuscript. According to your suggestion, we have revised the relevant section.

Specifically, in the revised manuscript (lines 140 to 142), we have supplemented the description to clarify that the “particles” in this study refer to SiC (silicon carbide) particles with varying sizes and concentrations. This addition not only enhances the professionalism and clarity of the text, but also enables readers to better understand the experimental conditions and variable settings. The relevant revisions have been highlighted in red for your convenience.

We believe that this modification significantly improves the accuracy and scientific rigor of the manuscript. Once again, we sincerely thank you for your careful review and valuable comments.

 

Comment 13:

Line 366: displacement of liquid metal is mentioned many times, the authors should mentioned LM droplet instead

Response:

Thank you very much for your valuable suggestion regarding the clarity of terminology. In response to your comment, we have carefully revised the manuscript to explicitly state "liquid metal droplet" instead of simply "liquid metal" when referring to displacement or related phenomena. Specifically, the term has been corrected in the revised manuscript at lines 153, 157, 163, and 218, with the changes highlighted in red for your convenience.

We believe this adjustment enhances the scientific accuracy and clarity of the manuscript, ensuring that the described physical object-the liquid metal droplet-is unambiguous throughout the relevant sections. Thank you again for helping us improve the precision and readability of our work.

 

Comment 14:

Including table 1 doesn’t make much difference since its just a single row, I would rather include it directly as a sentence.

Response:

Thank you for your valuable suggestion regarding Table 1. In accordance with your recommendation, we have removed Table 1 and replaced it with a concise sentence in the main text. The revised sentence now reads:

"All open-top PMMA channel samples used in the experiment had a rectangular cross-section with a width and depth of 5 mm, and lengths of 40, 50, 60, 70, or 80 mm."

This change appears in lines 160–162 of the revised manuscript, highlighted in red for your convenience.
We believe that this revision improves the clarity and conciseness of the manuscript and appreciate your constructive feedback.

 

Comment 15:

Results 3.1: The first and second paragraph is part of the theory and materials. Directly start with the results.

Response:

Thank you very much for your insightful comment regarding the structure of Section 3.1. In accordance with your suggestion, we have thoroughly revised the Results section to enhance its clarity and logical flow.

Specifically, the theoretical background and materials-related content that originally appeared in the first and second paragraphs of Section 3.1 have been removed from the Results section and relocated to Appendix A.4 (lines 614–621), as marked in red for your convenience. The revised Section 3.1 now begins directly with the presentation and discussion of experimental results, ensuring a focused and streamlined narrative.

We believe these adjustments improve the readability and scientific rigor of the Results section and better align the manuscript with standard academic conventions. Thank you again for your constructive feedback, which has contributed significantly to the overall quality of our work.

 

Comment 16:

Lines 461-469: why is the experimental part in the results section? Please move this.

Response:

Thank you very much for your constructive suggestion regarding the organization of the experimental section within the Results. According to your advice, we have carefully revised the manuscript structure.

Specifically, the content originally located in lines 461–469, which pertained to experimental setup and procedures, has now been appropriately condensed and relocated to the Materials and Methods section. The revised and streamlined content can be found in the updated manuscript between lines 226 and 242, and all relevant changes have been highlighted in red for your convenience.

We believe that this structural adjustment improves the logical flow of the manuscript, ensuring that all methodological details are clearly presented prior to the discussion of results. Thank you again for your valuable feedback, which has significantly enhanced the clarity and organization of our work.

 

Comment 17:

Section 3.2.1 line 482: these are experimental plots, why the mention of simulation plots? What is causing the droplet to slightly fluctuate from its targeted position over time? Perhaps the authors can include some videos to show this.

Response:

We sincerely appreciate the reviewer’s valuable suggestions regarding the experimental plots in Section 3.2.1 (Figure 6 in the revised manuscript) and their associated descriptions. Based on your feedback, we have made the following clarifications and improvements:

Clarification on Experimental and Simulation Data Presentation:
In the revised manuscript, Figure 6 exclusively presents the experimental trajectories of gallium-based liquid metal droplets at various target positions. Simulation results are not directly shown in this figure but are referenced in the main text as a comparative benchmark. The purpose of citing simulation data is to highlight the consistency in dynamic response trends between experimental observations and model predictions, thereby further validating the accuracy and effectiveness of the proposed control model.

Explanation of Droplet Trajectory Fluctuations:
We have added additional explanations in the text to address the minor oscillations observed in the experimental velocity and acceleration profiles. These slight fluctuations primarily arise from inevitable system noise, actuator response limitations, and delays inherent in closed-loop feedback control. Such minor perturbations are typical in real-world physical systems and do not compromise the overall positioning accuracy or stability of the system.

Supplementary Video Evidence:
In accordance with your recommendation, we have provided a supplementary video of the experiments as additional supporting material to allow for a more intuitive comparison of the dynamic behavior. The video file demonstrating experiment has been uploaded as supplementary material.

All related revisions have been incorporated in the revised manuscript between lines 279 and 292, and are marked in red for your convenience. We believe these improvements significantly enhance the clarity and scientific rigor of the data presentation. Once again, we thank you for your insightful comments, which have greatly contributed to the overall quality of our work.

 

Minor suggestions/comments and responses:

Comment 1:

The word limit of abstract is exceeding 200 words. Please rectify this and make it more concise.

Response:

Thank you very much for your valuable suggestion regarding the length of the abstract. According to your recommendation, we have revised and condensed the abstract to within 200 words. The revised abstract is now presented between lines 10 and 23 in the manuscript, and the changes are highlighted in red for your convenience.

We believe this revision has improved the conciseness and focus of the abstract, ensuring that it communicates the essential information of our study in a clear and succinct manner. We greatly appreciate your constructive feedback, which has contributed significantly to enhancing the quality of our manuscript.

 

Comment 2:

Introduction lines 37-40: Would be better to directly include some values of conductivities, surface tension etc. Also nice to mention which alloys of gallium (galinstan, EGain etc.).

Response:

We sincerely appreciate the reviewer’s valuable suggestion regarding the inclusion of specific physical properties of the liquid metal and clarification of the type of gallium-based alloy used. In response, we have revised the introduction to directly present the electrical conductivity and surface tension values of the employed liquid metal, and explicitly indicate the typical properties of common gallium-based alloys such as Galinstan and EGaIn. Furthermore, we have specified in the Materials and Methods section that EGaIn was used as the working fluid in this study. These modifications have been incorporated between lines 28 and 34 of the revised manuscript and are highlighted in red for your convenience.

We believe these clarifications not only enhance the scientific rigor and transparency of the manuscript, but also provide readers with a clearer understanding of the experimental context and material selection. Thank you again for your constructive feedback, which has contributed to improving the quality and clarity of our work.

 

Comment 3:

Lines 44-45. LMs have been successfully used for soft robot applications, the authors can cite them here. For eg: Chen, S., Wang, H., Liu, T. and Liu, J. (2023), Liquid Metal Smart Materials toward Soft Robotics. Adv. Intell. Syst., 5: 2200375. https://doi.org/10.1002/aisy.202200375

Response:

Thank you very much for your valuable suggestion regarding the inclusion of relevant references on the application of liquid metal in soft robotics. In response to your comment, we have added the recommended citation (Chen, S., Wang, H., Liu, T., & Liu, J. (2023), Liquid Metal Smart Materials toward Soft Robotics, Adv. Intell. Syst.) at line 39(citation[19]) of the revised manuscript. The reference is highlighted in red text for your convenience.

We believe this addition strengthens the scholarly foundation of our work and provides readers with a comprehensive overview of the state-of-the-art in liquid metal applications for soft robotics. We greatly appreciate your insightful feedback, which has further improved the quality and rigor of our manuscript.

 

Comment 4:

 Lines 50-51: What do the authors mean by NaOH maintains the chemical stability of LM? Its basically used to reduce/dissolve the oxide and form an EDL to actuate it; please also include appropriate citations in this paragraph, also for the silicon carbide section.

Response:

We sincerely appreciate the reviewer’s insightful comments regarding the description of the role of NaOH and the need for appropriate references in this section, as well as the suggestion to clarify the SiC (silicon carbide) aspect.

In accordance with the reviewer’s suggestion, we have revised the description in lines 44–48 of the revised manuscript (marked in red). The previous statement that “NaOH maintains the chemical stability of liquid metal” was replaced with the following, more accurate formulation:

“In the application environment of liquid metal droplets, an NaOH solution is commonly employed as the electrolyte not only to facilitate the dissolution of the native oxide layer on the liquid metal surface but also to promote the formation of a stable electrical double layer, thereby enabling electrocapillary actuation and maintaining surface activity during operation.”

Relevant references have been cited to support this revised statement.

As for the SiC (silicon carbide) particles, we would like to clarify that this topic constitutes a key component of our current National Natural Science Foundation of China project. While previous studies have primarily focused on the motion of liquid metal droplets in pure NaOH-based or other electrolyte solutions, the investigation of liquid metal droplets in SiC-laden NaOH suspensions-addressing complex multiphase fluid environments-remains an original contribution of our work. To the best of our knowledge, this is a novel direction, and thus prior references specifically addressing this scenario are currently lacking. We kindly ask for the reviewer’s understanding in this regard.

We believe these clarifications and additional references enhance the rigor and accuracy of the manuscript. Thank you again for your constructive feedback, which has significantly improved the quality of our work.

 

Comment 5:

Lines 59-64: please add appropriate citations to support these statements.

Response:

Thank you very much for your valuable suggestion regarding the addition of appropriate literature references to the statements in lines 59–64 of the original manuscript. In accordance with your advice, we have carefully revised the relevant section of the manuscript (now lines 56–60, citation[21]), adding suitable references to support the scientific statements. These additions are highlighted in red in the revised manuscript for your convenience.

We believe that the inclusion of these references further enhances the academic rigor and credibility of the manuscript. We greatly appreciate your constructive feedback, which has significantly contributed to improving the quality of our work.

 

Comment 6:

Line 86: Galinstan components – missing wt.%

Response:

Thank you very much for your valuable comment regarding the omission of the mass percentages of the constituent elements in Galinstan (liquid metal alloy). In response to your suggestion, we have revised the manuscript to include the mass fractions of each element in Galinstan. Specifically, this information has been added in line 83 of the revised manuscript and highlighted in red for your convenience.

We believe this addition enhances the clarity and completeness of the material description, ensuring the experimental details are sufficiently transparent and reproducible. We greatly appreciate your insightful feedback, which has contributed to the overall improvement of our manuscript.

 

Comment 7:

Lines 95-98 could use citations.

Response:

Thank you very much for your valuable suggestion regarding the need for supporting references in lines 95–98 of the manuscript. In accordance with your recommendation, we have now added appropriate literature citations to substantiate the statements in this section. These references have been incorporated in the revised manuscript between lines 92 and 94(citation[34]), and the changes are highlighted in red for your convenience.

We believe this addition strengthens the scientific rigor and credibility of the relevant discussion. We appreciate your insightful feedback, which has significantly improved the overall quality and scholarly standard of our work.

 

Comment 8:

Please separate the entire paragraph into 2-3 individual sentences (lines 117-121).

Response:

Thank you very much for your valuable suggestion regarding the paragraph structure in lines 117–121. In response to your comment, we have revised this section by splitting the original long paragraph into two shorter and more concise paragraphs. The revised text now appears between lines 114 and 130 in the revised manuscript, with all changes highlighted in red for your convenience.

We believe that this modification enhances the readability and logical flow of the manuscript, making it easier for readers to follow the narrative. We sincerely appreciate your attention to detail, which has greatly contributed to improving the clarity and quality of our work.

 

Comment 9:

Line 136, unit of angstrom is incorrect, please rectify.

Response:

Thank you very much for your valuable feedback regarding the unit annotation error of "Å" (angstrom) in line 136. According to your suggestion, we have corrected the annotation of the unit “Å” in the revised manuscript (now at line 430), and the changes have been highlighted in red for your convenience.

We believe this revision has improved the accuracy and professionalism of the manuscript. Thank you again for your careful review and constructive suggestions, which have contributed to enhancing the quality of our work.

 

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

All my concerns have been revised.

Author Response

Comment 1:

Comments and Suggestions for Authors: All my concerns have been revised.

Response:

We sincerely appreciate your thoughtful review and valuable comments during the revisions. We are delighted to know that you are satisfied with the revisions we made, and that all of your concerns have been appropriately addressed.

We are grateful for your careful review and guidance, as your suggestions have played a crucial role in improving the quality of our manuscript.

Thank you once again for your valuable contribution to our work, and we look forward to your final approval.

 

Reviewer 2 Report

Comments and Suggestions for Authors

Accept in present form.

Author Response

Comment 1:

Comments and Suggestions for Authors:Accept in present form.

Response:

We would like to express our sincere gratitude for your thorough review and constructive feedback. We are pleased to hear that you are satisfied with the revised version of the manuscript and that you find it acceptable in its present form.

Your valuable comments and suggestions have greatly contributed to the improvement of the manuscript, and we appreciate your support throughout the revision process.

Thank you once again for your time and expertise in reviewing our work.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors did a nice job. The manuscript can be accepted.

Author Response

Comment 1:

Comments and Suggestions for Authors:The authors did a nice job. The manuscript can be accepted.

Response:

Thank you for your positive feedback and recognition of our work. We are pleased to hear that you are satisfied with the revisions made and that the manuscript is now considered acceptable. Your constructive comments and valuable suggestions have played a crucial role in enhancing the quality of the paper.

We sincerely appreciate the time you have taken to review our work and for supporting our research. We look forward to our paper contributing to the field.

Reviewer 4 Report

Comments and Suggestions for Authors

The authors have revised the manuscript, included videos that look good, and overall, it reads much better. However, there are still certain points that need to be addressed. 

1. Abbreviation of melting point is either MP or mp, not m.pt.
2. Line 44-46: NaOh solution is employed as NaOH solution doesn't make sense. Please correct this. 
3. Line 79-81 could also include this reference which shows the generation and manipulation of LM droplets in NaOH solution: 
   https://advanced.onlinelibrary.wiley.com/doi/10.1002/adma.202201469
4. Maybe combine the 2 paragraphs in introduction 92-113, since they essentially say the same and most of the text is repeating. 
5. Line 160: Units should be mPa.s; please check once for all units especially for spacing between the value and unit etc,. 
6. The materials and methods section should only include the materials used and the methods implemented. In many cases, results are mentioned - for eg. lines 165-172.
7. Figures are still of low quality and should be improved- the labels are not easily readable: for fig 1 as an example, the authors could add a white background around the text box so the red colour is read better.
8. Fig 2 its seems like the LM droplet exceeds the channel width, please rectify this
9. Fig 2 and 3 can be combined, would be nice to see the actual channel with the droplet and electrodes instead of the rendering (fig 3)
10. Lines 226-234 basically repeat the first para of methods; please check this once and I would highly recommend the authors to make subsections for methods and include them accordingly. I would also divide the results in sections for simulated and experimental because the figure captions lack important information (in some cases) for the data if its for experimental, simulation or juxtaposed. 
11. Line 335: 'Smaller' font size is different. 

Author Response

Comment 1:

Abbreviation of melting point is either MP or mp, not m.pt.

Response:

Thank you for your helpful suggestion regarding the abbreviation of "melting point." In accordance with your comments, we have revised the manuscript and now use "mp" as the abbreviation for melting point throughout the text. This correction has been applied in line 29 of the revised manuscript, which is highlighted in blue for your convenience.

We appreciate your attention to detail, which has contributed to improving the consistency and professionalism of our work.

 

Comment 2:

Line 44-46: NaOh solution is employed as NaOH solution doesn't make sense. Please correct this.

Response:

Thank you for your helpful comment regarding the clarity of the expression in lines 44–46. In response to your suggestion, we have revised the original phrase “NaOh solution is employed as NaOH solution” to the more accurate and concise “NaOH solution is commonly employed as the electrolyte.” This revision has been implemented in lines 44–45 of the revised manuscript, and the change is highlighted in blue for your convenience.

We appreciate your attention to detail, which has further improved the accuracy and readability of our manuscript.

 

Comment 3:

Line 79-81 could also include this reference which shows the generation and manipulation of LM droplets in NaOH solution:
https://advanced.onlinelibrary.wiley.com/doi/10.1002/adma.202201469

Response:

Thank you for your helpful suggestion regarding the inclusion of additional references to support the generation and manipulation of liquid metal droplets in NaOH solution. In accordance with your recommendation, we have added the reference you suggested (https://advanced.onlinelibrary.wiley.com/doi/10.1002/adma.202201469)to the revised manuscript. The citation has been incorporated in line 80 and is highlighted in blue for your convenience.

We appreciate your careful review and believe that this addition further strengthens the scientific context and rigor of our work.

 

Comment 4:

Maybe combine the 2 paragraphs in introduction 92-113, since they essentially say the same and most of the text is repeating.

Response:

We sincerely thank the reviewer for highlighting the redundancy in the introductory section (lines 92–113) of the original manuscript. In accordance with your suggestion, we have carefully revised this portion by consolidating the two repetitive paragraphs into a single, streamlined, and focused paragraph. The revised version now appears in lines 91–103 of the manuscript and is highlighted in blue for your convenience.

We believe that this modification enhances the clarity, conciseness, and logical flow of the introduction, making the research objectives and scope more accessible to readers. Thank you again for your valuable feedback, which has contributed to the overall improvement of the manuscript.

 

Comment 5:

Line 160: Units should be mPa⸳s; please check once for all units especially for spacing between the value and unit etc,.

Response:

Thank you very much for your careful review and helpful comments regarding the formatting of units throughout the manuscript. In accordance with your suggestion, we have revised the unit in line 165 to “mPa·s”, using the standard SI notation with a middle dot for clarity.

In addition, we have systematically reviewed the entire manuscript to ensure that all physical quantities and units conform to international standards. We have also carefully checked for proper spacing between numerical values and units, and made consistent corrections wherever necessary, so that all units are now presented in a standardized and uniform manner.

All these changes are marked in blue font in the revised manuscript for your convenience. We believe these adjustments improve both the clarity and the professional quality of the manuscript. Thank you again for your attention to detail and valuable suggestions.

 

Comment 7:

The materials and methods section should only include the materials used and the methods implemented. In many cases, results are mentioned - for eg. lines 165-172.

Response:

Thank you for your valuable feedback regarding the content of the materials and methods section. In response to your suggestion, we have carefully revised the manuscript to ensure that the materials and methods section is strictly limited to the materials used and the experimental methods implemented.

Specifically, we have removed the previous description in lines 165–172, which discussed the well-known surface properties (such as wettability and contact angle) of the PMMA channel walls. As these properties are widely established in the literature and do not directly pertain to the unique experimental procedures of this study, we agree that their inclusion in this section was unnecessary.

All related content has now been deleted to maintain the clarity and focus of the materials and methods section, as per your recommendation. The revision has been clearly incorporated in the updated manuscript (Above Figure 1).

We appreciate your attention to detail, which has helped us to further improve the rigor and organization of our paper.

 

Comment 8:

Figures are still of low quality and should be improved- the labels are not easily readable: for fig 1 as an example, the authors could add a white background around the text box so the red colour is read better.

Response:

Thank you very much for your valuable feedback regarding the clarity and readability of the figure labels, particularly in Figure 1. In response to your suggestion, we have thoroughly revised Figure 1 to address the issue of difficult-to-read labels. Specifically, all labels in Figure 1 are now enclosed in text boxes with a white background, which significantly enhances the visibility and legibility of the red font. This adjustment ensures that the key information is clearly presented and easily distinguishable, even after typesetting and publication.

We believe these improvements have substantially increased the figure’s clarity and effectiveness in communicating the intended content. All related modifications have been implemented in the revised manuscript, and we appreciate your helpful comments, which have contributed to improving the overall quality and presentation of our work.

Comment 9:

Fig 2 its seems like the LM droplet exceeds the channel width, please rectify this.

Response:

Thank you very much for your valuable feedback regarding Figure 2. In accordance with your suggestion, we have carefully revised Figure 2 to ensure that the size of the liquid metal (LM) droplet is consistent with the actual channel width and accurately reflects the physical dimensions of the experimental setup. The updated figure now faithfully represents the scale relationship between the LM droplet and the PMMA channel, thereby eliminating any potential confusion.

This correction has been made in the revised manuscript and highlighted in blue font for your convenience. We appreciate your attention to detail, which has greatly improved the clarity and accuracy of our graphical presentation.

 

Comment 9:

Fig 2 and 3 can be combined, would be nice to see the actual channel with the droplet and electrodes instead of the rendering (fig 3).

Response:

We sincerely appreciate the reviewer’s suggestion regarding the presentation of Figures 2 and 3. In response to the reviewer’s comments, we have decided to present these two figures separately as they serve different purposes:

Figure 2 is retained as a schematic diagram of the liquid metal droplet control framework, illustrating a conceptual overview of the experimental system, including the vision feedback system, power supply, and control system.

Figure 3 has been revised according to the reviewer’s suggestion by replacing the rendered image with an actual experimental photograph. This figure shows the PMMA channel with graphite electrodes and the liquid metal droplet, offering a clearer representation of the physical structure of the experimental system, better aligning with the practical application of the study.

We believe this modification enhances the clarity of the manuscript, ensuring the effective presentation of both conceptual and practical aspects. Once again, we would like to thank the reviewer for their valuable feedback, which has greatly contributed to the improvement of the quality and clarity of our paper.

 

Comment 10:

Lines 226-234 basically repeat the first para of methods; please check this once and I would highly recommend the authors to make subsections for methods and include them accordingly. I would also divide the results in sections for simulated and experimental because the figure captions lack important information (in some cases) for the data if its for experimental, simulation or juxtaposed.

Response:

We sincerely appreciate your valuable suggestions regarding the structure of the Methods and Results sections. In response to your recommendations, we have made the following adjustments to the manuscript:

Redundancy in the Methods section: We have merged the redundant content from lines 226-234 with the first paragraph of the Methods section into a concise paragraph, and reorganized it into lines 123-141.

Subdivision of the Methods section: We have divided the Materials and Methods section into two subsections: “2.1 Experimental Materials and Setup” and “2.2 Experimental Procedure and Closed-Loop Control,” making the structure clearer and easier to follow.

Subdivision of the Results and Discussion section: We have divided the Results and Discussion section into three subsections, each discussing the effects of different target positions, particle size and concentration, and droplet radius on the motion of liquid metal droplets. These revisions appear in lines 240, 283-284, and 318 of the revised manuscript.

All these changes have been highlighted in blue for your convenience.

 

Comment 11:

Line 335: 'Smaller' font size is different.

Response:

Thank you for your valuable feedback regarding the font size inconsistency in line 335. In accordance with your suggestion, we have carefully revised the manuscript to ensure that the 'Smaller' font size is now fully consistent with the other text throughout the paper. The formatting has been standardized to maintain clarity, uniformity, and a professional appearance. This revision can be found in line 323 of the revised manuscript, with the changes highlighted in blue for your convenience.

We believe that these formatting improvements further enhance the readability and overall quality of the manuscript. Thank you again for your helpful suggestion.

Author Response File: Author Response.pdf