Growth and Collapse Dynamics of a Vapor Bubble near or at a Wall
Round 1
Reviewer 1 Report
The work is written correctly and has elements of scientific novelty.
Overall, I did not find any significant errors in the article.
I recommend publishing the article in its current form.
Author Response
Answer: Thanks for the reviewer’s comments. We have further improved the manuscript.
Reviewer 2 Report
Increase the font size in figures 2, 3, and 8, they are difficult to read.
You seem to define stage (d) as the period after Rmax where the bubble density continues to decrease [pg. 8, L. 185]. It appears that the bubble density reaches its lowest point just prior to Rmax in the L2 case, and is in fact increasing at the time point of Rmax. The definition of stage (e) [pg. 8, L. 186] is defined as the region after the last inflection point in the bubble density before the bubble reaches it's final collapse point. It seems that stage (d) should be defined with respect to the fact that inflection points in the bubble density exist after the bubble reaches Rmax, not that the bubble density continues to decrease even after the bubble reaches Rmax, which is violated by the L2 case. The description in the conclusion is more accurate.
I appreciate the discussion about the conversion of mechanical energy to thermal, but your discussion of how that relates to cavitation erosion damage is confusing. I don't know if you are trying to say that the impact of the fluid on the wall during collapse leads to the generation of damage, or the conversion of that energy to heat and subsequent re-conversion to fluid / shockwave energy results in damage, or something in between.
The dynamics of the simulated bubble in Fig 11 don't seem to agree very well with the experimentally measured dynamics for a bubble generated under (presumably) equivalent conditions. It's difficult to evaluate the fidelity of the other results presented if the dynamics of the bubble are noticeably not well captured. It might be that the mismatch is a result of the closed-top container used in the experiments vs the open-topped container in the simulations, but if that's the case, why not run simulations in a closed-top container for a more accurate comparison?
Author Response
Question: Increase the font size in figures 2, 3, and 8, they are difficult to read.
Answers: The figures have been revised according to the reviewer’s comments.
Question: You seem to define stage (d) as the period after Rmax where the bubble density continues to decrease [pg. 8, L. 185]. It appears that the bubble density reaches its lowest point just prior to Rmax in the L2 case, and is in fact increasing at the time point of Rmax. The definition of stage (e) [pg. 8, L. 186] is defined as the region after the last inflection point in the bubble density before the bubble reaches it's final collapse point. It seems that stage (d) should be defined with respect to the fact that inflection points in the bubble density exist after the bubble reaches Rmax, not that the bubble density continues to decrease even after the bubble reaches Rmax, which is violated by the L2 case. The description in the conclusion is more accurate.
Answers: The expression in the original text is not clear. It has been revised as:
“From Figure 7, we could clearly observe that the transition time from state (a) to stage (b) as the first inflection point, and transition time from state (b) to stage (c) as the second inflection point. After bubble radius reaches the maximum, there still exists a gap time before the bubble density increases continuously, which we call it stage (d). Stage of (d) pre-collapse is from the point of largest bubble radius to the next minimum value of bubble density.”
Question: I appreciate the discussion about the conversion of mechanical energy to thermal, but your discussion of how that relates to cavitation erosion damage is confusing. I don't know if you are trying to say that the impact of the fluid on the wall during collapse leads to the generation of damage, or the conversion of that energy to heat and subsequent re-conversion to fluid / shockwave energy results in damage, or something in between.
Answers: We think that the fluid pressure and thermal energy increase simultaneously during bubble collapse, and both of them contribute to the cavitation erosion damage on the wall. From Fig. 12, both pw and Tw have an abrupt peak once the bubble finishes collapse. The emergence of Tw peak is even earlier and longer than pw peak. However, researchers pay more attention to erosion by pressure, but less to energy. We believe that with the energy increase, the pressure impact would make worse erosion damage. Of course, more detail is needed for their individual effect, and further quantitative study might be conducted in the future.
Question: The dynamics of the simulated bubble in Fig 11 don't seem to agree very well with the experimentally measured dynamics for a bubble generated under (presumably) equivalent conditions. It's difficult to evaluate the fidelity of the other results presented if the dynamics of the bubble are noticeably not well captured. It might be that the mismatch is a result of the closed-top container used in the experiments vs the open-topped container in the simulations, but if that's the case, why not run simulations in a closed-top container for a more accurate comparison?
Answers: We appreciated with this opinion and might use a closed-top container in the future study for better comparison. Explanation about this comparison has been added into the manuscript as: “Though our simulation and experiment show similar bubble size evolution during growth and collapse, the bubble attachment on the wall is a little bit different. This might be caused by the mismatch of meniscus-covered container used in the experiments vs the open-topped container in our simulations. Such meniscus cover is used to suppress the bubble but difficult to model in simulation. Further validation might be conducted in the future, either with model improvement or more precise experiments.”
Reviewer 3 Report
This study investigates the dynamics of vapor bubble nucleation, growth and collapse after a brief and local deposition of energy (with a laser pulse). The modelling accounts for many effects and notably wall effetcs, compressibility... The manuscript is well-prepared, interesting and a good scientific soundness although I'm not fully aware of the last developments in this field.
103-105 There is no verb in this sentence
105-104 Does Eq. (7) requires the thermodynamic or quasi-static equilibrium?
106 Like in many places, a few references would be welcome for most readers!
Maxwell, has a huge scientist, has provided many references & solutions in many fields... Please tell us more about this relation (text book).
Figure 1.(a) It is not clear to me whether you assume the symmetry of the energy deposition zone.
Something sure and well know, is that the region heated by a
laser is definitively not spherical and homogeneous (energy density). May be you should add some comment about this.
Figure 1.(b) "The snapshot of vapor-filled nanobubble." Nanotubes requires more comments
Figure 2. L128 The results of this figure are not sufficiently discussed "Comparing our SPH numerical results with Eq.14, it shows great agreement as seen in Figure2" means nothing.
You have to give a comment on the dispersion of the numerical data regarding Eq. 14. Is is due to some numerical instabilities or physical oscillations? You give the answer later on in the manuscript but it should be given here (at least you should write something like "oscillations observed in Fig. 2 (b) will be discussed later on)")
134 stage' '(a)
171 - 173 "frequently before the bubble reaches its maximum size, usually decrease, then increase, then decrease again". This sentence is average.
Oscillates or fluctuates is not enough ?
Figure 10 The vectors of the velocity fields are strongly pixillated, too smalls,... Consider the possibility to provide a higher resolution in a supplementary figure? or try to increase the scale of the vectors and reduce their number...
Figure 11.(a) The contrast of "Nguyen experiments" (by Shadowgraphy, or Schlieren Imaging) is much higher than the numerical calculation. Is is a effect of the numerical dispersion, the rough comparison between two "representations": a 2D numerical map of the density and a 3D strioscopic imaging method of the gradients ? By the way, in the perspectives of this work, at least this manuscript, more precise comparisons with experimental data based on advanced optical diagnostics would be welcomed, e.g. [X, XX]. Some of them could estimate the bubble density profile in real time.
[X] F. R. A. Onofri and M. P. L. Sentis, "Light Scattering by Large Bubbles," in Springer Series in Light Scattering: Volume 2: Light Scattering, Radiative Transfer and Remote Sensing, A. Kokhanovsky, ed. (Springer International Publishing, Cham, 2018), pp. 109-149.
[XX] F. R. A. Onofri, M. A. Krzysiek, S. Barbosa, V. Messager, K.-F. Ren, and J. Mroczka, "Near-critical-angle scattering for the characterization of clouds of bubbles: particular effects," Appl. Opt 50, 5759-5769 (2011).
Author Response
Question: 103-105 There is no verb in this sentence
Answers: This sentence have been corrected according to the reviewer’s comments.
Question:105-104 Does Eq. (7) requires the thermodynamic or quasi-static equilibrium?
Answers: Eq. (7) requires local thermodynamic equilibrium.
Question: 106 Like in many places, a few references would be welcome for most readers! Maxwell, has a huge scientist, has provided many references & solutions in many fields... Please tell us more about this relation (text book).
Answers: A reference has been added into the manuscript as:
[31] Greiner, W.; Neise, L.; Horst, Stöcker. Thermodynamics and Statistical Mechanics; D. Rischke: New York, NY, USA, 1995; pp 107-110.
Question: Figure 1.(a) It is not clear to me whether you assume the symmetry of the energy deposition zone. Something sure and well know, is that the region heated by a laser is definitively not spherical and homogeneous (energy density). May be you should add some comment about this.
Answers: The region heated by a laser is spherical and homogeneous in this paper. The non-spherical or inhomogeneous energy density might be discussed in our further study.
Question: Figure 1.(b) "The snapshot of vapor-filled nanobubble." Nanotubes requires more comments
Answers: Here, nanobubble is not clear and we have changed it to laser-induced bubble.
Question: Figure 2. L128 The results of this figure are not sufficiently discussed "Comparing our SPH numerical results with Eq.14, it shows great agreement as seen in Figure2" means nothing.
You have to give a comment on the dispersion of the numerical data regarding Eq. 14. Is is due to some numerical instabilities or physical oscillations? You give the answer later on in the manuscript but it should be given here (at least you should write something like "oscillations observed in Fig. 2 (b) will be discussed later on)")
Answers: Discussion about Figure 2 has been rewritten according to the reviewer’s comments as:
“Our model is based on diffuse interface description of a two-phase liquid–vapor system endowed with thermal fluctuations. After bubble growth, we could observe that the inertial driven bubble oscillates slightly in the confined systems. The average fluid density agrees well with Eq.14 in Figure 2. Gallo et al. have investigated the nucleation of vapor bubbles in stretched or overheated liquids, and found similar phenomenon of bubble oscillation [29].”
[29] Gallo M.; Magaletti F.; Cocco D. Nucleation and growth dynamics of vapor bubbles. Journal of Fluid Mechanics, 2020, 883.
Question:134 stage' '(a)
Answers: This sentence have been corrected according to the reviewer’s comments.
Question:171 - 173 "frequently before the bubble reaches its maximum size, usually decrease, then increase, then decrease again". This sentence is average. Oscillates or fluctuates is not enough ?
Answers: This sentence has been revised according to the reviewer’s comments as: “The vapor, as well as the liquid, is compressible, thus we could capture the oscillation of bubble density during bubble growth and collapse as shown in Figure 7.”
Question：Figure 10 The vectors of the velocity fields are strongly pixillated, too smalls,... Consider the possibility to provide a higher resolution in a supplementary figure? or try to increase the scale of the vectors and reduce their number...
Answers：We appreciated with this opinion and increased the scale of the vectors and reduce their number in Fig.10.
Question: Figure 11.(a) The contrast of "Nguyen experiments" (by Shadowgraphy, or Schlieren Imaging) is much higher than the numerical calculation. Is is a effect of the numerical dispersion, the rough comparison between two "representations": a 2D numerical map of the density and a 3D strioscopic imaging method of the gradients ? By the way, in the perspectives of this work, at least this manuscript, more precise comparisons with experimental data based on advanced optical diagnostics would be welcomed, e.g. [X, XX]. Some of them could estimate the bubble density profile in real time.
[X] F. R. A. Onofri and M. P. L. Sentis, "Light Scattering by Large Bubbles," in Springer Series in Light Scattering: Volume 2: Light Scattering, Radiative Transfer and Remote Sensing, A. Kokhanovsky, ed. (Springer International Publishing, Cham, 2018), pp. 109-149.
[XX] F. R. A. Onofri, M. A. Krzysiek, S. Barbosa, V. Messager, K.-F. Ren, and J. Mroczka, "Near-critical-angle scattering for the characterization of clouds of bubbles: particular effects," Appl. Opt 50, 5759-5769 (2011).
Answers: Thank you very much for your comments and literature recommendation. We have examined carefully about light scattering measurement from these literatures. Shadowgraph could hardly reflect the subtle structure between the bubble and the wall, but near critical angle scattering is announced to be able to observe these small-scale bubble morphologies. However, we have not found a suitable published paper for such application into vapor bubble, and looking forward to more precise picture for further validation in the future.
Reviewer 4 Report
This is a nice paper with some interesting application of SPH to study bubble formation and evolution in a multi-fluid mixture, vapor+liquid.
The paper needs some revisions, such as:
1) The actual SPH description of the implemented model starts at line 112 and ends at line 121. That is absolutely insufficient. Please elaborate much more on your numerical implementation, stating all the relevant details (kernel used, resolution approach, WCSPH-ISPH for the liquid, particle convergence, errors due to non-uniform distribution of particles, diffusion terms, etc.) This is critical.
2) In figure 2, your density field for the liquid is very noisy, so you are not really enforcing incompressibility.
3) Comparison between Figures 3a and 3b is very confusing. Either you have axes on the same scale to allow for a direct evaluation of your findings against those in the literature or you explain much better what's going on in Figure 3b.
4) Overall, one validation case seems weak. The authors are encouraged to choose one more validation case where the physics differs from the one presented and show capabilities and weakness of their proposed method.
Author Response
Question:1) The actual SPH description of the implemented model starts at line 112 and ends at line 121. That is absolutely insufficient. Please elaborate much more on your numerical implementation, stating all the relevant details (kernel used, resolution approach, WCSPH-ISPH for the liquid, particle convergence, errors due to non-uniform distribution of particles, diffusion terms, etc.) This is critical.
Answers: Our research is bases on compressible van der Waals fluid. More details, such as kernel used, resolution approach, particle convergence, errors due to non-uniform distribution of particles, and diffusion terms have been published in our previous paper and omitted here for space limitation. “Further information about this numerical model could be referred in our previous work [32].”
[32] Xiong, H.; Zhang, C.; Yu, Z. Multiphase SPH modeling of water boiling on hydrophilic and hydrophobic surfaces. Int. J. Heat Mass Transf. 2019, 130, 680–692.r
Question:2) In figure 2, your density field for the liquid is very noisy, so you are not really enforcing incompressibility.
Answers: First, we choose van der Waals fluid, the fluid is compressible. Next, our model is based on diffuse interface description of a two-phase liquid–vapor system endowed with thermal fluctuations. After bubble growth, we could observe that the inertial driven bubble oscillates slightly in the confined systems. The average fluid density agrees well with Eq.14 in Figure 2. Gallo et al. have investigated the nucleation of vapor bubbles in stretched or overheated liquids, and found similar phenomenon of bubble oscillation [29].
[29] Gallo M.; Magaletti F.; Cocco D. Nucleation and growth dynamics of vapor bubbles. Journal of Fluid Mechanics, 2020, 883.
Question：3) Comparison between Figures 3a and 3b is very confusing. Either you have axes on the same scale to allow for a direct evaluation of your findings against those in the literature or you explain much better what's going on in Figure 3b.
Answers：Here, we choose van der Waals fluid and use the non-dimensional parameter which is different from the real physical parameters, so it is difficult to compare our results with theirs directly. Here we show the power-law exponent of bubble radius to time in stage (a) to that in stage (c) is 2:1, same ratio with the analytical result of Lee & Merte.
Question: 4) Overall, one validation case seems weak. The authors are encouraged to choose one more validation case where the physics differs from the one presented and show capabilities and weakness of their proposed method.
Answers：We appreciated with this opinion and might find more validation case for better comparison in the future. We added some explanation for the validation of bubble shape: “Though our simulation and experiment show similar bubble size evolution during growth and collapse, the bubble attachment on the wall is a little bit different. This might be caused by the mismatch of meniscus-covered container used in the experiments vs the open-topped container in our simulations. Such meniscus cover is used to suppress the bubble but difficult to model in simulation. Further validation might be conducted in the future, either with model improvement or more precise experiments.”
Round 2
Reviewer 2 Report
Much improved, nice work.
Reviewer 4 Report
The authors did not satisfy my concerns. Below my comments to their answer.
Question:1) The actual SPH description of the implemented model starts at line 112 and ends at line 121. That is absolutely insufficient. Please elaborate much more on your numerical implementation, stating all the relevant details (kernel used, resolution approach, WCSPH-ISPH for the liquid, particle convergence, errors due to non-uniform distribution of particles, diffusion terms, etc.) This is critical.
Answers: Our research is bases on compressible van der Waals fluid. More details, such as kernel used, resolution approach, particle convergence, errors due to non-uniform distribution of particles, and diffusion terms have been published in our previous paper and omitted here for space limitation. “Further information about this numerical model could be referred in our previous work [32].”
[32] Xiong, H.; Zhang, C.; Yu, Z. Multiphase SPH modeling of water boiling on hydrophilic and hydrophobic surfaces. Int. J. Heat Mass Transf. 2019, 130, 680–692.r
New comment by reviewer: The fact that you have previously published work with this formulation doesn't free you from the need to have a stand-alone manuscript here. A sound work should be reproducible, so you have to share more details about your SPH formulation and set-up for others to be able to replicate your simulations.
Question:2) In figure 2, your density field for the liquid is very noisy, so you are not really enforcing incompressibility.
Answers: First, we choose van der Waals fluid, the fluid is compressible. Next, our model is based on diffuse interface description of a two-phase liquid–vapor system endowed with thermal fluctuations. After bubble growth, we could observe that the inertial driven bubble oscillates slightly in the confined systems. The average fluid density agrees well with Eq.14 in Figure 2. Gallo et al. have investigated the nucleation of vapor bubbles in stretched or overheated liquids, and found similar phenomenon of bubble oscillation [29].
[29] Gallo M.; Magaletti F.; Cocco D. Nucleation and growth dynamics of vapor bubbles. Journal of Fluid Mechanics, 2020, 883.
New comment by reviewer: Then you have to thoroughly explain this in the paper.
Question：3) Comparison between Figures 3a and 3b is very confusing. Either you have axes on the same scale to allow for a direct evaluation of your findings against those in the literature or you explain much better what's going on in Figure 3b.
Answers：Here, we choose van der Waals fluid and use the non-dimensional parameter which is different from the real physical parameters, so it is difficult to compare our results with theirs directly. Here we show the power-law exponent of bubble radius to time in stage (a) to that in stage (c) is 2:1, same ratio with the analytical result of Lee & Merte.
New comment by reviewer: the question here is about using same scales in the figure, which is absolutely doable.
Question: 4) Overall, one validation case seems weak. The authors are encouraged to choose one more validation case where the physics differs from the one presented and show capabilities and weakness of their proposed method.
Answers：We appreciated with this opinion and might find more validation case for better comparison in the future. We added some explanation for the validation of bubble shape: “Though our simulation and experiment show similar bubble size evolution during growth and collapse, the bubble attachment on the wall is a little bit different. This might be caused by the mismatch of meniscus-covered container used in the experiments vs the open-topped container in our simulations. Such meniscus cover is used to suppress the bubble but difficult to model in simulation. Further validation might be conducted in the future, either with model improvement or more precise experiments.”
New comment by reviewer: I still think another validation case would make this paper more sound.
Author Response
Question:1) The actual SPH description of the implemented model starts at line 112 and ends at line 121. That is absolutely insufficient. Please elaborate much more on your numerical implementation, stating all the relevant details (kernel used, resolution approach, WCSPH-ISPH for the liquid, particle convergence, errors due to non-uniform distribution of particles, diffusion terms, etc.) This is critical.
Answers: Our research is bases on compressible van der Waals fluid. More details, such as kernel used, resolution approach, particle convergence, errors due to non-uniform distribution of particles, and diffusion terms have been published in our previous paper and omitted here for space limitation. “Further information about this numerical model could be referred in our previous work [32].”
[32] Xiong, H.; Zhang, C.; Yu, Z. Multiphase SPH modeling of water boiling on hydrophilic and hydrophobic surfaces. Int. J. Heat Mass Transf. 2019, 130, 680–692.r
Question: The fact that you have previously published work with this formulation doesn't free you from the need to have a stand-alone manuscript here. A sound work should be reproducible, so you have to share more details about your SPH formulation and set-up for others to be able to replicate your simulations.
Answers: This sentence have been revised according to the reviewer’s comments. We added relevant details about the kernel function [pg.4, L.122], boundary method [pg.4, L.124] and set-up [pg.6, L.154-157].
Question:2) In figure 2, your density field for the liquid is very noisy, so you are not really enforcing incompressibility.
Answers: First, we choose van der Waals fluid, the fluid is compressible. Next, our model is based on diffuse interface description of a two-phase liquid–vapor system endowed with thermal fluctuations. After bubble growth, we could observe that the inertial driven bubble oscillates slightly in the confined systems. The average fluid density agrees well with Eq.14 in Figure 2. Gallo et al. have investigated the nucleation of vapor bubbles in stretched or overheated liquids, and found similar phenomenon of bubble oscillation [29].
[29] Gallo M.; Magaletti F.; Cocco D. Nucleation and growth dynamics of vapor bubbles. Journal of Fluid Mechanics, 2020, 883.
Question: Then you have to thoroughly explain this in the paper.
Answers: The relevant explanation has been added in the article [pg.4, L.132-136].
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Question：3) Comparison between Figures 3a and 3b is very confusing. Either you have axes on the same scale to allow for a direct evaluation of your findings against those in the literature or you explain much better what's going on in Figure 3b.
Answers：Here, we choose van der Waals fluid and use the non-dimensional parameter which is different from the real physical parameters, so it is difficult to compare our results with theirs directly. Here we show the power-law exponent of bubble radius to time in stage (a) to that in stage (c) is 2:1, same ratio with the analytical result of Lee & Merte.
Question: the question here is about using same scales in the figure, which is absolutely doable.
Answers: The figures Figure 3 have been revised according to the reviewer’s comments.
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Question: I still think another validation case would make this paper more sound.
Answers: We agree well with the reviewer's opinion. Here we have used three validation cases: first is the analytical solution of bubble density distribution, second is the ratio of radius curve slope at two typical growth stages of (a) and (c), the last one is the experimental bubble shape at wall. The former two cases have fairly good agreement. The third one has shown our capability of properly predicting the bubble volume during whole stages of growth and collapse. The only difference is the bubble attachment on the wall. But this part is really too difficult to improve. We have tried our best to find proper experimental case for validation. This is the best what we could find. Reason is that vapor bubble has small time scale and need high resolution to capture it. From the aspect of numerical modeling, we believe that our current SPH modeling could reveal fundamental physics mechanism for vapor bubble. But adding a meniscus cover over the liquid is a really hard mission, where a model of non-Newtonian fluids might be needed. We plan to add it in, but it would be another research work in the future.
Round 3
Reviewer 4 Report
OK
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
