Buoyancy Driven Flow with Gas-Liquid Coatings of Peristaltic Bubbly Flow in Elastic Walls
Round 1
Reviewer 1 Report
This work deals with the bubbly flow with peristaltic motion inside elastic walls. The authors used homotopic perturbation method (HPM) to derive analytical results of simplified constructed equations.
Points for possible improvement:
Please, add at section 2 (Mathematical Formulation) a scheme describing the problem (governing equations, initial and boundary conditions, etc) Please, describe the homotopic perturbation method (HPM) It is not clear the derivation of the problem solution (lines 121-128). Did the authors use any software? Please explain in the manuscript or add an appendix. In section 4, the flow of biological fluid in peristaltic motion circulating in human body is investigated. However it is not clear how the above problem is related to coatings. Please explain in full detail how the problem of the flow of biological fluid in peristaltic motion circulating in human body is related to an actual coating process. Please make a patent literature review to clarify that the bubbly flow with peristaltic motion inside elastic walls is an actual coating process. There is not any comparison with experimental data from an actual coating process Please, explain how the model could describe the main features of an actual coatings process.Author Response
We first appreciate this reviewer for his/her time and valuable suggestions.The manuscript is now revised in the light of comments/suggestion made by this reviewer. All changes have been highlighted in the revised paper. Viz a viz comments and responses are as follows:
Reviewer 1:
This work deals with the bubbly flow with peristaltic motion inside elastic walls. The authors used homotopic perturbation method (HPM) to derive analytical results of simplified constructed equations. Points for possible improvement:
Comment # 1: Please, add at section 2 (Mathematical Formulation) a scheme describing the problem (governing equations, initial and boundary conditions, etc)
Response: Agreed and done as suggested.
Comment # 2: Please, describe the homotopyic perturbation method (HPM) It is not clear the derivation of the problem solution (lines 121-128).
Response: Agreed and done. Appropriate references have also been added.
Comment # 3: Did the authors use any software? Please explain in the manuscript or add an appendix.
Response: Yes, software Mathematica 10 is used and has been mentioned in the revised version.
Comment # 4: In section 4, the flow of biological fluid in peristaltic motion circulating in human body is investigated. However it is not clear how the above problem is related to coatings. Please explain in full detail how the problem of the flow of biological fluid in peristaltic motion circulating in human body is related to an actual coating process. Please make a patent literature review to clarify that the bubbly flow with peristaltic motion inside elastic walls is an actual coating process. There is not any comparison with experimental data from an actual coating process Please, explain how the model could describe the main features of an actual coatings process.
Response: Agreed, due weight-age is given to rectify this comment. The bubbles are generated when air trapped and couldn’t escape coating material due to viscosity of the rheological fluid. The presence of bubbles can lead to long-term product reliability issues. It can lead to corrosion of exposed areas and cracked coating due to temperature changes, shock or vibration. So bubbles in coating material are destructive and should be avoided whereas, peristaltic transport is inspired by natural food transport process and is also available in many transport machines. The rise of bubbles and its elimination is the subject of focus in the transport of coating material.
Reviewer 2 Report
In this paper, the authors use the two-fluid model to study gravity-driven bubbly flow with a peristaltic movement of the walls. The research idea fits the topics of the journal, but the paper needs to be strongly improved before it can be considered for the publication. Overall, the paper lacks in (i) depth of the discussion of the results, (ii) literature review in the introduction and the problem formulation needs to be integrated with more details.
Here I have a series of major comments that may help the authors in improving the manuscript:
The authors refer generally to bubbly flow. Do you refer to homogenous dispersed bubbly flow? What bubble diameter are you looking at? Are you proposing a model for bubbly flow or slug flow?
The introduction lacks in literature review. I suggest extending the review on modelling of bubbly flow. The authors can also mention recent advancements in modeling bubbly and dispersed flows in conduits using the two-fluid model. Nowadays, new methods allow to incorporate the dispersed drag between the continuous and the dispersed phase in the two-fluid model accounting for the bubble dimension. One example is the work of Picchi et al. (2015), Experimental Thermal and Fluid Science, 60, 28-34. https://doi.org/10.1016/j.expthermflusci.2014.07.016
The authors study gravity-driven flows. One of the peculiarities of multiphase gravity-driven flows is that multiple steady-state solutions can occur. This means that more configurations are possible at the same volumetric flux. Do you see any multiplicity of steady-state solutions in the problem studied? This topic has been extensively studied in the literature, and I suggest referencing the existence of this issue for bouncy-driven multiphase flows: Suckale et al. (2018), Journal of Fluid Mechanics, 850, 525-550. https://doi.org/10.1017/jfm.2018.382 ; Picchi and Poesio (2016), International Journal of Multiphase Flow, 84, 176-187. https://doi.org/10.1016/j.ijmultiphaseflow.2016.03.002 ; Picchi et al. (2018), International Journal of Multiphase Flow, 99, 111-131. https://doi.org/10.1016/j.ijmultiphaseflow.2017.10.001
Section 2.1. Please add a cartoon with the geometry studied and the reference system of coordinates. Is it a vertical or a horizontal pipe? Why in Eq. 3 and 4, the gravity vector appears both in the equation in the x and the y-direction? What are a,b, c and lambda in Eq. 1? All the variables need to be defined.
Eq.s 8,9,10. Please define all the terms Cam, Ws, Cl, Cw. Please use subscripts in defining the variables, i.e., C_am, …
The definition of the Eotvos number it seems to be not correct. Usually, it is defined using the density difference between the phases and not just one of the densities. What is the length scale in the definition of the Eo number?
What is the definition of the length scale in the definition of Rbe? Please use the subscript in defining the variable.
I suggest adding more details on how Eqs. 2-12 reduced to 15-16.
Page 5, line 117. There is s a typo “,,”.
The solution on page 5-6-7 is too cumbersome. I suggest simplifying the symbols using the subscripts to increase readability and to try to present it more compactly. If it is not possible, please move it to the appendix.
Section 4. More physical insights need to be extracted from the results. In its current form, the discussion is more a parametric study than a critical analysis of the plots. Is the perimetric study motivated by any scaling analysis or a specific application?
I suggest collecting figures using subplots. For example, looking at figures 1-4, the pressure drop is always linear with the total flow rate Q. Why is the effect of all the parameters investigated the same on the curves?
The quality of the figures needs to be improved. In most of the figures, the legend overlaps with the curves.
What is the range of Eotvos number of interest for the problem?
Author Response
We first appreciate this reviewer for his/her time and valuable suggestions.The manuscript is now revised in the light of comments/suggestion made by this reviewer. All changes have been highlighted in the revised paper. Viz a viz comments and responses are as follows:
Reviewer 2: In this paper, the authors use the two-fluid model to study gravity-driven bubbly flow with a peristaltic movement of the walls. The research idea fits the topics of the journal, but the paper needs to be strongly improved before it can be considered for the publication. Overall, the paper lacks in (i) depth of the discussion of the results, (ii) literature review in the introduction and the problem formulation needs to be integrated with more details. Here I have a series of major comments that may help the authors in improving the manuscript:
Comment # 1: The authors refer generally to bubbly flow. Do you refer to homogenous dispersed bubbly flow? What bubble diameter are you looking at? Are you proposing a model for bubbly flow or slug flow?
Response: Yes. The moderate-sized (>4mm) spherical bubbles are homogeneously dispersed in the liquid.
Comment # 2: The introduction lacks in literature review. I suggest extending the review on modelling of bubbly flow. The authors can also mention recent advancements in modeling bubbly and dispersed flows in conduits using the two-fluid model. Nowadays, new methods allow to incorporate the dispersed drag between the continuous and the dispersed phase in the two-fluid model accounting for the bubble dimension.
One example is the work of Picchi et al. (2015), Experimental Thermal and Fluid Science, 60, 28-34. https://doi.org/10.1016/j.expthermflusci.2014.07.016
Response: Agreed, due weightage is given to this comment and we had tried to improve the introduction section as suggested.
Comment # 3: The authors study gravity-driven flows. One of the peculiarities of multiphase gravity-driven flows is that multiple steady-state solutions can occur. This means that more configurations are possible at the same volumetric flux. Do you see any multiplicity of steady-state solutions in the problem studied? This topic has been extensively studied in the literature, and I suggest referencing the existence of this issue for bouncy-driven multiphase flows:
Suckale et al. (2018), Journal of Fluid Mechanics, 850, 525-550. https://doi.org/10.1017/jfm.2018.382 ; Picchi and Poesio (2016), International Journal of Multiphase Flow, 84, 176-187. https://doi.org/10.1016/j.ijmultiphaseflow.2016.03.002 ; Picchi et al. (2018), International Journal of Multiphase Flow, 99, 111-131. https://doi.org/10.1016/j.ijmultiphaseflow.2017.10.001
Response: The most appropriate references have been added, please see [28-30] for the best understanding of readers. In our future studies, we intend to focus on multiplicity of steady-state solutions.
Comment # 4: Section 2.1. Please add a cartoon with the geometry studied and the reference system of coordinates. Is it a vertical or a horizontal pipe? Why in Eq. 3 and 4, the gravity vector appears both in the equation in the x and the y-direction? What are a,b, c and lambda in Eq. 1? All the variables need to be defined.
Response: Agreed and done. The geometry of the problem has been added. Equations are rechecked and typo errors have been removed. All the variables are now defined based on comments.
Comment # 5: Eq.s 8,9,10. Please define all the terms Cam, Ws, Cl, Cw. Please use subscripts in defining the variables, i.e., C_am, …
Response: Agreed and done accordingly.
Comment # 6: The definition of the Eotvos number it seems to be not correct. Usually, it is defined using the density difference between the phases and not just one of the densities. What is the length scale in the definition of the Eo number?
Response: Definition is corrected.
Comment # 7: What is the definition of the length scale in the definition of Rbe? Please use the subscript in defining the variable.
Response: Agreed and done as suggested.
Comment # 8: I suggest adding more details on how Eqs. 2-12 reduced to 15-16.
Response: Agreed and done.
Comment # 9: Page 5, line 117. There is s a typo “,,”.
Response: Agreed and typo error has been removed.
Comment # 10: The solution on page 5-6-7 is too cumbersome. I suggest simplifying the symbols using the subscripts to increase readability and to try to present it more compactly. If it is not possible, please move it to the appendix.
Response: Agreed and done
Comment # 11: Section 4. More physical insights need to be extracted from the results. In its current form, the discussion is more a parametric study than a critical analysis of the plots. Is the perimetric study motivated by any scaling analysis or a specific application?
Response: Agreed and more physics has been added.
Comment # 12: I suggest collecting figures using subplots. For example, looking at figures 1-4, the pressure drop is always linear with the total flow rate Q. Why is the effect of all the parameters investigated the same on the curves?
Response: It can be observed that the effect of key parameters in figures 2 and 3 are quite the opposite. In one case the magnitude of pressure drop is increasing whereas in other case it deceases. Moreover, the behaviour of pressure drop is quantitatively different in all four figures. Furthermore, results of pressure drop are in accordance with the physical expectation because in Newtonian fluid shear stresses are linearly proportional to the rate of deformation.
Comment # 13: The quality of the figures needs to be improved. In most of the figures, the legend overlaps with the curves.
Response: Agreed and we had tried to improve the quality of figures at our level.
Comment # 14: What is the range of Eotvos number of interest for the problem?
Response: As in fluid dynamics the Eötvös number (Eo), also called the Bond number (Bo), is a dimensionless number measuring to characterize the shape of bubbles or drops moving in a surrounding the fluid. A moderate value of Eotvos available in the existing literature is taken as greater than one.
Final remarks: In preparing the revised manuscript, we have done the necessary changes as suggested by this reviewer. Thus, we sincerely hope that the amendments are in order and honorable reviewer will be satisfied with our replies to his/her valuable comments and suggestions.
Round 2
Reviewer 1 Report
congratulations!
Reviewer 2 Report
The authors implemented the modifications requested.
