Dynamics and Mutual Influence of Droplets in a Rotating Liquid Under Centrifugal Forces
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis paper presents an interesting experimental study on the mutual influence of droplets in a chain within a centrifugal field. The topic is relevant to applications in extraction and centrifugal separation processes. The authors have developed a specialized experimental setup and methodology, and have derived a generalized empirical correlation for the satellite trail velocity. The work provides useful insights into droplet dynamics; however, several significant issues need to be addressed before the manuscript can be considered for publication. My specific comments are as follows:
- Figure 7 contains Cyrillic text. This should be corrected to English to ensure international readability and consistency.
- Figure 7 lacks error bars and does not indicate the uncertainty in the experimental data. It is essential to include error margins (e.g., standard deviation or confidence intervals) to assess the reliability of the results and the goodness of fit.
- The authors propose a generalized formula for the satellite trail velocity. However, no comparison with existing models or literature data is provided. It is recommended to validate the proposed correlation against previously published results to demonstrate its broader applicability and accuracy.
- Although the experimental setup includes a camera and stroboscopic photography, no actual experimental images (e.g., droplet chains, trajectories, or multiple-exposure shots) are presented in the manuscript. Including such images would enhance the credibility of the methodology and help readers visualize the phenomenon.
- It is suggested to include a photograph of the actual experimental setup alongside the schematic diagram (Figure 1). This would help readers better understand the physical implementation and scale of the apparatus.
- The manuscript currently lacks a detailed fluid dynamics analysis of the droplet interactions, such as wake structure, vorticity, or turbulence effects. Incorporating a discussion on the underlying hydrodynamic mechanisms-supported by dimensionless numbers (e.g., Reynolds, Weber)-would strengthen the scientific rigor of the study.
Author Response
Dear Reviewer,
Thank you for the careful evaluation of our work and for the constructive comments. Below we provide detailed responses to each point.
Comments 1: Figure 7 contains Cyrillic text. This should be corrected to English to ensure international readability and consistency.
Response 1: The text in Figure 7 has been replaced with English to ensure international readability and consistency.
Comments 2: Figure 7 lacks error bars and does not indicate the uncertainty in the experimental data. It is essential to include error margins (e.g., standard deviation or confidence intervals) to assess the reliability of the results and the goodness of fit.
Response 2: Following your recommendation, we have added the MAPE (Mean Absolute Percentage Error) value to the manuscript to assess the reliability of the results and the quality of the approximation at lines 243 - 244.
Comments 3: The authors propose a generalized formula for the satellite trail velocity. However, no comparison with existing models or literature data is provided. It is recommended to validate the proposed correlation against previously published results to demonstrate its broader applicability and accuracy.
Response 3: At this moment, we are not aware of previously published studies with a comparable experimental design and parameter set that would allow for a direct comparison. If we identify similar works in the future, we will perform such a comparison and introduce appropriate adjustments if necessary in the future works.
Comments 4: Although the experimental setup includes a camera and stroboscopic photography, no actual experimental images (e.g., droplet chains, trajectories, or multiple-exposure shots) are presented in the manuscript. Including such images would enhance the credibility of the methodology and help readers visualize the phenomenon.
Response 4: The laboratory regulations prohibit us from publishing photographs of the equipment or images related to the internal experimental process. Therefore, the manuscript includes only schematics and descriptions.
Comments 5: It is suggested to include a photograph of the actual experimental setup alongside the schematic diagram (Figure 1). This would help readers better understand the physical implementation and scale of the apparatus.
Response 5: Due to the prohibition on publishing photos and videos in this laboratory, we are unable to provide them.
Comments 6: The manuscript currently lacks a detailed fluid dynamics analysis of the droplet interactions, such as wake structure, vorticity, or turbulence effects. Incorporating a discussion on the underlying hydrodynamic mechanisms-supported by dimensionless numbers (e.g., Reynolds, Weber)-would strengthen the scientific rigor of the study.
Response 6: Performing a detailed analysis of wake structure, vortex formation, or turbulence effects requires specialized diagnostic equipment that was not available within the scope of this experiment. The focus of our study was primarily on obtaining empirical dependencies for droplet dynamics. However, we agree that such an extended hydrodynamic analysis is of significant interest and may serve as a direction for future research.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors perform experiments on the velocities of droplets ejected into a rotating fluid. While the contribution is valuable, I would recommend changing a few expressions in the manuscript.
Why did the authors rotate the container and not the droplet injection nozzle?
For interaction to occur, the droplet concentration is crucial.
The word "droplet" indicates a small liquid drop that is separated from the other phases. From the title and the abstract, I would have assumed that the second phase is gaseous. Therefore, I would recommend being explicit in the abstract. - Secondly, why did the authors not use water and air as the fourth case? That should be relatively easy to do, but it will significantly enhance the manuscript's impact.
The authors write: "The following analytical expression for velocity is known to describe a single drop moving in a centrifugal field [2]." Please provide this analytical expression!
The manuscript contains only a limited number of references. However, numerous works have been conducted on the fluid dynamics between droplets, e.g., Kekesi et al. (2019), "Interaction between two deforming liquid drops in tandem and various off-axis arrangements subject to uniform flow." Moreover, work on droplet separators utilizing centrifugal effects should be referenced, e.g., Dudasko et al. (2024), "On the Numerical Efficacy Evaluation of Industrial Droplet Separators."
Figure 7 contains Cyrillic words. Please change them.
Author Response
Dear Reviewer,
Thank you for the careful evaluation of our work and for the constructive comments. Below we provide detailed responses to each point.
Comments 1: Why did the authors rotate the container and not the droplet injection nozzle?
Response 1: Rotating the entire liquid volume ensures a uniform centrifugal field with a constant angular velocity at every point of the medium. This condition cannot be achieved by rotating only the injection nozzle, as the liquid in the vessel would not form a homogeneous rotational field. Therefore, rotating the container is essential for obtaining physically consistent and reproducible results.
Comments 2: For interaction to occur, the droplet concentration is crucial.
Response 2: We fully agree with this remark. The droplet concentration indeed plays a key role in the formation of interactions. In our experiments, it was controlled by adjusting the detachment frequency of droplets from the feeder nozzle, which allowed us to regulate the number of droplets in the chain.
Comments 3: The word "droplet" indicates a small liquid drop that is separated from the other phases. From the title and the abstract, I would have assumed that the second phase is gaseous. Therefore, I would recommend being explicit in the abstract.
Response 3: We would like to note that the title of the manuscript (Dynamics and mutual influence of droplets in a rotating liquid under centrifugal forces) explicitly indicates that the study is performed in a uniformly rotating liquid medium. The compositions of both phases are also provided in Table 1, where all liquid–liquid systems used in the experiments are listed (kerosene–water, CClâ‚„–water with 20% glycerin, and CClâ‚„–water with 60% glycerin) at lines 196 - 197.
Nevertheless, we agree that the term droplet is often associated with liquid drops dispersed in a gaseous phase. To avoid any possible ambiguity and to improve clarity for the reader, we are ready to explicitly state in the abstract that the dispersed phase is introduced into a liquid continuous phase at lines 10 - 11.
Comments 4: Secondly, why did the authors not use water and air as the fourth case? That should be relatively easy to do, but it will significantly enhance the manuscript's impact.
Response 4: In a gas–liquid system such as air–water, it is not possible to establish a uniform centrifugal field, because the gas phase does not form a stable rotational field and cannot transmit a constant angular velocity throughout the volume. Since the analysis of droplet interactions requires a homogeneous rotational field, gas–liquid systems are not methodologically suitable for this study. For this reason, we intentionally restricted the work to liquid–liquid systems.
Comments 5: The authors write: "The following analytical expression for velocity is known to describe a single drop moving in a centrifugal field [2]." Please provide this analytical expression!
Response 5: Thank you for pointing this out. The reference in the Introduction was not precise. The analytical expression is presented in Section 2 (“Materials and Methods”), and we have corrected the wording to avoid confusion at lines 33 - 36.
Comments 6: The manuscript contains only a limited number of references. However, numerous works have been conducted on the fluid dynamics between droplets, e.g., Kekesi et al. (2019), "Interaction between two deforming liquid drops in tandem and various off-axis arrangements subject to uniform flow." Moreover, work on droplet separators utilizing centrifugal effects should be referenced, e.g., Dudasko et al. (2024), "On the Numerical Efficacy Evaluation of Industrial Droplet Separators."
Response 6: We appreciate this suggestion. We have expanded the reference list and added citations to studies on droplet interactions and centrifugal separation processes, including Kekesi et al. (2019) and Dudasko et al. (2024) at lines 33 - 57, as recommended.
Comments 7: Figure 7 contains Cyrillic words. Please change them.
Response 7: Figure 7 has been updated, and all labels are now presented in English to ensure international readability.
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsAll my concerns have been adequately addressed in the revised version of the manuscript. The authors' responses and the corresponding changes are satisfactory. I have no further comments and recommend acceptance.
