Mathematical Models for Removal of Pharmaceutical Pollutants in Rehabilitated Treatment Plants

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In the paper under review, the author deals with optimization in the p-Laplacian problem, which arises in modelling cleaning processes, focusing on mathematical aspects such as well-posedness of corresponding boundary value problems. I think that the obtained results can have some interest for the readership of the journal "Mathematics" (MDPI). However, I have the following concerns:
1) The novelty of the work should be justified. Although the author provides a quite large reference list (37 elements), she makes a deficiency effort to align its work with existing research.  The author should point out what are the principal difficulties in the considered setup and what differences in the applied methods.
2) The volume of the results of this paper is not enough to publish a new separate publication. The work should be extended. In particular, numerical examples and figures illustrating the results of the work would be desirable.
3) The neatness of the article's presentation requires improvement. For example, the formula (2.4) contains misprints. 
4) It is necessary to more clearly distinguish between the new results obtained by the author and the results known from the literature.
5) The section "Сonclusions" section is short and rather poor. The author should respond to the question: “What do the results of the paper mean for the topical area and applications?” It is important to provide interpretation of the obtained results as well as explicitly point out aims for future investigations of problems under consideration.
Conclusion:
Only when the above-mentioned flaws have been corrected, this article can be considered for acceptance in Mathematics.

Author Response

Comments 1: The novelty of the work should be justified. Although the author provides a quite large reference list (37 elements), she makes a deficiency effort to align its work with existing research. The author should point out what are the principal difficulties in the considered setup and what differences in the applied methods. 

Response 1:  The novelty has been highlighted in the red parts of the Sections 1 and 5. New explanations have been added to mark the differences between my contributions and other cited works.

Comments 2: The volume of the results of this paper is not enough to publish a new separate publication. The work should be extended. In particular, numerical examples and figures illustrating the results of the work would be desirable.

Response 2: I made an effective extension of the paper by presenting the entire way from data collected at some rehabilitated cleaning plants until the CFD application; moreover I highlighted the novelty as consisting in the application of a number of ten abstract results in solving the real problems issued from our models.

Comments 3: The neatness of the article's presentation requires improvement. For example, the formula (2.4) contains misprints.

Response 3: In the relation (2.4) a problem due to the last version of math type appeared. I solved it. For others, I think that now they are revised.

Comments 4: It is necessary to more clearly distinguish between the new results obtained by the author and the results known from the literature.

Response 4: I followed the reviewer recommendations and I hope that now the paper gains more clarity especially with the aid of "red parts".

Comments 5: The section "Сonclusions" section is short and rather poor. The author should respond to the question: “What do the results of the paper mean for the topical area and applications?” It is important to provide interpretation of the obtained results as well as explicitly point out aims for future investigations of problems under consideration.

Response 5. I consider this remark as being the most important and consequently I improved the conclusions section by completing it with the most relevant findings of the study.

In the paper, all the changes have been operated in red.

Please, find some other considerations bellow.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Report on “Mathematical Models for Removal of Pharmaceutical Pollutants in Rehabilitated Treatment Plants” by Irina Meghea, submitted for a possible publication in Mathematics.

In this paper, the author considered a mathematical model involved with an optimization problem related to pharmaceutical contaminants removal. More precisely, Navier-Stokes problem under described parameters has been considered.  Then some properties were investigated using standard methodologies and techniques.

The paper is interesting, however Major revision is needed associated with second round of review.

1/ There are many grammatical issues needed to be fixed for a clear reading.

2/ Update the Abstract: some phrases have no senses, such as,

In our previous recent works has been reported that a possibility for removal from water sources of this type of micropollutants is to rehabilitate the existing cleaning plants by introducing efficient techniques such as adsorption on granulated active carbon filters, micro-, nano- or ultrafiltration.

3/ The Introduction section also should be modified, in particular, present clearly the Advantages, Motivation and Scientific Contribution  of this work with respect to the existing literature.

4/ Check the bounds of integrals in (2.4).

5/ The Introduced PDEs, including Navier-Stokes Equation, should have formulated weak solutions via test function in appropriate spaces.

6/ the regularity of solution for “Navier-Stokes Equation” stills an open problem since many decades ago, so what’s your opinion here?

7/ There are much Propositions (1--10)! Referenced to [35] or [36] without indicating their use in the main results. This will decrease the value of work, try to update.

8/ Reference [36] is citing everywhere! This increase the similarities and doesn’t justify the required originality. Try to update.  

 

 

Comments on the Quality of English Language

Can be improved.

Author Response

Comments 1: There are many grammatical issues needed to be fixed for a clear reading.

Response 1: The manuscript has been carefully corrected.

Comments 2: Update the Abstract: some phrases have no senses, such as,

In our previous recent works has been reported that a possibility for removal from water sources of this type of micropollutants is to rehabilitate the existing cleaning plants by introducing efficient techniques such as adsorption on granulated active carbon filters, micro-, nano- or ultrafiltration.

Response 2: This text has been rephrased as was suggested. It is marked in red.

Comments 3: The Introduction section also should be modified, in particular, present clearly the Advantages, Motivation and Scientific Contribution  of this work with respect to the existing literature.

Response 3: These requests have been achieved in Introduction section in red.

Comments 4: Check the bounds of integrals in (2.4).

Response 4: Related to the formula (2.4), it was a problem of math type, which I solved by using an older version.

Comments 5: The Introduced PDEs, including Navier-Stokes Equation, should have formulated weak solutions via test function in appropriate spaces.

Response 5: Weak solutions were considered in Sobolev spaces, not in distributions.

Comments 6: The regularity of solution for “Navier-Stokes Equation” stills an open problem since many decades ago, so what’s your opinion here?

Response 6: Starting from their particular form given by the concrete data of the considered real problem, we will answer when we this part of the research completed in another work.

Comments 7: There are much Propositions (1--10)! Referenced to [35] or [36] without indicating their use in the main results. This will decrease the value of work, try to update.

Response 7: The abstract results from papers [35] and [36] which are now, under a new counting of references [54] and [55], may be used in the characterization of the solution of the Dirichlet problem. Only the statements have been taken here. The rest of the citations from [35], renamed [54], was done to avoid the repetition of some definitions and explanations. The aim of these abstract results has been clarified in the paper at the conclusion red parts.

Comments 8: Reference [36] is citing everywhere! This increase the similarities and doesn’t justify the required originality. Try to update.

Response 8: I think that it was reference [35] which is now [54]. This is cited in order to not repeat some definitions and other clarifications.

The modifications have been marked everywhere in red.

Please, find some other responses attached bellow.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Unfortunately, the submitted article does not contain new results. It is noteworthy that after each substantial statement, the author indicates the references [54] or [55], i.e. the work has a rather descriptive type. The contribution of the article is insufficient for a separate publication. Therefore, I cannot recommend the acceptance of this manuscript.

Author Response

Comments 1: Unfortunately, the submitted article does not contain new results. It is noteworthy that after each substantial statement, the author indicates the references [54] or [55], i.e. the work has a rather descriptive type. The contribution of the article is insufficient for a separate publication. Therefore, I cannot recommend the acceptance of this manuscript.

Response 1: The novelty of this work lies, first of all, in the application of certain models and methods in the study of pharmaceutical pollutants removal from water sources. Secondly, the work outlines all the aspects of an approach to modeling these complex processes. The use of variational or surjectivity results mentioned in solving certain problems formulated in the work justifies their completion, starting from concrete data, numerical modeling, visualization, and validation of the model, thus indicating a significant volume of future work.

All the references are relevant to the content of the manuscript. The most of them have been placed in the Introduction section to highlight the setting of the problem, its actuality and the novelty of the approach that I proposed in this paper.
I highlighted the new revisions in green.
I responded to reviewer no. 1 to his unique remark by presenting to him my opinion and how I understood the novelty of this work.
There was only one recommended reference which is indeed in the field of the article, and it was another general recommendation to improve the References section that I considered reasonable since recent papers were missing, then I updated the literature state of the art with 15 newer papers.
Regarding the suggestions of additional experiments and figures, they are not complying with the paper structure and aim.

Reviewer 2 Report

Comments and Suggestions for Authors

All my comments have been addressed. Hence, I suggest to accept the paper for publication.

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

The author has not made any significant changes to the manuscript. There are no new results in the work. Therefore, unfortunately, I cannot recommend this article for publication in Mathematics.