Spherical Droplet Deposition—Mechanistic Model

Round 1

Reviewer 1 Report

see attached review

Comments for author File: Comments.docx

Author Response

Reply to the Reviewer 1

 

We would like to thank the reviewer for the great effort put into reviewing our manuscript and formulating many insightful comments.

Below is our answer to the problems raised in the review. To make checking the corrections easier, the comment is quoted carefully, followed by our answer (written in green font). Additionally, the places where we have made changes are marked in the text of the revised manuscript.

 

Review

Spherical Droplet Deposition – Mechanistic model

Jacek A. Michalski and Sławomir Jakieła

The draft by Michalski and Jakieła is an interesting despite pure theoretical approach to discuss the forces acting on a droplet placed on a solid surface. I do recommend the paper for publication. However, the authors should re-work some parts of the text.

1. The abstracts must clearly state the outcomes of the study. What are the main results and to what extend do they exceed the current knowledge?

In line with your suggestion, the entire abstract has been reformulated. Unfortunately, it is slightly longer than the required 200 words, and taking into account what the reader considers the most important in the paper, it may raise doubts anyway.

 

2. The assumptions made (line 141 to 149) are far reaching. The authors should keep in mind and discuss in the text that real droplets show capillarity driven and Marangoni flows. Especially Marangoni flow affects the droplet interface.

 

 

The adopted assumptions are consistent, and in principle identical, to those commonly applied in theoretical models describing the equilibrium of forces acting on a droplet deposited on a solid substrate [7-9, 11-14]. Moreover, in a very large part of the papers (including experimental ones), the deposited droplets are assumed to be isothermal, if only because the physicochemical constants are assumed to be independent of temperature. There are exceptions to this rule for relatively large droplets, e.g. S.Y. Misyura, Contact angle and droplet evaporation on the smooth and structured wall surface in a wide range of droplet diameters, Applied Thermal Engineering 113 (2017) 472–480. The isochoric nature of the drops was assumed for decades ad hoc, ignoring the phenomenon of their evaporation. For theoretical purposes, a trick was used to justify such a procedure - see Appendix of [14].

Thank you very much for your remark due to the lack of assumptions regarding the Marangoni effect causing the loss of the droplet mass as it spreads over a solid substrate. Appropriate corrections were introduced in the following points of the assumptions.

 

3. Figure 1: What is the meaning of the cross in the circle at the lower right part of the sketch?

The symbol shown indicates the direction of the axis of an angular variable  in a cylindrical coordinate system perpendicular to the plane of the drawing. Due to the axial symmetry of the spherical drop with respect to the  axis, it is only introduced pro forma. Such markings are used quite commonly in publications on physics. However, an appropriate explanation was introduced in the figure caption.

 

4. Are the parameter E, B and D (line 249 to 251) similarity numbers? Do they have a physical meaning?

The parameters E, B, and D are similarity numbers. A description of their physical meaning was formulated and the appropriate correction was introduced into the text of the paper.

 

5. I do not know reference [5]. However, I guess that the physical assumptions made in this text are different to the assumption made by the authors. That may make the “unfortunate” different between the two results. The authors should discuss their results more in the light of a physical interpretation compared to other approaches.

The paper [5] is purely experimental and refers to gas (air) bubbles deposited on a solid surface in liquid (water) environment. None of the assumptions presented in our paper were included in it. The effect of evaporating liquid into gaseous phase was completely ignored. On the other hand, the introduction of the  component improved the quality of fitting the experimental data to the Young's equation (1) –  is radius of wetted area. The physical sense of this correction was justified many years later in the thermodynamic model formulated by Schwartz [16] and finally developed by Drelich [11]. It should be emphasized that all models, up to the paper [14], assumed ad hoc isothermal and isochoric nature of all phases present in the system, neglecting without any discussion the phenomenon of liquid evaporation and the dependence of the vapour pressure above its curved surface on its curvature radii.

 

6. Figure 2 and following figures: Figure 2 represents the parameter D in dependency of the contact angle. Shouldn’t that be the other way round? Here I am again by the physical interpretation of the findings especially the parameters E, B and D. The variables of these three parameters must be seen as given. The contact angle follows from these given conditions.

From a formal point of view, this remark is correct because the variables are the values of the parameters , , , and the result obtained from the model is the contact angle. It should be noted, however, that the contact angle only varies between 0-180 degrees, which limits the "width" of the graph. However, its "height" depends only on the currently unknown values of one of the parameters mentioned. Thus, to trace the variability of the contact angle for several ranges of variation of a parameter, it is more convenient to place several graph slices one above the other than to place them next to each other. The second reason (probably the most important now) is that in the models formulated so far, the contact angle was placed on the horizontal axis, and the corresponding parameter on the vertical axis. Thus, we believe that the presented form of presenting the results is also more convenient for the readers of the paper.

 

7. Line 529: The reference 24 needs square brackets.

It is improved.

 

8. Line 540: An alternative to the ISS would be parabolic flights.

The duration of the weightless effect during parabolic flight is approximately 1 minute. The results of experiments carried out with the deposition of liquid droplets on solid substrates indicate that the time needed to reach the state of equilibrium of forces may be much longer. Thus, the results of measurements obtained during parabolic flight can be characterized by a significant error.

An appropriate explanation was introduced into the text of the paper.

 

9. The English of the text is good. However, a proofreading and correction of the writing style by a native speaker would increase the readability.

In this matter, we have done everything we can.

Author Response File: Author Response.docx

Reviewer 2 Report

At least a good work about droplets during its deposition on the substrate. This is a nightmare in coatings as it was stated in: Enhanced performance of nanostructured coatings for drilling by droplet elimination, Materials and Manufacturing Processes 31 (5), 593-602 by the way, missed, and it was defined previously in: DOI 10.1007/s00170-014-5844-1 How much time would be saved if your approach and model could be applied, please a better state of the art, I see you do not apply coatings in industrial sacale, as it was the case of the latter in the nanostructured AlTiSiN coating, commercial denomination nACo, as the one with the best performance for turning austenitic stainless steel.

Some point to enhance:

State of the art: make it a little better with a more practical above view

Very good reference to 1936 work, history is important in classic theories.

Section 4 is weak, verification is poorly explained. One will expect to see pictures or erro determination.

Droplet are a real problem in PVD, a lot of money is spent in polishing. I did not see any India or China work about that, is because they did not work on that?

Author Response

Reply to the Reviewer 2

We would like to thank the reviewer for the time spent reading and analyzing the issues raised in our manuscript. We would also like to thank you for formulating a number of comments relating to the essence and form of presenting the obtained results.

Below we address all the comments contained in the review of our paper. Under each issue raised by the reviewer, our answer is written in green font. In addition, all the places where we've made changes are marked in the revised manuscript.

 

At least a good work about droplets during its deposition on the substrate. This is a nightmare in coatings as it was stated in: Enhanced performance of nanostructured coatings for drilling by droplet elimination, Materials and Manufacturing Processes 31 (5), 593-602 by the way, missed, and it was defined previously in: DOI 10.1007/s00170-014-5844-1 How much time would be saved if your approach and model could be applied, please a better state of the art, I see you do not apply coatings in industrial sacale, as it was the case of the latter in the nanostructured AlTiSiN coating, commercial denomination nACo, as the one with the best performance for turning austenitic stainless steel.

Some point to enhance:

State of the art: make it a little better with a more practical above view

This is a very valid point. In the Introduction, a paragraph was introduced that indicates the most important disadvantage of the models to date, which does not appear in the model shown in the paper.

Very good reference to 1936 work, history is important in classic theories.

Thank you very much for the approbation.

Section 4 is weak, verification is poorly explained. One will expect to see pictures or error determination.

Our paper is purely theoretical. On the other hand, the determination of the maximum radius (volume) of the drop, below which the measured contact angle will weakly depend on the force of gravity, was to prove the feasibility of conducting experiments in terrestrial conditions.

The material presented in the article is only a part of the entire thermodynamic model related to the deposition of droplets on solid substrates. In the next paper, we will present the results of experiments in which the object of measurement will be the contact angle as a function of droplet volume, and droplets of various liquids will be deposited on different surfaces. If possible, we will also change the fluids surrounding the substrate and the droplets. We have already performed some of the experiments, and the obtained results indicate that the model equations can properly approximate them. However, this is statistically too small sample to discuss the quality of the fit and possible errors. Unfortunately, the repeated lockdowns caused by the epidemic significantly hinder laboratory work.

Droplet are a real problem in PVD, a lot of money is spent in polishing. I did not see any India or China work about that, is because they did not work on that?

When it comes to wetting hardly wettable surfaces (hydrofobic, superhydrofobic e.t.c.), I have already read some Chinese papers. However, none of them applied to PVD methods, even though some of them had the metal wetting process at elevated temperature. I have not come across papers written by Indians on these issues yet. However, not knowing the principles of cooperation between scientists and industry in these countries, I cannot prejudge whether such works are carried out there. For example, in Poland, the vast majority of work for industry is confidential, while in the United States, the confidentiality status of the results obtained is negotiated with the company.

From the scientific point of view, we mainly deal with issues related to microfluidic devices. This means that we need surface wetting issues to predict droplet parameters and their interaction with the walls of very narrow channels.

 

Author Response File: Author Response.docx