Interactions between gas–liquid mass transfer and bubble behaviours

Interactions between gas–liquid mass transfer and bubble behaviours were investigated to improve the understanding of the relationship between the two sides. The CO2/N2-water system was applied to study the bubble behaviours based on the volume-of-fluid (VOF) model. The mass transfer conditions were taken into consideration when the fluid field was analysed. The bubble behaviours were compared with and without mass transfer. The results show that the absolute slopes of the curves for mass fraction inside the single rising bubbles, with diameters from 3 to 6 mm, decrease from 0.09325 to 0.02818. It means that small single bubbles have higher mass transfer efficiency. The daughter bubbles of cutting behaviour and initial side-by-side bubbles of coalescence behaviour also perform better than the initial large bubbles and coalesced bubbles, respectively. The bubble behaviours affect the mass transfer process. However, the latter also reacts upon the former. The critical intervals between the side-by-side bubbles decrease from 2.0 to 0.9 mm when the bubble diameter changes from 3 to 7 mm. For the coalescence behaviour without mass transfer, the critical intervals are larger because there is no influence of concentration around the bubbles on the bubble motion. The coalescence of cut daughter bubbles is also influenced by the concentration. It was suggested that the interaction between the gas–liquid mass transfer and bubble behaviours cannot be ignored.

considered during the bubble rising, why? Show the force analysis. (3) Did the paper [32] and [33] consider "Interactions between gas-liquid mass transfer and bubble behaviors"? If not, how can you use their data for validation? If it is, what are the differences between your researches and theirs? Show more details about the two references. 4. Results and discussion: (1) you said "Bubbles with initial diameters of 4 mm, 5 mm, and 6 mm were investigated when they were cut by a wire." So add modeling information about the wire.
(2) Only show the modeling result is not enough, try to show the mechanism and explain why the process occurs. For example, you say "To further study the influence of mass transfer on bubble motions, the rising process of 5 mm bubble was investigated (see Fig. 12). The white lines are axel wires. When there is no mass transfer happened, the bubble rises vertically at the very start and then it deviates from the axel wire. As a result, the bubble is cut into two unequal-diameter daughter bubbles. While as for the bubble with mass transfer, it rises along the axel wire and then is cut into two equal-diameter daughter bubbles. The comparison shows that the mass transfer cannot be ignored when studying the bubble behaviors." So, why that happen? 5. Discussion and conclusions did not clearly focus on your subject," Interactions between gasliquid mass transfer and bubble behaviors". In your discussion section please link your modeling results with a broader and deeper literature review, and explain how the mass transfer influence the bubble behaviors. 6. The English should be polished for publish. In general, I recommend this manuscript "major revision".
Decision letter (RSOS-190136.R0) 12-Mar-2019 Dear Dr Chen: Title: Interactions between gas-liquid mass transfer and bubble behaviors Manuscript ID: RSOS-190136 Thank you for your submission to Royal Society Open Science. The chemistry content of Royal Society Open Science is published in collaboration with the Royal Society of Chemistry.
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Reviewer: 2
Comments to the Author(s) Comments to RSOS-190136 MS TITLE: Interactions between gas-liquid mass transfer and bubble behaviors In this manuscript, the interactions between gas-liquid mass transfer and bubble behaviors (bubble breakup and coalescence) were studied with the support of VOF numerical modeling. Overall, it makes good sense for assessing the mass transfer efficiency for bubbling system and the transport of gas bubble in liquid phase. This manuscript demonstrates well the methodology and clear objectives. However, the grammar and English used to write the manuscript needs to be double checked for errors. There are some occasions when the sentences are not clearly understood by the reader. 1. Abstract: Please provide more quantitative information of the results. Show us how the interactions between gas-liquid mass transfer and bubble behaviors happen, not only the general description. 2. Introduction: Do not just "list" the references, try to summarize and clearly show the state-ofthe-art in this field. 3. Model setup: (1) Reorganize this part, try to follow the procedure: concept model, hypothesis, numerical model (include main equations, the initial and boundary condition), geometry and solving method, parameters for model building and data for validation. (2) Only buoyancy is considered during the bubble rising, why? Show the force analysis. (3) Did the paper [32] and [33] consider "Interactions between gas-liquid mass transfer and bubble behaviors"? If not, how can you use their data for validation? If it is, what are the differences between your researches and theirs? Show more details about the two references. 4. Results and discussion: (1) you said "Bubbles with initial diameters of 4 mm, 5 mm, and 6 mm were investigated when they were cut by a wire." So add modeling information about the wire.
(2) Only show the modeling result is not enough, try to show the mechanism and explain why the process occurs. For example, you say "To further study the influence of mass transfer on bubble motions, the rising process of 5 mm bubble was investigated (see Fig. 12). The white lines are axel wires. When there is no mass transfer happened, the bubble rises vertically at the very start and then it deviates from the axel wire. As a result, the bubble is cut into two unequal-diameter daughter bubbles. While as for the bubble with mass transfer, it rises along the axel wire and then is cut into two equal-diameter daughter bubbles. The comparison shows that the mass transfer cannot be ignored when studying the bubble behaviors." So, why that happen? 5. Discussion and conclusions did not clearly focus on your subject," Interactions between gasliquid mass transfer and bubble behaviors". In your discussion section please link your modeling results with a broader and deeper literature review, and explain how the mass transfer influence the bubble behaviors. 6. The English should be polished for publish. In general, I recommend this manuscript "major revision".

Appendix A
The coalescence and cutting behavior of bubbles and mass transfer were investigated numerically. It can be published after a major revision.
1. How to control the quantity of gas from inner gas to gas-liquid interface, similarly to the mass transfer rate of CO2 form interface to liquid? 2. Eq. 8, how to obtain Ngas-int and Nint-liq?
3. Letters in fig. 3 are too little to present clearly.
4. The serial number of table should be rewritten in text. For example, Table 2 in page 9 line 25 should be Table 3.
5. The mass of CO2 bubble with diameter 2 mm is about 7.5 × 10 -9 kg. However, the dissolved CO2 from bubble with diameter 2 mm into liquid is about 10 -6 kg at 0.5 s in fig. 8. It is impossible. It is the same to other bubbles.
6. In fig. 9, please check the order of magnitude. 7. Page 13, lines 44-50, "For 3 mm bubbles with mass transfer, the ratio of 0.67 is 86.1% and 4.15 times higher than that for 5 mm bubbles and 7 mm bubbles, respectively." It is incomprehensible. In addition, the critical interval is 2.0 mm for 3 mm bubbles, and 1.8 mm and 0.9 mm for 5 mm and 7 mm bubbles, respectively. Therefore, smaller side-by-side bubbles are more difficult to coalesce. 8. Page 14, line 7, "the 3 mm side-by-side bubbles rise on negative direction initially…" what does "negative direction" mean? 9. Nomenclature, "S" is not mentioned in text.

Responses to the Comments of Reviewer 1 General Comment
The coalescence and cutting behavior of bubbles and mass transfer were investigated numerically. It can be published after a major revision.

Response:
We greatly appreciate your positive comments.
Comment 1: How to control the quantity of gas from inner gas to gas-liquid interface, similarly to the mass transfer rate of CO 2 form interface to liquid?
Response: Thank you a lot for your suggestion. In the simulation, the quantity of gas from inner gas to gas-liquid interface and the mass transfer rate of CO 2 from interface to liquid are not controlled. Based on the mass transfer mechanism, the continuous mass flux through the interface means that there is no mass accumulation. Hence, the quantity of CO 2 in the gas phase of the meshes belong to the interface was transferred to the liquid phase completely. As for the mass transfer processes in the gas phase and liquid phase, they are related to the fluid flow and species diffusion.

Comment 2: Eq. 8, how to obtain N gas-int and N int-liq ?
Response: Thank you for your advice. The mass transfer processes in the gas phase and liquid phase are related to the species diffusion and fluid flow. The N gas-int which represents the mass flux from gas to interface can be determined by the following equation. , int , The N int-liq which represents the mass flux from interface to liquid can be determined by Eq.R2. , int , There is no mass accumulation at the interface. Hence, the Eq.8 in the manuscript was revised as follow: (Please see the highlighted parts in Paragraph 4 Page 4 in the revised manuscript) Comment 3: Letters in fig. 3 are too little to present clearly.
Response: Thank you for your suggestion. The letters in Fig.3 of the original manuscript (Fig.4 in the revised manuscript) have been enlarged and they can be read clearly. (Please see the highlighted parts in Page 6 in the revised manuscript) 135:76-88). In 2D simulations, only x and y (or x and z, y and z, etc) coordinates were used. The third coordinate was set as 1 automatically which is related to the unit system. In the simulation of this study, the unit system is set as SI unit so that the length unit is meter. When calculate the dissolved CO 2 in water, volume is needed so that the deviation occurred. The size of computational domain is in the magnitude of "mm" while the third coordinate is in the magnitude of "m". Therefore, the deviation of 10 3 exists. The order of magnitude for the relevant contents in the manuscript was corrected.
Comment 6: In fig. 9, please check the order of magnitude.
Response: Thank you for your suggestion. The order of the magnitude in the manuscript has been checked and revised. Response: Thank you for your suggestion. The "S" in the nomenclature has been deleted.

In this manuscript, the interactions between gas-liquid mass transfer and bubble behaviors
(bubble breakup and coalescence) were studied with the support of VOF numerical modeling.
Overall, it makes good sense for assessing the mass transfer efficiency for bubbling system and the transport of gas bubble in liquid phase.
This manuscript demonstrates well the methodology and clear objectives. However, the grammar and English used to write the manuscript needs to be double checked for errors. There are some occasions when the sentences are not clearly understood by the reader.

Response:
We greatly appreciate your encouraging and positive comments.

Comment 1: Abstract: Please provide more quantitative information of the results. Show us how the interactions between gas-liquid mass transfer and bubble behaviors happen, not only the general description.
Response: Thank you for your instructive advice. The abstract is revised and more quantitative information of the results is provided. The revision could reflect the interaction between gas-liquid mass transfer and bubble behavior. The contents are shown as follow.
The results show that the absolute slopes of the curves for mass fraction inside the single rising bubbles with the diameters from 3 mm to 6 mm decreases from 0.09325 to 0.02818. It means that small single bubbles have higher mass transfer efficiency. The daughter bubbles of cutting behavior and initial side-by-side bubbles of coalescence behavior also perform better than the initial large bubbles and coalesced bubbles, respectively. The bubble behaviors effect the mass transfer process. However, the latter also reacts upon the former. The critical intervals between the side-by-side bubbles decreases from 2.0 mm to 0.9 mm when the bubble diameter changes from 3 mm to 7 mm. For the coalescence behavior without mass transfer, the critical intervals are larger because there is no influence of concentration around the bubbles on the bubble motion.

The coalescence of cut daughter bubbles is also influenced by the concentration. It was suggested that the interaction between the gas-liquid mass transfer and bubble behaviors cannot be ignored
in the future studies.
(Please see the highlighted parts in the "Abstract" of Page 1 in the revised manuscript) (Please see the highlighted parts in the "Introduction" of Page 1 in the revised manuscript) Response: Thank you for your insightful suggestions.
(1) The "Model setup" was reorganized as you suggested. Please see the relevant section.
(2) The initial bubbles are driven by buoyancy but there is also gravity force acts on the bubbles.
The force analysis was added in the revised manuscript as follow.
The buoyancy force and gravity force act on the bubble during the whole rising process (see figure 3). The total force can be calculated by Eq.9. More details about the two references were added as follow.
In (1) The modeling information about the wire was revised in the "Geometry and Solution methods" section as follow. (Please see the highlighted parts in Paragraph 1 Page 5 in the revised manuscript) (2) The concentration distribution could reflect the influence of the mass transfer on bubble motion. Huang and Saito (Chemical Engineering Science, 2017, 157:182-199) verified the influence through analyzing the rising path under different conditions in the experiments. In this paper, the differences between the behaviors with and without mass transfer processes can also be analyzed by the concentration distribution. The added contents are shown as follow. For the more detailed information about the mechanism, quantitative data of simulation and experiments need to be obtained and the analysis method also needs to be developed. This is a great research direction and we will try our best to conduct a thorough study in the future works.
Thanks again for your instructive suggestion. Response: Thank you for your suggestion. The English has been polished. The grammar and spelling errors have been revised. Some of the revisions are shown as follow.

Interactions between gas-liquid mass transfer and bubble behaviors were investigated to
improve the understanding of the relationship between the two sides. (Please see the highlighted parts in "Abstract" of Page 1 in the revised manuscript) The above studies are of great guiding significance to the coalescence and breakup behaviors, but the influences of the behaviors on mass transfer have not been investigated and the interaction between them is also rarely investigated.