Exploring the Role of Initial Droplet Position in Coalescence-Induced Droplet Jumping: Lattice Boltzmann Simulations

Round 1

Reviewer 1 Report

1. The reviewer thinks English is not the authors’ first language. The quality of the writing is needed to improve. The wrong structure, as well as lousy punctuation in some sentences, prevents proper understanding.
2. In the abstract, the authors just define the problem, and it is like the introduction part. In contrast, it should be included a brief explanation of their work.
3. Some references are older than 2016, and therefore, they are abolished. May the reviewer ask the authors to change these references to newer ones? Some suggested papers are as below: LBM simulation of free convection in a nanofluid filled incinerator containing a hot block. Lattice Boltzmann method to simulate convection heat transfer in a microchannel under heat flux: gravity and inclination angle on slip-velocity.  The investigation of thermal radiation and free convection heat transfer mechanisms of nanofluid inside a shallow cavity by lattice Boltzmann method. 
4. Please explain more about the novelty of your work.
5. Add more quantitative results to the conclusion part.
6. What is the actual application of this work?
7. Please add the nomenclature table to your paper.
8. Where is the Author Contributions part?
9. When reviewing the references, a strong impression can be created that the manuscript should be submitted to another journal: To give journal readers a sense of continuity, the reviewer encourages the authors to identify present journal publications of similar research in your papers. Please, do a literature check of the documents published in recent years (2021 and 2022) and relate the content of relevant documents to the results and findings presented in your publication. The authors can also reference articles in print using their DOI:

Author Response

Dear editor and reviewers:

 

Thank you for your kind letter and for reviewers’ constructive comments concerning our paper (Manuscript processes-1700475). These comments are all valuable and helpful for improving our paper. According to the reviewers’ comments, we have tried best to modify our manuscript to meet with the requirements of your journal. In this revised version, changes to our manuscript within the document were all highlighted by using red colored text. Point-by-point responses to the editor and the reviewers are listed below this letter.

 

If there are any other modifications we could make, we would like very much to modify them and we really appreciate your help. We hope that our manuscript could be considered for publication in your journal. Thank you very much for your help.

 

Thank you and best regards.

May 2, 2022

Yours sincerely,

Zhichun Liu

Professor

School of Energy and Power Engineering

Huazhong University of Science and Technology

China

E-mail: zcliu@hust.edu.cn

 

To Reviewer #1:

1. The reviewer thinks English is not the authors’ first language. The quality of the writing is needed to improve. The wrong structure, as well as lousy punctuation in some sentences, prevents proper understanding.

Response: Thanks for the comment from the reviewer. We have carefully reviewed and revised the manuscript. The wrong structure, as well as punctuation have been checked and corrected.

2. In the abstract, the authors just define the problem, and it is like the introduction part. In contrast, it should be included a brief explanation of their work.

Response: Thanks for the comment from the reviewer. The abstract has been revised and a brief explanation of our work is included. The revised texts are as follows:

Coalescence-induced droplet jumping on superhydrophobic surfaces with different initial posi-tions is numerically simulated using 2D multi-relaxation-time (MRT) lattice Boltzmann method (LBM). (Line 11, page 1)

Droplet morphologies and vector diagrams at different moments are considered. It is revealed that the asymmetric droplet detachment from the structured surface leads to the directional transport of liquid mass in the droplet and further results in the oblique jumping of the coalesced droplet. (Line 17, page1)

Furthermore, the effects of droplet/structure scale on droplet jumping are investigated. The in-fluence of initial positions on coalescence-induced droplet jumping from the refined surface can be ignored when the droplet scale is larger than 3 times the structure scale. This study illustrates the role of droplet initial position in coalescence-induced droplet jumping and provides guide-lines for the rational design of structured surfaces with enhanced droplet self-shedding for energy and heat transfer applications. (Line 22，page 1)

3. Some references are older than 2016, and therefore, they are abolished. May the reviewer ask the authors to change these references to newer ones? Some suggested papers are as below: LBM simulation of free convection in a nanofluid filled incinerator containing a hot block. Lattice Boltzmann method to simulate convection heat transfer in a microchannel under heat flux: gravity and inclination angle on slip-velocity. The investigation of thermal radiation and free convection heat transfer mechanisms of nanofluid inside a shallow cavity by lattice Boltzmann method.

Response: Thanks for the comment from the reviewer. We have changed some references to newer ones including the recommended papers_.

4. Please explain more about the novelty of your work.

Response: Thanks for the comment from the reviewer. The introduction has been revised to explain the novelty into two parts. First of all, coalescence-induced oblique jumping is a relatively new phenomenon discovered in microfluidics. Such a phenomenon has been observed in experiments when the droplet is trapped in a microgroove, indicating that the initial position has a certain effect on droplet jumping direction. However, in the case of both droplets on top of the microstructure, the effect of initial position has not been studied. Secondly, since the droplet scale is often set much larger than the structure scale in most numerical studies, the position effect has rarely been considered in simulations. Given that droplet sizes vary widely in nature, it is still worth investigating the influence of initial positions on coalescence-induced droplet jumping. The revised texts are as follows:

For droplets with comparable size to the roughness length scale, the surface structure can participate in the coalescence process directly [17, 18]. It is found that the direction of the jumping droplet is not necessarily perpendicular to the surface when the droplet scale is close to the structure scale [9]. Coalescence-induced oblique jumping of a droplet inside a microgroove and a droplet on an adjacent plateau is observed [11]. This is caused by the impact of the liquid bridge on the edge of the microgroove, which generates a momentum component parallel to the surface plane. However, in the case of both droplets on top of the microstructure, the effect of initial position has not been studied. In addition, since the coalescence-induced droplet jumping can occur at different surface locations with the random nature of nucleation, it is of importance to further study the effect of droplet initial position on coalescence-induced droplet jumping when the droplet scale is slightly larger than the surface roughness. (Line 44, page 3)

In most numerical studies, the droplet scale is often set much larger than the structure scale, thus the position effect is not considered. Given that droplet sizes vary widely in nature, it is still worth investigating the influence of initial positions on coalescence-induced droplet jumping. (Line 70, page 3)

5. Add more quantitative results to the conclusion part.

Response: Thanks for the comment from the reviewer. The conclusion part has been revised and more quantitative results are added. The revised texts are as follows:

On the other hand, the maximum horizontal velocity in Case Rj’ (0.066 m/s) is about 1.4 times higher than that in Case Rj (0.048 m/s), indicating a slight increase in the deviation between the jumping direction and the normal direction. (Line 391, page 15)

It is found that the influence of initial position on droplet jumping velocity weakens with the increase of droplet radius. The deviation of jumping velocity on the flat-topped surface reduces from ~0.34 m/s (r = 30 mm) to ~0.02 m/s (r = 60 mm). With the increase of droplet size, the proportion of liquid-solid adhesion work to the excess surface energy decreases, leading to the deviation reduction. For r = 60 mm (droplet/structure scale ~3), the deviation of jumping velocity on the new surface has been reduced to ~0.008 m/s. (Line 395, page 15)

6. What is the actual application of this work?

Response: Thanks for the comment from the reviewer. The actual application is stated in the discussion part. The revised texts are as follows:

Our study provides guidelines for the design of micro/nanostructures to prevent droplet jumping failure, which is of great importance for enhancing dropwise condensation heat transfer. The analysis of droplet initial position, surface structure and droplet/structure scale on droplet jumping behavior helps to understand the irregular jumping of droplets and to further study controllable droplet jumping used for water harvesting. (Line 372, page 14)

7. Please add the nomenclature table to your paper.

Response: Thanks for the comment from the reviewer. The nomenclature table has been added in the manuscript.

8. Where is the Author Contributions part?

Response: Thanks for the comment from the reviewer. We have added the Author Contributions part in the end of the manuscript.

9. When reviewing the references, a strong impression can be created that the manuscript should be submitted to another journal: To give journal readers a sense of continuity, the reviewer encourages the authors to identify present journal publications of similar research in your papers. Please, do a literature check of the documents published in recent years (2021 and 2022) and relate the content of relevant documents to the results and findings presented in your publication. The authors can also reference articles in print using their DOI:

Response: Thanks for the comment from the reviewer. Some similar researches of the present journal publication have been cited in the manuscript. Besides, recent researches related to the topic are discussed in the introduction part. The revised texts are as follows:

Lattice Boltzmann method (LBM) as a mesoscopic approach has been widely applied to simulating multiphase flows [27-29], heat transfer and phase change [30-32]. (Line 57, page 3)

Shi et al. [22] pointed out that the coalesced droplet is more likely to jump on the textured surface with larger conical post height and small spacing between the conical posts. Wang et al. [34] found that triangle microstructured surface can enhance the jumping ability of coalesced droplets during condensation. Chen et al. [35] studied self-propelled jumping of non-equal sized droplets and concluded that non-equal sized droplets are less efficient in transferring the released surface energy to effective jumping kinetic energy than in the equal sized case. (Line 63, page 3)

Author Response File: Author Response.docx

Reviewer 2 Report

The authors of the manuscript use an established numerical method to thoroughly study a relatively new phenomenon discovered in microfluidics. Namely, the discovery that on a hydrophobic surface immersed in a liquid merging of droplets may result in a jump of the final droplet. The phenomenon itself is very relevant and was modeled numerous times. The work done by the authors is still interesting and useful. There are, however, some concerning assumptions and validation results that the authors should address. Given that I do recommend the manuscript for publication in Processes, but only after reconsideration following major revisions.

The points that the authors should address are as follows:

 

1. The authors make an assumption that the gravity force can be neglected. While their explanation may be valid, they should verify this statement through simulations. They should show that their main results without gravity are not changed if gravity is included. Alternatively, they can include it. 

 

2. The authors should provide validation of the contact angles formed between liquid, droplet, and solid substrate. It does not need to be a part of the main article, however, since the manuscript concerns fluid-solid interactions, such a plot would be desired. In particular, the authors should simulate a stationary droplet on a solid surface for different hydrophobicities and hydrophilicity, showing that their model yields different and expected contact angles.

 

3. Authors should define all the variables and values used in Equation 17.

 

4. Authors should provide the definition of ui in Equation 18.

 

5. The results shown in Figure 2 indicated large discrepancies between the authors' results and the results in [2]. The results in [2] actually agree very well with the experimental results. This may partially stem from the assumption that gravity is negligible. The authors should verify if that is the case and provide a more detailed explanation of the differences. The authors should also compare the other two quantities reported in [2] and the experimental article. Finally, I assume that the range of velocities comes from the positions the droplet are initially placed in. This should be stated in the text, and perhaps even in the caption.

 

6. The initial positions of the droplets described on lines 178-192 are not clear. It would be good to see the exact configurations as in the image, possibly in the Supplementary Material.

 

7. The definitions of mi and ui in Equation 20 should be provided.

 

8. The statement on the inverse motion on lines 235-236 is unclear.

 

9. Equation 21 is unclear, given the definition shown in Equation 20.

 

10. The claim that the uncertainty increases when sharp patterns are used should be revisited. First, it is unclear how the uncertainty is defined in the model. Secondly, the difference between the angles that the authors use to support this statement is very small. Possibly marginal, depending on the method the authors used to measure the angles.

 

11. The authors should specify why they get ranges of results in Figure 9.

 

12. The authors should extend their introduction to cover many similar publications related to the topic and discuss their results in the light of other findings.

 

Minor comments:

 

1. There is a typographic error in the inline equation on line 118 - the square should apply to the squared bracket, as in [1]

 

[1] Gong, Shuai, and Ping Cheng. "Numerical investigation of droplet motion and coalescence by an improved lattice Boltzmann model for phase transitions and multiphase flows." Computers & Fluids 53 (2012): 93-104.

 

[2] Liu, Xiuliang, Ping Cheng, and Xiaojun Quan. "Lattice Boltzmann simulations for self-propelled jumping of droplets after coalescence on a superhydrophobic surface." International Journal of Heat and Mass Transfer 73 (2014): 195-200.

Author Response

Dear editor and reviewers:

 

Thank you for your kind letter and for reviewers’ constructive comments concerning our paper (Manuscript processes-1700475). These comments are all valuable and helpful for improving our paper. According to the reviewers’ comments, we have tried best to modify our manuscript to meet with the requirements of your journal. In this revised version, changes to our manuscript within the document were all highlighted by using red colored text. Point-by-point responses to the editor and the reviewers are listed below this letter.

 

If there are any other modifications we could make, we would like very much to modify them and we really appreciate your help. We hope that our manuscript could be considered for publication in your journal. Thank you very much for your help.

 

Thank you and best regards.

May 2, 2022

Yours sincerely,

Zhichun Liu

Professor

School of Energy and Power Engineering

Huazhong University of Science and Technology

China

E-mail: zcliu@hust.edu.cn

 

To Reviewer #2:

1. The authors make an assumption that the gravity force can be neglected. While their explanation may be valid, they should verify this statement through simulations. They should show that their main results without gravity are not changed if gravity is included. Alternatively, they can include it.

Response: Thanks for the comment from the reviewer. We have simulated droplet coalescence process with and without gravity under the same condition to ensure the explanation is valid. The simulation results are shown in Fig. S1. The revised texts and figure are as follows:

In order to verify the statement, droplet coalescence process with and without gravity under the same condition is simulated. The velocity change during droplet coalescence is shown in the Fig. S1 (see supplementary material). There is no obvious difference between two cases, and thus the gravity force can be neglected. (Line 112, page 5)

Figure S1. Simulation results of velocity-time evolution with and without gravity. The initial state of two droplets are shown in the picture with surface apparent contact angle ~150°. Therefore, it is reasonable to ignore the effect of gravity.

2. The authors should provide validation of the contact angles formed between liquid, droplet, and solid substrate. It does not need to be a part of the main article, however, since the manuscript concerns fluid-solid interactions, such a plot would be desired. In particular, the authors should simulate a stationary droplet on a solid surface for different hydrophobicities and hydrophilicity, showing that their model yields different and expected contact angles.

Response: Thanks for the comment from the reviewer. Simulation results of a stationary droplet on a solid surface for different wettability are shown in Fig. S2. The revised texts and figure are as follows:

Gs is the interaction strength between solid and fluid for controlling the wetting conditions (contact angles), and s(x) is an indicator function, which is equal to 1 for solid and 0 for fluid. (Line 123, page 5)

Besides, the relationship between contact angle and the interaction strength Gs is shown in Fig. S2 (see supplementary material). (Line 149, page 6)

Figure S2. Simulation results of contact angles with different Gs, where Gs is the interaction strength between solid and fluid for controlling the wetting conditions (contact angles).

3. Authors should define all the variables and values used in Equation 17.

Response: Thanks for the comment from the reviewer. We have defined all the variables and values used in Equation 17.

The subscript ‘real’ represents the physical units, ‘lu’ represents the lattice units, (m_l)_lu = 0.0177 is the dynamic viscosity, (r_l)_lu = 6.62 is the density of droplet and (g_lv)_lu = 0.159 is the surface tension. (Line 159, page7)

4. Authors should provide the definition of ui in Equation 18.

Response: Thanks for the comment from the reviewer. We have defined the variable ui used in Equation 18.

 is the inertial capillary velocity. (Line 169, page7)

5. The results shown in Figure 2 indicated large discrepancies between the authors' results and the results in [2]. The results in [2] actually agree very well with the experimental results. This may partially stem from the assumption that gravity is negligible. The authors should verify if that is the case and provide a more detailed explanation of the differences. The authors should also compare the other two quantities reported in [2] and the experimental article. Finally, I assume that the range of velocities comes from the positions the droplets are initially placed in. This should be stated in the text, and perhaps even in the caption.

Response: Thanks for the comment from the reviewer. We have added the state that the range of velocities comes from the positions the droplets are initially placed in. The main reason for the difference is also given. Besides, the comparison of simulated jumping velocities after droplet coalescence with experimental results is also added in Fig. S3. The revised texts are as follows:

By adjusting the droplet radius and the initial positions, the velocity range of jumping droplet is achieved. As shown in Fig. 2(b), the dimensionless velocity range for small droplets (r = 20 mm) obtained by our simulation is large, containing both Liu and Cheng’s simulation results [21] and the experimental data [1]. The main reason for the deviation is that the structure scale used in our simulation is close to the droplet radius, which makes the droplet jumping more sensitive to positions. For comparison, the droplet radius in Liu and Cheng’s simulation is set much larger, about 7.5 times the structure scale. The further influence of initial droplet position on velocity deviation will be explained in subsequent chapters. (Line 169, page 7)

The comparison of simulated jumping velocities after droplet coalescence with experimental results is shown in Fig. S3 (see supplementary material). Since the droplet radius is only slightly larger than the structure scale, it is easier for droplets to get trapped in the microstructure, which increases solid-liquid contact area during coalescence. Therefore, the jumping velocities are basically lower than the experimental results. (Line 178, page 7)

Figure S3. The comparison of simulated jumping velocities after droplet coalescence with experimental results.

 

6. The initial positions of the droplets described on lines 178-192 are not clear. It would be good to see the exact configurations as in the image, possibly in the Supplementary Material.

Response: Thanks for the comment from the reviewer. The exact configurations are added in the Supplementary Material. The revised texts are as follows:

Figure S4. Different initial positions of Case Rj (j = 0~5). The initial position of the droplet pair is indicated by the mutual tangent of two droplets (the dotted line).

7. The definitions of mi and ui in Equation 20 should be provided.

Response: Thanks for the comment from the reviewer. In order to be consistent with the content mentioned above, the equation is adjusted. The revised texts are as follows:

where u_drop is the droplet velocity, r is the local fluid density and u is the local velocity defined in Eq. (10).

8. The statement on the inverse motion on lines 235-236 is unclear.

Response: Thanks for the comment from the reviewer. We have modified the expression on lines 235-236. The revised texts are as follows:

During stage II, the droplet is in complete contact with the surface structure and starts to move upwards. (Line 259, page 10)

9. Equation 21 is unclear, given the definition shown in Equation 20.

Response: Thanks for the comment from the reviewer. In order to be consistent with the content mentioned above, the equation is also modified according to Equation 20. The revised equation is as follows:

10. The claim that the uncertainty increases when sharp patterns are used should be revisited. First, it is unclear how the uncertainty is defined in the model. Secondly, the difference between the angles that the authors use to support this statement is very small. Possibly marginal, depending on the method the authors used to measure the angles.

Response: Thanks for the comment from the reviewer. We have modified the statement to ensure the description is accurate. The revised texts are as follows:

On the other hand, the maximum horizontal velocity in Case Rj’ (0.066 m/s) is about 1.4 times higher than that in Case Rj (0.048 m/s) (Fig. 8(b)), indicating a slight increase in the deviation between the jumping direction and the normal direction. (Line 307, page12)

11. The authors should specify why they get ranges of results in Figure 9.

Response: Thanks for the comment from the reviewer. We have modified Figure 9 for easier understanding. The revised texts are as follows:

By adjusting the initial position of the droplet, the maximum velocity and minimum velocity with different radius are obtained. (Line336, page13)

 

Figure 9. (a) Deviation of droplet jumping velocity on the original surface. (b) Deviation of droplet jumping velocity on the refined surface. The range of results are achieved by adjusting the initial position of the droplet.

12. The authors should extend their introduction to cover many similar publications related to the topic and discuss their results in the light of other findings.

Response: Thanks for the comment from the reviewer. We have extended our introduction into two parts to cover the related publications. The revised texts are as follows:

For droplets with comparable size to the roughness length scale, the surface structure can participate in the coalescence process directly [17, 18]. It is found that the direction of the jumping droplet is not necessarily perpendicular to the surface when the droplet scale is close to the structure scale [9]. Coalescence-induced oblique jumping of a droplet inside a microgroove and a droplet on an adjacent plateau is observed [11]. This is caused by the impact of the liquid bridge on the edge of the microgroove, which generates a momentum component parallel to the surface plane. However, in the case of both droplets on top of the microstructure, the effect of initial position has not been studied. In addition, since the coalescence-induced droplet jumping can occur at different surface locations with the random nature of nucleation, it is of importance to further study the effect of droplet initial position on coalescence-induced droplet jumping when the droplet scale is slightly larger than the surface roughness. (Line 44, page 3)

Shi et al. [22] pointed out that the coalesced droplet is more likely to jump on the textured surface with larger conical post height and small spacing between the conical posts. Wang et al. [34] found that triangle microstructured surface can enhance the jumping ability of coalesced droplets during condensation. Chen et al. [35] studied self-propelled jumping of non-equal sized droplets and concluded that non-equal sized droplets are less efficient in transferring the released surface energy to effective jumping kinetic energy than in the equal sized case. In most numerical studies, the droplet scale is often set much larger than the structure scale, thus the position effect is not considered. Given that droplet sizes vary widely in nature, it is still worth investigating the influence of initial positions on coalescence-induced droplet jumping. (Line 63, page 3)

 

Minor comments:

 

1. There is a typographic error in the inline equation on line 118 - the square should apply to the squared bracket, as in [1]

 

[1] Gong, Shuai, and Ping Cheng. "Numerical investigation of droplet motion and coalescence by an improved lattice Boltzmann model for phase transitions and multiphase flows." Computers & Fluids 53 (2012): 93-104.

[2] Liu, Xiuliang, Ping Cheng, and Xiaojun Quan. "Lattice Boltzmann simulations for self-propelled jumping of droplets after coalescence on a superhydrophobic surface." International Journal of Heat and Mass Transfer 73 (2014): 195-200.

 

Response: Thanks for the comment from the reviewer. We have corrected the inline equation.

 

Author Response File: Author Response.docx

Reviewer 3 Report

Dear Authors,

This paper provides clear insights into the droplet-surface interaction during droplet coalescence and jumping. The originality of this paper is to present a 2D  numerical simulations of coalescence-induced droplet jumping on micro-structured surfaces using a pseudo-potential multi-phase lattice Boltzmann method (LBM) integrating with the Multi-Relaxation-Time (MRT) collision matrix. The equations are here provided in the framework of a D2Q9 model. The methodology consists in implementing a pseudo-potential multi-phase LBM with MRT collision matrix, using the Exact Difference Method (EDM) in the forcing scheme and incorporating the Peng–Robinson (P-R) equation of state in the interaction potential. 

A validation of the implemented method is proposed in two ways:
-1- Validation of the hydrodynamic effects through the Laplace law checking.
-2- Validation of the collision process by two droplets touch together leading to a liquid bridge formation and a rapid widening over time.

Then the results of numerical simulation are highlighted for two cases:
-Case 1 for studying effects of Initial Droplet Position on Coalescence induced Jumping.
-Case 2- Refinement of structures for enhancing coalescence-induced jumping.

These results indicates that for coalesced droplets having radii close to the structure length scale, the variation of droplet initial positions leads to a significant deviation of jumping velocity and direction due to the asymmetric droplet-structure adhesion and interaction.

In conclusion this paper provides a precise guidelines for the design of micro-structures and nano-structures with enhanced droplet jumping performance and will find application for energy and heat transfer applications. More precisely, the authors demonstrate that: "Specifically, for Cassie-Baxter state equally-sized binary droplets residing on uniformly micro-structured surfaces, variation of droplet initial positions governs the jumping velocity and direction due to the different solid-liquid adhesion and uneven force of the structural surface."

However to enrich this paper, it would make sens to incorporate some explanations and references in order to perform a 3D numerical simulation for definitively validate the role of droplet initial position in coalescence-induced droplet jumping, in future developments.

*Remarks:
-Even if it not directly the same topic, it seems the reference to papers such as those of A. Dupuis et al. entitled "Droplet Spreading on Heterogeneous Surfaces using a Three-Dimensional Lattice Boltzmann Model" will be relevant for adding.
-In the references of the paper, it could be considered to add the title of the cited papers, to be more readable.

-Presentation of figures could be improved. 

Sincerely.

Author Response

Dear editor and reviewers:

 

Thank you for your kind letter and for reviewers’ constructive comments concerning our paper (Manuscript processes-1700475). These comments are all valuable and helpful for improving our paper. According to the reviewers’ comments, we have tried best to modify our manuscript to meet with the requirements of your journal. In this revised version, changes to our manuscript within the document were all highlighted by using red colored text. Point-by-point responses to the editor and the reviewers are listed below this letter.

 

If there are any other modifications we could make, we would like very much to modify them and we really appreciate your help. We hope that our manuscript could be considered for publication in your journal. Thank you very much for your help.

 

Thank you and best regards.

May 2, 2022

Yours sincerely,

Zhichun Liu

Professor

School of Energy and Power Engineering

Huazhong University of Science and Technology

China

E-mail: zcliu@hust.edu.cn

 

To Reviewer #3:

1. Even if it not directly the same topic, it seems the reference to papers such as those of A. Dupuis et al. entitled "Droplet Spreading on Heterogeneous Surfaces using a Three-Dimensional Lattice Boltzmann Model" will be relevant for adding.

Response: Thanks for the comment from the reviewer. We have added more relevant references including the recommended paper.

2. In the references of the paper, it could be considered to add the title of the cited papers, to be more readable.

Response: Thanks for the comment from the reviewer. the titles of the cited papers have been added in the references.

3. Presentation of figures could be improved.

Response: Thanks for the comment from the reviewer. Some of the figures and its captions have been modified.

 

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The author did not answer all of my questions accordingly. They just have responded to some parts of issues and have left some others! I give one more chance to authors to answer ALL of my questions/ comments. If they cannot address all of my questions/ comments, I have no choice just to reject the paper.

Author Response

Dear editor and reviewers:

 

Thank you for your kind letter and for reviewers’ constructive comments concerning our paper (Manuscript processes-1700475). These comments are all valuable and helpful for improving our paper. According to the reviewers’ comments, we have tried best to modify our manuscript to meet with the requirements of your journal. In this revised version, changes to our manuscript within the document were all highlighted by using red colored text. Point-by-point responses to the editor and the reviewers are listed below this letter.

 

If there are any other modifications we could make, we would like very much to modify them and we really appreciate your help. We hope that our manuscript could be considered for publication in your journal. Thank you very much for your help.

 

Thank you and best regards.

May 10, 2022

Yours sincerely,

Zhichun Liu

Professor

School of Energy and Power Engineering

Huazhong University of Science and Technology

China

E-mail: zcliu@hust.edu.cn

To Reviewer #1:

The author did not answer all of my questions accordingly. They just have responded to some parts of issues and have left some others! I give one more chance to authors to answer ALL of my questions/ comments. If they cannot address all of my questions/ comments, I have no choice just to reject the paper.

Response: Thanks for the comment from the reviewer. We sincerely regret for not responding all of the issues. We attentively studied the questions and have provided more detailed responses to all parts of issues. Point-by-point responses to the issues are listed below. We hope you approve of the amended responses.

1. The reviewer thinks English is not the authors’ first language. The quality of the writing is needed to improve. The wrong structure, as well as lousy punctuation in some sentences, prevents proper understanding.

Response: Thanks for the comment from the reviewer. The manuscript has been thoroughly checked. The punctuation and incorrect structure have been reviewed and rectified.

2. In the abstract, the authors just define the problem, and it is like the introduction part. In contrast, it should be included a brief explanation of their work.

Response: Thanks for the comment from the reviewer. The abstract has been rewritten to include a brief description of our work. The revised texts are as follows:

“Abstract: Coalescence-induced droplet jumping on superhydrophobic surfaces with different initial positions is numerically simulated using 2D multi-relaxation-time (MRT) lattice Boltzmann method (LBM). Simulation results show that for coalesced droplets with radii close to the structure length scale, the change of droplet initial positions leads to a significant deviation of jumping velocity and direction. By finely tuning the droplet initial positions on a flat-pillared surface, perpendicular jumping, oblique jumping, and non-jumping are successively observed on the same structured surface. Droplet morphologies and vector diagrams at different moments are considered. It is revealed that the asymmetric droplet detachment from the structured surface leads to the directional transport of liquid mass in the droplet and further results in the oblique jumping of the coalesced droplet. In order to eliminate the influence of droplet initial position on droplet jumping probability, a surface with pointed micropillars is designed. It is demonstrated that compared to flat-topped micropillars, a surface with pointed micropillars can sup-press the initial droplet position effects and enhance droplet jumping probability. Furthermore, the effect of droplet/structure scale on droplet jumping is investigated. The influence of initial positions on coalescence-induced droplet jumping from the refined surface can be ignored when the droplet scale is larger than 3 times the structure scale. This study illustrates the role of drop-let initial position in coalescence-induced droplet jumping and provides guidelines for the rational design of structured surfaces with enhanced droplet self-shedding for energy and heat transfer applications.”

3. Some references are older than 2016, and therefore, they are abolished. May the reviewer ask the authors to change these references to newer ones? Some suggested papers are as below: LBM simulation of free convection in a nanofluid filled incinerator containing a hot block. Lattice Boltzmann method to simulate convection heat transfer in a microchannel under heat flux: gravity and inclination angle on slip-velocity. The investigation of thermal radiation and free convection heat transfer mechanisms of nanofluid inside a shallow cavity by lattice Boltzmann method.

Response: Thanks for the comment from the reviewer. We have carefully studied the papers recommended by the reviewer which inspired us profoundly. We further searched for more work related to the study and rewrote the introduction according to these references. The revised manuscript provides more resources after 2016 and some of the old references is replaced. Part of the revised texts are as follows:

“Lattice Boltzmann method (LBM) as a mesoscopic approach has been widely applied to simulating multiphase flows [30, 31], heat transfer and phase change [32-35]. Abbassi et al. [33] studied nanofluid magnetohydrodynamics (MHD) natural convection in an incinerator shaped enclosure and investigated the effect of different parameters including nanoparticles volume fraction, nanofluid flow and Rayleigh number. Safaei et al. [34] investigated the interaction between thermal surface radiation and nanofluid free convection in a two-dimensional shallow cavity. Mozaffari et al. [35] simulated convection heat transfer in an inclined microchannel and found that the buoyancy caused by gravity can affect the hydrodynamic properties of the flow. (Line 63)”

“Besides, a variety of hydrophobic structures have been conducted by LBM in order to optimize the droplet jumping ability [24, 27, 37]. Wang et al. [38] found that triangle microstructured surface can enhance the jumping ability of coalesced droplets during condensation. Chen et al. [39] studied self-propelled jumping of non-equal sized droplets and concluded that non-equal sized droplets are less efficient in transferring the released surface energy to effective jumping kinetic energy than in the equal sized case. (Line 75)”

33. Abbassi, M. A.; Safaei, M. R.;  Djebali, R.;  Guedri, K.;  Zeghmati, B.; Alrashed, A. A. A. A., LBM simulation of free convection in a nanofluid filled incinerator containing a hot block. International Journal of Mechanical Sciences 2018, 144, 172-185.
34. Safaei, M. R.; Karimipour, A.;  Abdollahi, A.; Nguyen, T. K., The investigation of thermal radiation and free convection heat transfer mechanisms of nanofluid inside a shallow cavity by lattice Boltzmann method. Physica A: Statistical Mechanics and its Applications 2018, 509, 515-535.
35. Mozaffari, M.; D’Orazio, A.;  Karimipour, A.;  Abdollahi, A.; Safaei, M. R., Lattice Boltzmann method to simulate convection heat transfer in a microchannel under heat flux. International Journal of Numerical Methods for Heat & Fluid Flow 2020, 30 (6), 3371-3398.
36. Zhang, L.-Z.; Yuan, W.-Z., A lattice Boltzmann simulation of coalescence-induced droplet jumping on superhydrophobic surfaces with randomly distributed structures. Appl. Surf. Sci. 2018, 436, 172-182.
37. Wang, X.; Xu, B.;  Chen, Z.;  Yang, Y.; Cao, Q., Lattice Boltzmann simulation of dropwise condensation on the microstructured surfaces with different wettability and morphologies. International Journal of Thermal Sciences 2021, 160, 106643.
38. Chen, X.; Lu, J.; Tryggvason, G., Numerical simulation of self-propelled non-equal sized droplets. Phys. Fluids 2019, 31 (5), 052107.
39. Please explain more about the novelty of your work.

Response: Thanks for the comment from the reviewer. In this manuscript, we studied the effect of initial position on droplet jumping and found that droplet jumping failure may occur at certain initial position. The position effect has often been ignored in previous simulations, because the droplet scale is usually set much larger than the structure scale in most numerical studies. Although, such a phenomenon was observed in experiments when the droplet is trapped in a microgroove, in the case of both droplets on top of the microstructure, the effect of initial position has rarely been studied. From the viewpoint of initial position influence, we further designed a surface with pointed micropillars to eliminate the influence of droplet initial position on droplet jumping probability, which is important for the enhancement of droplet condensation. We have rewritten the introduction to highlight the novelty of the study. Correspondingly, we have also reorganized the conclusion section. However, the revised content is too long to be attached here. Please see the revised introduction part for details.

5. Add more quantitative results to the conclusion part.

Response: Thanks for the comment from the reviewer. The conclusion part has been revised and more quantitative results are added. The revised texts are as follows:

“On the other hand, the maximum horizontal velocity in Case Rj’ (0.066 m/s) is about 1.4 times higher than that in Case Rj (0.048 m/s), indicating a slight increase in the deviation between the jumping direction and the normal direction. (Line 408)”

“It is found that the influence of initial position on droplet jumping velocity weakens with the increase of droplet radius. The deviation of jumping velocity on the flat-topped surface reduces from ~0.34 m/s (r = 30 mm) to ~0.02 m/s (r = 60 mm). With the increase of droplet size, the proportion of liquid-solid adhesion work to the excess surface energy decreases, leading to the deviation reduction. For r = 60 mm (droplet/structure scale ~3), the deviation of jumping velocity on the new surface has been reduced to ~0.008 m/s. (Line 412)”

6. What is the actual application of this work?

Response: Thanks for the comment from the reviewer. Coalescence-induced droplet jumping possesses potential applications in self-cleaning, water harvesting and condensation heat transfer. As droplet jumping failure can occur at certain initial position, it is of importance to improve the surface structure from the viewpoint of initial position influence. The refined structure can effectively prevent jumping failure, which is of great importance for enhancing dropwise condensation heat transfer. The actual application is stated in the discussion part. The revised texts are as follows:

“As droplet jumping failure can occur at certain initial position, it is of importance to improve the surface structure from the viewpoint of initial position influence. Our study provides guidelines for the design of micro/nanostructures to prevent droplet jumping failure, which is of great importance for enhancing dropwise condensation heat transfer. The analysis of droplet initial position, surface structure and droplet/structure scale on droplet jumping behavior helps to understand the irregular jumping of droplets and to further study controllable droplet jumping used for water harvesting. (Line 386)”

7. Please add the nomenclature table to your paper.

Response: Thanks for the comment from the reviewer. The nomenclature table has been added in the manuscript. Please see the revised manuscript for details.

8. Where is the Author Contributions part?

Response: Thanks for the comment from the reviewer. We have added the Author Contributions part in the end of the manuscript. Please see the revised manuscript for details.

9. When reviewing the references, a strong impression can be created that the manuscript should be submitted to another journal: To give journal readers a sense of continuity, the reviewer encourages the authors to identify present journal publications of similar research in your papers. Please, do a literature check of the documents published in recent years (2021 and 2022) and relate the content of relevant documents to the results and findings presented in your publication. The authors can also reference articles in print using their DOI:

Response: Thanks for the comment from the reviewer. We have carefully searched the documents of the present journal publication published in recent years. Our study aims at exploring the effects of droplet initial position on droplet jumping and enhancing droplet jumping probability, whose potential applications include self-cleaning, inkjet printing and condensation heat transfer enhancement. The references from the present journal on inkjet printing and condensation heat transfer are as follows:

3. Zhang, Y.; Hu, G.;  Liu, Y.;  Wang, J.;  Yang, G.; Li, D., Suppression and Utilization of Satellite Droplets for Inkjet Printing: A Review. Processes 2022, 10 (5).
4. Oktavianty, O.; Haruyama, S.; Ishii, Y., Enhancing Droplet Quality of Edible Ink in Single and Multi-Drop Methods by Optimization the Waveform Design of DoD Inkjet Printer. Processes 2022, 10 (1).
5. Fedorova, N.; Lindner, C.;  Prado, L. H.;  Jovicic, V.;  Zbogar-Rasic, A.;  Virtanen, S.; Delgado, A., Effect of Steam Flow Rate and Storage Period of Superhydrophobic-Coated Surfaces on Condensation Heat Flux and Wettability. Processes 2021, 9 (11).
6. Zhou, W.; Wang, S.;  Zhu, J.;  Xie, J.; Cai, C., Parameter Optimization and Experimental Study of Jet Mixing Device Based on CFD. Processes 2022, 10 (5).

The references performed to study the droplet behavior include:

23. Tran, D. T.; Nguyen, N.-K.;  Singha, P.;  Nguyen, N.-T.; Ooi, C. H., Modelling Sessile Droplet Profile Using Asymmetrical Ellipses. Processes 2021, 9 (11).
24. Liao, M.-J.; Duan, L.-Q., Investigation of Coalescence-Induced Droplet Jumping on Mixed-Wettability Superhydrophobic Surfaces. Processes 2021, 9 (1), 142.
25. Tembely, M.; Vadillo, D.;  Soucemarianadin, A.; Dolatabadi, A., Numerical Simulations of Polymer Solution Droplet Impact on Surfaces of Different Wettabilities. Processes 2019, 7 (11).
26. Zhang, J.; Yu, X.; Tu, S.-T., Lattice Boltzmann Simulation on Droplet Flow through 3D Metal Foam. Processes 2019, 7 (12).

We can be sure that our research is a step forward on the basis of these literatures, so we believe that our research has great relevance to this journal and is suitable to be submitted to the journal. We introduce these documents in the introduction for comparison with our research. Besides, the content of some relevant documents is related to the results and findings presented in our manuscript. Part of the revised texts are as follows:

“Due to its potential applications including self-cleaning [2], inkjet printing [3, 4] and condensation heat transfer enhancement [5-7], coalescence-induced droplet jumping has drawn extensive attention in the past few years. (Line 35)”

“With intrinsic advantages in parameter and scale setting, a number of numerical simulations have been performed to study the self-propelled droplet behavior [21-28]. For example, Liao et al. [28] studied coalescence-induced droplet jumping on the surfaces of periodic strip-like wettability patterns using the molecular dynamics simulation method. The effects of the surface wettability and the relative positions of the center of two droplets on droplet jumping are analyzed. Tembely et al. [29] studied droplet impact on surfaces with different contact angles using the volume of fluid (VOF) method. Lattice Boltzmann method (LBM) as a mesoscopic approach has been widely applied to simulating multiphase flows [30, 31], heat transfer and phase change [32-36]. (Line 57)”

Author Response File: Author Response.pdf

Reviewer 2 Report

The revised manuscript addressed all my concerns, therefore I recommend it for publication in its current form.

Author Response

We really appreciate your help for improving our manuscript.

Round 3

Reviewer 1 Report

Accept