Development of a Partial Clustering Model of Alloy Viscosity

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper presents a partial clustering model of viscosity including the influence of different types of clusters, which can establish a quantitative correlation between a dynamic viscosity of alloys and temperature. And the theoretical calculation is verified on an example of Cu-Sn alloy. The topic is attractive and prospective, the description of modeling approach is reasonable and rigorous logically, and the discussion for the mechanism is understandable. I believe that the essential contribution of this paper is give us a strategy for predicting the behavior of dynamic viscosity characteristic at the high temperature of binary and even multi-component alloys. Besides, there are some problems that should be revised before it is considered for publication. The main comments are listed as follows:

1. Equation 13 give the modified dynamic viscosity that considering the effect of clusters, i.e., the “coldest” part – clusters, the “cool” part – single crystal-mobile, a “warm” part – single liquid- mobile, and the “hot” part – single vapor-mobile. X_A and X_B are the partial shares of substances A and B. however, in some binary alloys containing intermetallic compounds, like in Ni-Al, Co-B, Ti-Al, etc, the effect of element A and B maybe non-independent, how to describe the contribution of coupling effect among elements to the total viscosity?  In addition, how to calculate the value of Δ_chH? Where is the origin of Δ_mixH and Δ_fH, from literature?

2. The clusters can affect the physical parameter of liquid significantly, except for the division of temperature of clusters, whether other factors like the sizes, aggregation and chemical bonds also affect the viscosity or not?

3. In Table 2, where is the origin of the obtained η_{𝑻𝒍𝒊𝒒} at Tliq, using Arrhenius equation or models? For better comparison, the value of η should be given at lower temperature (< T_Liq like No.9).

4. In table 2, what is the possible reason for the discrepancy between the model (top row) and the value by Arrhenius equation for the experimental data (bottom row). What might be the unaccounted factor.

5. In Figure 1, the X-axis represents the composition of Cu-Sn alloy, with Sn increasing or Cu increasing? Please give a clear indication.

6. Combined with Table 1, please give the possible explanation about the relationships between the dynamic viscosity and the composition of Cu-Sn alloy.

7. Please check the manuscript carefully about the English grammar, sentence structure and reference part. For example, the font format is not uniform in line 349 to 351. The subscript or superscript are not correct in line 286 and 288. the journal information format should be unity (abbreviate or not).

8. I suggest that more figures should be given from the Table for visualization.

Author Response

Comments 1: Equation 13 give the modified dynamic viscosity that considering the effect of clusters, i.e., the “coldest” part – clusters, the “cool” part – single crystal-mobile, a “warm” part – single liquid- mobile, and the “hot” part – single vapor-mobile. X_A and X_B are the partial shares of substances A and B. however, in some binary alloys containing intermetallic compounds, like in Ni-Al, Co-B, Ti-Al, etc, the effect of element A and B maybe non-independent, how to describe the contribution of coupling effect among elements to the total viscosity?  In addition, how to calculate the value of Δ_chH? Where is the origin of Δ_mixH and Δ_fH, from literature?

Response 1:

The partial clustering model of viscosity has been previously validated using a Cu-Al alloy [27]. And in this paper, it is applied to the Cu-Sn alloy, i.e. more detailed phase diagrams were found for these alloys.

According to the Boltzmann distribution for the thermal (kinetic) energy of the chaotic motion of particles, these particles are considered virtual and, as a result of random collisions, they are interconvertible.

The potential energy further accounts for their mutual attraction or repulsion, leading to the formation or destruction of bonds of a certain type. Since the total energy contribution consists of both kinetic and potential energies, this process is accompanied by the release or absorption of heat. It is indirectly (in total) accounted for in the thermal effects of melting (for pure substances) or in formation of the liquidus line (for alloys). These effects are measurable when constructing phase diagrams of alloys. Intermetallic compounds have been not considered in this research; however, based on the additivity and interconvertibility of different energy types, the influence of elements A and B can be incorporated.

All values of Δ_mixH and Δ_fH are taken from the literature.

 

Comments 2: The clusters can affect the physical parameter of liquid significantly, except for the division of temperature of clusters, whether other factors like the sizes, aggregation and chemical bonds also affect the viscosity or not?

Response 2: As demonstrated in the paper, the consideration of cluster size based on the number of crystal-mobile particles within the cluster, as well as the distinction between these and the free (unbound) particles, refines the concept of a cluster and elucidates their impact on viscosity.

 

Comments 3: In Table 2, where is the origin of the obtained η_???? at Tliq, using Arrhenius equation or models? For better comparison, the value of η should be given at lower temperature (< T_Liq like No.9).

Response 3: Calculations for η_????  were conducted according to the Arrhenius equation (h = А×exp[E_v/RT]) using data from Table 1.

Comments 4: In table 2, what is the possible reason for the discrepancy between the model (top row) and the value by Arrhenius equation for the experimental data (bottom row). What might be the unaccounted factor.

Response 4: First and foremost, the Arrhenius equation is smoothed when linearization of the dotted dependences of viscosity on an inverse temperature, despite the evident nonlinearity in their distribution, especially when extrapolating this equation beyond the studied interval. This is emphasized by the data in the final column of Table 2.

 

Comments 5: In Figure 1, the X-axis represents the composition of Cu-Sn alloy, with Sn increasing or Cu increasing? Please give a clear indication.

Response 5: w(Sn) is increasing. The correction has been made.

 

Comments 6: Combined with Table 1, please give the possible explanation about the relationships between the dynamic viscosity and the composition of Cu-Sn alloy..

Response 6: This relationship is multifactorial and correlational, with a defined functionality. It is manifested in the magnitude and sign of the gradients, as well as the lower and upper limits. Additionally, it involves the partial dependence on each factor, all while being strictly governed by the laws of thermodynamics and kinetics.

 

Comments 7: Please check the manuscript carefully about the English grammar, sentence structure and reference part. For example, the font format is not uniform in line 349 to 351. The subscript or superscript are not correct in line 286 and 288. the journal information format should be unity (abbreviate or not).

Response 7: We agree and we have made the corrections.

 

Comments 8: I suggest that more figures should be given from the Table for visualization.

Response 8: We agree and we have added 2 figures.

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

   The paper ” Development of a partial-cluster model of the alloy viscosity’’ can be published in Applied Sciences after some corrections:

 

   1. The introduction section is relatively brief and does not fully expose essential elements in this field of study and at the same time, concrete, practical examples, with similar research are needed to clearly expose the degree of novelty and scientific progress brought by this research work.

2.     2. The work obviously exposes mathematical analysis models and it should be mentioned whether or not special software is used to generate mathematical models and perform calculations behind the analyses and if such software is used, all their characteristics, databases of alloy systems, etc. should be clearly mentioned.

3.     3.  Row 111, the formula number is not placed correctly to the right of the row

4.      4. Row 137, the formula is not numbered

5.   5. A check should be made on the entire work on compliance with the template and instructions, for example, several empty rows such as rows 304, 315, 319, etc. are observed. and errors of overlapping information with lines 246,247,248 that appear clearly when downloading the pdf of the paper.

6.      6. Figure 1 presents a relatively low clarity. It is advisable to replace it with a figure that presents a higher quality.

7.      7. The conclusions section should mention each conclusion point by point

8.      8. The scope of the paper is relatively small and briefly presents the present study.

Author Response

Comments 1: The introduction section is relatively brief and does not fully expose essential elements in this field of study and at the same time, concrete, practical examples, with similar research are needed to clearly expose the degree of novelty and scientific progress brought by this research work.

Response 1: The initial concept of viscosity was expressed through the assumption that interlayer frictional forces act to slow down the movement of liquids. A broader perspective on this property emerged with the recognition that it also manifests in the stationary state. This conclusion directly followed from the Boltzmann distribution for an ideal gas, based on a statistical justification of the spectrum of energy-distinguishable particles scattered throughout the volume. These particles can be detected using beam diagnostic methods, revealing a tangible variety of energy levels, which can be specified with arbitrary variation steps. It was at this point that research began to develop, enabling the establishment of a correlation between the distribution of energy levels (spectrum) according to Boltzmann and various physicochemical properties (more than 60 known, such as density, electrical conductivity, volatility, etc.), with viscosity being one of the foremost. Therefore, the Boltzmann distribution in this context was first used in such studies.

 

Comments 2: The work obviously exposes mathematical analysis models and it should be mentioned whether or not special software is used to generate mathematical models and perform calculations behind the analyses and if such software is used, all their characteristics, databases of alloy systems, etc. should be clearly mentioned.

Response 2: The obtained partial-cluster data were developed using a specific viscosity calculation algorithm based on thermochemical literature (or proprietary) data.  However, due to the inherent compactness of the partial clustering model, its simplicity, and the fact that no specialized software was required or utilized, it was implemented without the need for such tools.

 

Comments 3: Row 111, the formula number is not placed correctly to the right of the row

Response 3: We agree. The corrections have been made. When entering data on the journal’s website, a technical failure occurred.

 

Comments 4: Row 111, the formula number is not placed correctly to the right of the row

Response 4: We agree. The corrections have been made. When entering data on the journal’s website, a technical failure occurred.

 

Comments 5: Row 111, the formula number is not placed correctly to the right of the row

Response 5:  We agree. The corrections have been made. When entering data on the journal’s website, a technical failure occurred.

 

Comments 6: Figure 1 presents a relatively low clarity. It is advisable to replace it with a figure that presents a higher quality.

Response 6:  We agree. The corrections have been made.

 

Comments 7: The conclusions section should mention each conclusion point by point.

Response 7:  We agree. The corrections have been made.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This is a work with great potential. However, several shortcomings in the text itself, which I point out below, are present. I do not analyze the mathematical side of the presented relationships; the basic formulas are not controversial. Please complete the information as suggested and take a new approach to discussing the results, scaling it to the approach to model development. 

The introduction says that the way it is heated can affect the properties, which is a very interesting observation. Whether this applies to liquids or whether we know more, this is a promising statement that needs more attention. (line 42)
In lines 119 - 124 the authors highlight their approach to the liquid in which the crystallites float, below we have this suggestion, which you have to guess that we are at T=Tm, the melting point - please point out more explicitly this thermal state, as it is extremely important, where did these crystallites come from? What was the waiting time for them to appear in the isothermal state, or are they secreted heterogeneously? This is the kind of passage where it's explained a little badly, you have to guess 
Moving on to the results, the first question - why this alloy and the answer is not - because we have a set of results from the publication, but why do these two metals with such a large difference in melting point, this carries huge implications for the behavior of the alloy, it is known that the homogeneity of the chemical composition will also have an impact here, the system is sensitive to even subtle local changes - and this can affect precisely the appearance of these crystallites.
Why is the binary system of this alloy not posted? This is the No. 1 information for the analysis of phenomena 
I really like the description of the method, the sequence of phenomena indicated, and the attempts to explain them in the model - the transition to the analysis of the results cools down the enthusiasm of the reader a bit. The explanation is quick, even cursory referring to the introduction to the model. 

kind regards

reviewer

Author Response

Comments 1:  The introduction says that the way it is heated can affect the properties, which is a very interesting observation. Whether this applies to liquids or whether we know more, this is a promising statement that needs more attention. (line 42)

Response 1: Indeed, the behavior of alloys and the restoration of product shapes after complete destruction and melting are part of a broader issue - the recovery of initial forms, or the manifestation of “memory” effects. This is most likely a consequence of a certain probability associated with the classification of clusters, based on the equality of this probability for adjacent clusters of similar size. This ensures, at the very least, the reproduction of roughly spherical shapes with indeterminate geometric forms, but more importantly, it guarantees the instability of the clusters. This is akin to any situation where random events with equal probabilities exhibit similar behavior. The limitation of this probabilistic interpretation in cluster formation is, to some extent, addressed by a variety of structural research methods. These include defining strict geometric forms for cluster configurations and determining the principal coordination number for each substance, which, in the first approximation, correlates with the average number of particles in a cluster [29]. Therefore, it can be asserted that these data are also applicable to liquids.

 

Comments 2: In lines 119 - 124 the authors highlight their approach to the liquid in which the crystallites float, below we have this suggestion, which you have to guess that we are at T=Tm, the melting point - please point out more explicitly this thermal state, as it is extremely important, where did these crystallites come from? What was the waiting time for them to appear in the isothermal state, or are they secreted heterogeneously? This is the kind of passage where it's explained a little badly, you have to guess

Response 2: The partial clustering model of viscosity was based on the concept of chaotic particles, in which three classes of chaotic particles are considered: crystal-mobile, liquid-mobile and vapor-mobile particles. The equations for these particles were derived from the Boltzmann distribution (spectrum), taking into account only the thermal (kinetic) component. As the temperature increases, the ratio of these three classes of particles changes, and after the melting point, the sum of liquid-mobile and vapor-mobile particles predominates. However, crystal-mobile particles still exert a significant influence, and these may manifest as fragments of the crystalline lattice in the substance. According to the authors, clusters are composed of crystal-mobile particles. Therefore, they do not arise and disappear spontaneously, but rather are a result of the decomposition of the substance during the melting. All the derivations are detailed in our previous publications, so we have refrained from repeating them here and instead refer to our articles [16 and 27].

 

Comments 3: Moving on to the results, the first question - why this alloy and the answer is not - because we have a set of results from the publication, but why do these two metals with such a large difference in melting point, this carries huge implications for the behavior of the alloy, it is known that the homogeneity of the chemical composition will also have an impact here, the system is sensitive to even subtle local changes - and this can affect precisely the appearance of these crystallites.

Response 3: The state upon reaching the melting temperature is governed by a systemic invariance of stability, which manifests as a harmony between the structural and non-structural (probabilistic) components, closely aligning with the golden ratio. Consequently, substances exhibit different melting temperatures, including significant discrepancies between copper and tin. However, in terms of the ratio between their constructive and probabilistic components, each substance maintains its relationship with the golden ratio proportion.

 

Comments 4: Why is the binary system of this alloy not posted? This is the No. 1 information for the analysis of phenomena.

Response 4: The partial clustering model of viscosity has been previously validated using a Cu-Al alloy [27]. And in this paper, it is applied to the Cu-Sn alloy, i.e. more detailed phase diagrams were found for these alloys.

 

Comments 5: I really like the description of the method, the sequence of phenomena indicated, and the attempts to explain them in the model - the transition to the analysis of the results cools down the enthusiasm of the reader a bit. The explanation is quick, even cursory referring to the introduction to the model.

Response 5: We agree, we have added information to the section.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

The article titled "Development of a partial-cluster model of the alloy viscosit" is well written.

 

In this paper was to obtain a partial clustering model of viscosity including the influence of

clusters. The aim has been achieved.

 

The topic is very relevant. This is evidenced by the correct solution to the problem and the

achievement of the assumed objective.

 

This article correctly established a quantitative correlation between a dynamic viscosity of

alloys and temperature of liquidus in isotherms. In this paper, was presented correctlyconcept of

the chaotic particles is applied to substantiate the existence of an energy class of particles present

in the liquid in a form of clusters. The novelty of the paper consists in the obtaining of a

quantitative physical and mathematical model of temperature dependences of the dynamic

viscosity based on destruction of clusters as the temperature increases.

 

It is innovative of the paper consists in the obtaining of a quantitative physical and mathematical

model of temperature dependences of the dynamic viscosity based on destruction of clusters as

the temperature increases.

 

The mathematical model was compared with viscosity data from a state diagram starting from the

liquidus barrier. This approach was developed for the first time and allows the construction of

viscosity isotherms based on thermochemical initial data with extrapolation to the ultrahigh

temperature region. The proposed new model was verified on the example of a Cu-Sn alloy.

 

The methodology and analysis of the research results were presented in the most appropriate way.

However, some aspects require improvement. In the chapter "2. Materials and Methods" there is

no detailed description of the type of material used for the research. Please complete this in the

text and also add a table with the chemical composition of the material used.

 

The information provided in chapter "5. Conclusions" is correct, but please expand the

description to include the practical use of the results. I propose to expand the summary of the

article and present the conclusions in points.

 

References to the literature are correctly included throughout the work. The bibliography is

properly prepared.

 

The data presented in Figure 1 is difficult to read.

 

Model 13 requires editing. The first letter of the formula is not visible.

 

I ask the authors to consider presenting the results in several figures. Maybe this would make the

article better perceived by the reader.

 

I accept for publication after making minor corrections

Author Response

Comments 1: However, some aspects require improvement. In the chapter "2. Materials and Methods" there is no detailed description of the type of material used for the research. Please complete this in the text and also add a table with the chemical composition of the material used.

Response 1: We used the data from reference [36] as the most reliable for the base materials copper and tin, as well as their alloys, including viscosity data from the same authors. This made their data the most objective for comparison with the partial-cluster model (13) we propose. Additionally, a table with the composition of the Cu-Sn alloy has been included in the text.

 

Comments 2: The information provided in chapter "5. Conclusions" is correct, but please expand the description to include the practical use of the results. I propose to expand the summary of the article and present the conclusions in points.

Response 2: The proposed model for the temperature dependence of dynamic viscosity is already suitable for practical application, particularly for extrapolation to temperatures above 1800 K. This temperature range is challenging to achieve experimentally, yet it is reliably represented in the model (13). Additionally, technological verification of the proposed model is feasible for viscosity-based control in the ultra-high temperature regime. This information has been added to Section 5.

 

Comments 3: The data presented in Figure 1 is difficult to read.

Response 3: We agree. The corrections have been made. When entering data on the journal’s website, a technical failure occurred.

 

Comments 4: Model 13 requires editing. The first letter of the formula is not visible.

Response 4: We agree. The corrections have been made. When entering data on the journal’s website, a technical failure occurred.

 

Comments 5: I ask the authors to consider presenting the results in several figures. Maybe this would make the article better perceived by the reader.

Response 5: We agree and we have added 2 figures.

 

 

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript was significantly improved. Acceptance is recommended.

Author Response

Thank you very much for taking the time to review this manuscript. 

Reviewer 2 Report

Comments and Suggestions for Authors

   The paper "Development of a partial-cluster model of the alloy viscosity" presents useful information about the clustering model of viscosity. The paper is of interest and can be published in Applied Sciences after a few corrections:

 

1. In the abstract (maybe even in the title) there should be a precise reference to the direction of applicability of this work. It is not clearly explained which are the applications where this study brings added value.
2. The introductory chapter treats the problem somewhat superficially. In this chapter, a comprehensive review of the current state of research and the most recent details of this subject should be made. This chapter requires a major revision in order to be able to give the reader all the necessary information. Only some essential aspects such as the influence of temperature on viscosity are not enough to make a clear and comprehensive introduction.
3. The materials and methods chapter and the results chapter express in some detail the study carried out in this work, but in order to truly be a work that lives up to expectations, practical achievements and testing would be useful, based on theoretical models with studies and concrete detailing.

The correlation between theory and practice is an aspect of great importance.

4. In general, the paper presents interesting and interesting aspects, but they are reported somewhat too succinctly in the paper and it does not seem to be an elaborate paper that fully exposes the issues of this study.
5. A re-verification of compliance with the template is necessary, several errors are observed, such as text dimensions, page placement or empty lines.

Overall, the paper presents interesting things but requires major revisions regarding the quality of the content, the way of expression and the detailing of the issues.

Comments on the Quality of English Language

I am not qualified to assess English.

Author Response

Response to Reviewer 2 Comments

 

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

 

Comments 1: In the abstract (maybe even in the title) there should be a precise reference to the direction of applicability of this work. It is not clearly explained which are the applications where this study brings added value.

Response 1: The application of the new partial clustering viscosity model can be utilized across various fields involving fluid dynamics. In our study, the practical implementation of this novel partial clustering viscosity model will ensure the effective execution of metallurgical processes designed using these values at extremely high temperatures, determine optimal operating conditions, and provide more substantiated requirements for metal and alloy production technologies.

This text has been incorporated into the article.

 

Comments 2: The introductory chapter treats the problem somewhat superficially. In this chapter, a comprehensive review of the current state of research and the most recent details of this subject should be made. This chapter requires a major revision in order to be able to give the reader all the necessary information. Only some essential aspects such as the influence of temperature on viscosity are not enough to make a clear and comprehensive introduction.

Response 2: Due to the absence of a comprehensive theory of the liquid state, any new viscosity model, particularly the partially-clustered model, may involve unexpected combinations of parameters that enable a broader understanding of the properties of liquids and matter in general.

In this study, this concept is applied to the activation energy of viscous flow, Е_а (fluidity), derived using the Arrhenius method from available viscosity data and the sum of thermal chaos barriers, Δ_chН, determined based on the distribution (energy spectrum) of Boltzmann. It was found that these two quantities are correlated,   Е_а » Δ_chН, with the activation energy being entirely expended in overcoming the chaos barriers at the liquidus and the alloy component mixing points in the Cu-Al system. This highlights the role of clusters in not only representing the liquid state but also in modeling the solid and gaseous states of matter, thus opening the way for further research in this area.

The following text has been added to the article:

Initial concepts of viscosity were based on the assumption that interlayer frictional forces acted to resist the motion of liquids. A more comprehensive perspective on this property emerged with the recognition of its manifestation even in the stationary state, which directly followed from the Boltzmann distribution for an ideal gas, based on the statistical justification of the energy spectrum of distinguishable particles dispersed throughout the volume. These particles, detectable through beam diagnostic methods, exhibit a discernible variety of energy levels, which can be defined with any arbitrary step of variation.

This marked the beginning of research aimed at establishing correlations between the distribution of energy levels (spectrum) according to the Boltzmann model and various physicochemical properties (more than 60 known properties, including density, electrical conductivity, vaporization, etc.), with viscosity being one of the primary properties investigated.

 

Comments 3: The materials and methods chapter and the results chapter express in some detail the study carried out in this work, but in order to truly be a work that lives up to expectations, practical achievements and testing would be useful, based on theoretical models with studies and concrete detailing.

Response 3: We agree with the reviewer that the relationship between theory and practice is of paramount importance. Therefore, the theoretical derivations of the proposed new model were validated using reliable experimental data obtained by the authors (Tan, M., Xiufang, B., Xianying, X., Yanning, Z., Jing, G., & Baoan, S. Correlation between viscosity of molten Cu-Sn alloys and phase diagram. Physica B, 2007, 387(2), 1-5. doi: 10.1016/j.physb.2005.10.140) and (Ghosh G., Asta M. Phase stability, phase transformations, and elastic properties of Cu₆Sn₅: Ab initio calculations and experimental results. J. Mater. Res. - 2005. - Vol. 20, No 11. - P. 3102-3117).

The following text has been added to the article:

The application of the new partial clustering viscosity model can be employed across various domains of fluid dynamics.

The direct practical application of the partial clustering viscosity model is essential for:

-Developing an optimal melting regime to prevent “freezing” of the melt in the ladle during technological transport;

- Addressing “washout” of furnace linings during overheating;

-Managing emergency situations related to casting speeds in continuous rolling mill lines;

-Understanding lava flow dynamics during volcanic eruptions.

As a result, a fundamental and well-supported finding has been obtained regarding the correlation between the activation energy of fluidity, Е_а, and the sum of the thermal chaos barriers, Δ_chН, during the heating of liquid alloys. This relationship is presented in Table 1 and Figure 1.

 

Comments 4: In general, the paper presents interesting and interesting aspects, but they are reported somewhat too succinctly in the paper and it does not seem to be an elaborate paper that fully exposes the issues of this study.

Response 4: The partial clustering viscosity model is based on the concept of chaotic particles, where three classes of chaotic particles are considered: crystal-mobile, liquid-mobile, and vapor-mobile particles. The equations for these particles are derived from the Boltzmann distribution (spectrum), taking into account only the thermal (kinetic) component. As the temperature increases, the ratio of these three classes of particles changes, and after the melting temperature, the sum of the liquid-mobile and vapor-mobile particles begins to dominate, although crystal-mobile particles continue to exert a significant influence (in the material, these may be fragments of the crystalline lattice).

According to the authors, clusters consist of crystal-mobile particles. Therefore, they do not arise and disappear but are the result of material breakdown during melting.

All the derivations were previously detailed by us between 2004 and 2009, and they have been utilized in the current study as a continuation of the promising direction we established.

 

Comments 5 A re-verification of compliance with the template is necessary, several errors are observed, such as text dimensions, page placement or empty lines.

Response 5: Agreed, corrections made.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Thank you very much for the proper approach to the comments sent, thank you very much for your attention and the changes made to the publication.

kind regards

Author Response

Thank you very much for taking the time to review this manuscript. 

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

As can be seen, the authors took into account the mentions made and even if the work is not exactly at a very high level, they made additional mentions to improve it.

Comments on the Quality of English Language

I am not qualified to assess the correctness of the English language.