Start-Up Multilayer Electro-Osmotic Flow of Maxwell Fluids through an Annular Microchannel under Hydrodynamic Slip Conditions
, Clara G. Hernández 1, Juan P. Escandón 1,*, Juan R. Gómez 1 and René O. Vargas 1Round 1
Reviewer 1 Report
In the article under review, the authors investigate the transient multilayer electroosmotic flow through an annular microchannel with hydrophobic walls. The Maxwell-type rheological model is used. In the problem, the linearized Poisson-Boltzmann and Cauchy momentum equations are used to determine the electric potential distribution and the flow field, respectively. Different interfacial phenomena are studied. The semi-analytic solution is based on the Laplace transform theory. The authors state that their research aims to predict the parallel flow behavior in microfluidic devices under electroosmotic effects.
In general, the present work will be interesting and useful for specialists in the field of hydrodynamics and other applications. But I have some concerns.
1. The authors use the linearized rheological equation of Maxwell-type (see formula (5)) replacing an objective derivative with the time derivative. Why is such linearization legitimate? I have some doubts related to this issue. Indeed, for example, the used rheological model does not satisfy the well-known principle of material objectivity.
2. The authors should explicitly indicate a general formula for the slip boundary condition since there exist many various slip conditions. It is unclear from what basic slip principles the formula (16) arises. Maybe, Navier's slippage? The authors should clarify this point.
3. Some related studies on slip problems for non-Newtonian fluids are missed in the current manuscript, for example,
https://doi.org/10.1016/j.aej.2023.06.074
https://doi.org/10.1155/2016/9428128
https://doi.org/10.3934/cpaa.2019036
By these and other works the introduction section can be enriched since one show diversity approaches to statement of slip problem for flow models.
4. The authors should clearly emphasize the strengths of their study and physical limitations of modeling.
Conclusion:
I recommend a major revision and the next round of the review.
Author Response
Responses to reviewer 1 have been attached in a pdf file
Author Response File: 
Author Response.pdf
Reviewer 2 Report
1- It would be useful to add to the manuscript information about real liquids that correspond to the model of Maxwell Fluids presented in the work;
methods of wall treatment that create slip conditions.
2. - It is necessary to clearly formulate all the initial conditions from which the transition process starts.
3. - What is the importance of velocity versus time graphs (Figs. 5-9). From a technological point of view, the simple (stationary) flow is more preferable. Therefore, an important parameter of the problem is the duration of the transition process, (the time of transition to a stationary flow). It would be interesting to see the dependence of this parameter on other parameters of the problem: ζI,O, ε¯n, κ¯n, Γ, η¯n.
4. - The manuscript does not specify the value of \eta_{ref}, which makes impossible to estimate the times of transients in dimensional units (for example, in seconds).
5. - Page11. There is no space in the unit kgm^{-1} s^{-1}.
Author Response
Responses to reviewer 2 have been attached in a pdf file
Author Response File: Author Response.pdf
Reviewer 3 Report
The paper is a good read. The methodology is sufficiently explained and validated. I only have a few comments:
Increase the front of numbers on the axis of each figure
Use legends in the figures for each graph.
Mention the prominent numerical finding in the Conclusion.
No comments
Author Response
Responses to reviewer 3 have been attached in a pdf file
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
I am satisfied with the responses of the authors to my comments from the first review. The manuscript is improved. The points that were initially unclear are now clear. I congratulate the authors for obtaining new important results.
The paper can be recommended for publication in Mathematics in the current form.
Reviewer 2 Report
The authors have made corrections to the manuscript in accordance with comments and suggestions, it can be published
