Suppression of hollow droplet rebound on super-repellent surfaces

Droplet rebound is ubiquitous on super-repellent surfaces. Conversion between kinetic and surface energies suggests that rebound suppression is unachievable due to negligible energy dissipation. Here, we present an effective approach to suppressing rebounds by incorporating bubbles into droplets, even in super-repellent states. This suppression arises from the counteractive capillary effects within bubble-encapsulated hollow droplets. The capillary flows induced by the deformed inner-bubble surface counterbalance those driven by the outer-droplet surface, resulting in a reduction of the effective take-off momentum. We propose a double-spring system with reduced effective elasticity for hollow droplets, wherein the competing springs offer distinct behavior from the classical single-spring model employed for single-phase droplets. Through experimental, analytical, and numerical validations, we establish a comprehensive and unified understanding of droplet rebound, by which the behavior of single-phase droplets represents the exceptional case of zero bubble volume and can be encompassed within this overarching framework.

In my opinion, the paper is very well written, interesting, and easy to read.The experiments have been carefully conducted with beautiful high-speed movies and the authors make a strong effort in discussing the possible reasons to why hollow drops do not bounce.Below, I list minor comments on how to further improve this work.After these changes, I warmly recommend this paper for publication in Nat.Commun.I believe the aesthetics of the experiments combined with the quite general system of a drop bouncing (or not) off a surface will attract a broad audience.Furthermore, the findings are important for the fluid dynamics and surface science community working on superhydrophobic surfaces, wetting, and drop dynamics.

Minor comments
1. Regarding the surface tension.
• In the Methods section, you mention that the concentration of SDBS was "up to 0.2 wt%".What does "up to" mean?Was the surface tension kept constant in all experiments or was there a big variation in the surface tension in different bouncing experiments?If the concentration is different in different experiments, the exact surface tension values should be mentioned in the captures of all figures and discussed in detail in the Methods section.• Why do you show profiles of drops with different SDBS concentrations in Supp.
Fig. 2b?Did a 0.2 wt% drop not bead up on a superhydrophobic surface?• Was SDBS added also to the SD water drops in the bouncing experiments of the paper?Please specify this in the main text.• Please mention the range of surface tensions used (35-?? mN/m) in the main text (Lines 55-56, p. 3) so that the reader understands that this is significantly below that of water.
2. I cannot easily follow how you reached the expression for  e ∼ ( 0 −  b )/ 0 on Line 157 (p. 7).Since this is an important result in describing why the effective surface tension can be considered much smaller in your system, its derivation would need a more extensive explanation.
3. I assume that the pre-factors C in Eqs. 2, 3 and 4 are not to be considered the same?If this is correct, I would suggest giving these constants different variable names (e.g., A, B, and C or C1, C2 and C3) to avoid confusion.

Reg. Fig 4:
• This is a beautiful graph!Can you please mention in the caption that the dashed line is a fit of the theoretical prediction of Eq. 4. • You write "N indicates the time of droplet rebound.".Do you mean "N indicates the number of droplet rebounds."? 5.In the discussion, you claim that you can "suppress the rebound, without altering the droplet composition or surface properties".However, you do significantly change the surface tension of water by adding the stabilising surfactant (SDBS, see my comment in 1 above).I would recommend rephrasing this sentence.
6.I find the final comparison with compound balloons delightful! 7. A similar system of hollow droplets impacting a solid substrate has been studied before (see papers below).Although these papers report on the spreading dynamics and not rebound inhibition, I think a reference to their work would be appropriate.
• "Hollow droplets impacting onto a solid surface", I. P. The manuscript concerns a study about droplets impacting on superhydrophobic surfaces.In particular, the inclusion of a bubble inside the droplet, as the authors claim, suppresses the rebound phenomenon observed when a droplet impacts on a superhydrophobic surface.The suppression of the rebound is interesting however the study seems premature, in the sense that the analysis is not clear and does not give a picture of what really happens.
For example, the inclusion of the bubbles notably changes the apparent density of the composite droplet.And when the Weber number is used to compare the single and the composite droplet, which density is used to calculate We? Also, in figure 1f the non-rebound is observed when the ratio, liquid/bubble volume, Φ, > 0.4.At this magnitude Φ, the composite system is completely different than the one of the single liquid.I mean that the systems are not comparable.We could mostly term it bubble and not droplet with a small bubble inside it.
The analysis in page 6 is not convincing.The argument that although the energy dissipation is very small but the velocity distribution, in the composite system, is such that rebound is suppressed is not solid.
The importance of using a relatively big bubble inside a droplet suffers from the fact that what suppression is only observed when gravity is present, i.e. in free fall.What happens in the case of a impact in side wall.Then the position of this big bubble could unpredictably change.
Reviewer #3 (Remarks to the Author): The article by Zhou et al. approaches the classical problem of bouncing of water drops on a waterrepellent surface, but with a twist: the drop in this case has a bubble encapsulated within.The authors compare the bouncing dynamics in the two cases to conclude that bubble inclusions may be utilized to trigger suppression of bouncing, without enhancing dissipation.The authors map this effect over Weber numbers varying over three orders of magnitude and supplement their arguments further with numerical simulations.
The work is (mostly) adequate, so is the writing (I also appreciate the video of the balloon).However, the observations in this case are perhaps better suited in a droplet-specific journal.I would just add a couple of remarks, which the authors could consider for their future endeavors with this work.
First, I think it would be wise to plot the actual contact time values, which the authors do not plot anywhere.To compare it with the original plot of Richard et al. which reported the Hertzian nature of the bouncing dynamics for the first time, they could plot the contact time against V for different \phi (the ratio of the bubble to total volume).If dissipation is indeed negligible, as the authors claim, then they should see flat horizontal lines for different \phi and even recover the line of Richard et al.
for \phi = 0. Similarly, the authors should plot the contact time against the radius on a log-log plot to check if the scaling is indeed 3/2.Finally, for the case presented by the authors, as we increase f for a given R0, we decrease the volume of water, yet increase the contact time.This is in sharp contrast to droplets impinging on superhydrophobic macrotextures (like lines or points), where the volume is diminished too (via reorganization) leading to a decrease in contact time Reviewer #4 (Remarks to the Author): The paper presents an experimental study on drop impact on phobic surfaces, showing how the presence of bubbles can promote rebound suppression.
Although the effect is limited to a relatively narrow region of We numbers (see Fig. 4), with the nonrebound to rebound threshold changing from ~0.1 to ~1, the effect appear to be consistent and observed also in other conditions, such as Leidenfrost boiling, as well as other macroscopic systems, such as water balloons.
I also appreciate that the authors have included a simple spring model, based on a two-spring system, that nonetheless seems to reproduce well the experimental data.
I have no comments on the paper, and I recommend its publication.
Reviewer #5 (Remarks to the Author): Non-rebound of hollow droplets on super-repellent surfaces The manuscript reports differences in the impact behavior of a simple and an air-encapsulated hollow droplet on superhydrophobic substrates.
There have been several papers over the last 2-3 years that have reported experimental observations and numerical analysis of impact of hollow droplets on different substrates Please note that this is not the comprehensive list of papers and there are several more.There are no citations to these papers in the manuscript.I am not sure if the authors are aware of these works.
• During impact of a hollow droplet on a substrate, a counterjet forms in addition to the liquid spreading to form a lamella.The authors do not mention the formation of the counterjet at allprobably because the height of impact is very small < 1 cm.In order to validate the model, the authors should explore the impact dynamics of hollow droplets when the height of impact is increased.
• The authors mention that with an increase in the volume fraction of air in the hollow droplet, the retraction velocity increases, and the coefficient of restitution decreases.Can the authors explain the physical significance of this behavior?
• The presence of a bubble increases the initial impact diameter of the bubble.How is the spreading radius defined?
• There is too much reference to the SI -the details of the relation between Weber number and encapsulated air are important and can be included in the main document.
• Line 130 -phrases such as kinetic energy of HD has a high positive value' are confusing and should be modified • Line 150 -how is the inner surface area calculated?Do the authors take into account the distortion of the shape due to refraction at the liquid shell?
• Line 158 -what is effective surface tension?Effective surface tension going to zero can be misleading.
• What is the energy conversion argument?
• In the supplementary video, different surfactant concentrations are reported to be used for different experimental data sets.What is the rationale?Surfactants are supposed to play a major role in the impact dynamics -especially in the case of hollow droplets with multiple air-liquid interfaces.
• The hollow droplet does bounce from the substrate even when the height of impact is 10 mm.Therefore, the title of the paper -'non-rebound of hollow droplets' can be misleading.

Response to the Comments by Reviewer #1
In this article, Zhou et al. reports an intriguing idea for inhibiting drops from bouncing off very liquid-repellent substrates.By including a large air bubble inside a water droplet, its jumping can be strongly suppressed on surfaces that are well-known for their repellent properties.I find this work nicely thought provoking as we often try to make superhydrophobic surfaces as repellent as possible.For example, the scientific discussion is often on how to further reduce the contact time between a bouncing drop and the substrate.Here, Zhou et al. argue for the need of a non-rebound (i.e., "infinite" contact time) yet highly liquid-repellent (i.e., low friction) substrate, since this will improve, e.g., the self-cleaning properties when keeping the impinging water drops on the sample while simultaneously allowing them to easily slide off.The inclusion of an air drop in the water drop is a beautifully simple solution to this problem.
In my opinion, the paper is very well written, interesting, and easy to read.The experiments have been carefully conducted with beautiful high-speed movies and the authors make a strong effort in discussing the possible reasons to why hollow drops do not bounce.Below, I list minor comments on how to further improve this work.After these changes, I warmly recommend this paper for publication in Nat.Commun.I believe the aesthetics of the experiments combined with the quite general system of a drop bouncing (or not) off a surface will attract a broad audience.Furthermore, the findings are important for the fluid dynamics and surface science community working on superhydrophobic surfaces, wetting, and drop dynamics.
Response: We express our gratitude to the referee for his/her recognition of our work and for recommending its publication.We also extend our sincere appreciation for providing us with valuable feedback and comments on our research paper.We have diligently reviewed the comments and have made the necessary revisions to improve the clarity of our work.
Minor comments 1. Regarding the surface tension.
• In the Methods section, you mention that the concentration of SDBS was "up to 0.2 wt%".
What does "up to" mean?Was the surface tension kept constant in all experiments or was there a big variation in the surface tension in different bouncing experiments?If the concentration is different in different experiments, the exact surface tension values should be mentioned in the captures of all figures and discussed in detail in the Methods section.

Response:
We used SDBS solutions with varying concentrations to demonstrate the universal nature of hollow droplet (HD) rebound suppression across liquids with different properties, such as surface tensions.In addition to pure water, we employed three concentrations of SDBS solutions: 0.003 wt%, 0.1 wt%, and 0.2 wt% with surface tensions of 53 mN/m, 43 mN/m, and 35 mN/m, respectively.These experiments also allowed us to validate our theoretical models using data obtained from impact of droplets with different surface tensions.
In response to the referee's comment, we have included the value of the liquid surface tension in the captions of Figures 1 and 2. Furthermore, within the 'Methods' section, we have provided a detailed description of the liquids used (Lines 277-285, Page 12).
• Why do you show profiles of drops with different SDBS concentrations in Supplementary Fig. 2b?Did a 0.2 wt% drop not bead up on a superhydrophobic surface?
Response: Supplementary Figure 2b was utilized to demonstrate that all liquid droplets exhibited a super-repellent state on their corresponding surfaces.Due to the varying surface tensions of the liquids, different solid surfaces were employed in our experiments to achieve the super-repellent state for each specific liquid.For instance, superhydrophobic surfaces were utilized for droplets of pure water and 0.003 wt% SDBS solution, while superamphiphobic surfaces were employed for droplets of 0.2 wt% SDBS solution and n-hexadecane.The low surface tension of the 0.2 wt% SDBS droplets caused them to wet the superhydrophobic surface, preventing them from beading up on the surface.Hence, superamphiphobic surfaces were utilized for 0.2 wt% SDBS droplets.
To address this comment appropriately, we have incorporated a detailed description of the liquids and solid surfaces employed within the 'Methods' section (Lines 277-282, Page 12).
• Was SDBS added also to the SD water drops in the bouncing experiments of the paper?
Please specify this in the main text.
Response: Yes, to ensure a fair comparison in our experiments, the liquid material of both the hollow droplet (HD) and single-phase droplet (SD) was kept consistent.In Figure 1, we presented a comparison of the rebound behavior between the HD and SD formed using a 0.003 wt% SDBS solution with a surface tension of 53 mN/m.To address the mentioned comment, we have explicitly stated this information in Line 65, Page 3 of our revised manuscript.
• Please mention the range of surface tensions used (35-?? mN/m) in the main text (Lines 55-56, p. 3) so that the reader understands that this is significantly below that of water.
Response: Following this this comment, we have clarified the range of surface tension (35-53 mN/m) in Lines 74-75, Page 3.
2. I cannot easily follow how you reached the expression for e ∼ (0 − b)/0 on Line157 (p. 7).Since this is an important result in describing why the effective surface tension can be considered much smaller in your system, its derivation would need a more extensive explanation.

Response:
In response to the referee's comment, we have included a more comprehensive discussion on the derivation of the apparent surface tension (referred to as "effective surface tension" in the original manuscript) in Lines 219-229, Pages 9-10.
It is crucial to acknowledge that the estimation offers a qualitative analogy rather than an analytical solution for the apparent surface tension, γa ~ (1 -Φ 1/3 )γ.The purpose of this estimation was to provide insights into the overall weakening of capillary effects resulting from the presence of an inner bubble within the droplets.
3. I assume that the pre-factors C in Eqs. 2, 3 and 4 are not to be considered the same?If this is correct, I would suggest giving these constants different variable names (e.g., A, B, and C or C1, C2 and C3) to avoid confusion.

Response:
In line with this comment, we have revised the pre-factors C into C1, C2, C3 and C4 in Eqs. ( 1), (2), (3), and (4), respectively.This revision clarifies that these pre-factors have distinct values and should not be considered identical, thus avoiding any potential confusion.

Reg. Fig 4:
• This is a beautiful graph!Can you please mention in the caption that the dashed line is a fit of the theoretical prediction of Eq. 4.
• Response: In agreement with the referee's observation, we acknowledge that SDBS solution was predominantly used in our experiments as we utilized SDBS as a surfactant to stabilize the bubble.However, it is important to note the following points: (1) The suppression of rebound was demonstrated by comparing HDs to SDs with identical mass, liquid material, and surface tension.
(2) This phenomenon was observed for various liquids, including water with different SDBS concentrations and oil (n-hexadecane), indicating its applicability across different droplet compositions.
To address the vague point raised, we created the HD consisting of an air bubble encapsulated in pure water and repeated the impingement experiment.The suppression of rebound was also observed in the pure-water HD without altering the surface tension of water.
We have included a video demonstration in Supplementary Movie 2.

I find the final comparison with compound balloons delightful!
Response: We thank the referee for acknowledging the comparison with compound balloons in our research.Our intention was to employ this analogy as a means to illustrate the concept and facilitate a better understanding of our findings.
7. A similar system of hollow droplets impacting a solid substrate has been studied before (see papers below).Although these papers report on the spreading dynamics and not rebound inhibition, I think a reference to their work would be appropriate.

Response to the Comments by Reviewer #2
The manuscript concerns a study about droplets impacting on superhydrophobic surfaces.In particular, the inclusion of a bubble inside the droplet, as the authors claim, suppresses the rebound phenomenon observed when a droplet impacts on a superhydrophobic surface.The suppression of the rebound is interesting however the study seems premature, in the sense that the analysis is not clear and does not give a picture of what really happens.
Response: We express our gratitude to the referee for providing valuable comments that have significantly contributed to clarifying the vague points in the original manuscript.The feedback has led to substantial improvements in the revised manuscript, allowing for a more detailed and comprehensive understanding of the phenomenon under investigation.We have diligently revised and enhanced the manuscript, incorporating in-depth explanations of theoretical models, conducting new simulations, and conducting additional experiments to address the raised points.These revisions have resulted in a more robust and informative presentation of our research findings.
--For example, the inclusion of the bubbles notably changes the apparent density of the composite droplet.And when the Weber number is used to compare the single and the composite droplet, which density is used to calculate We?
Response: We acknowledge the referee's comment regarding the influence of the inclusion of a bubble on the apparent density of the hollow droplet.Upon careful consideration, we have concluded that utilizing the liquid density, rather than the apparent density, is the most appropriate approach to define the Weber number in our study.To clarify this point, we have included a detailed discussion in the 'Methods' section (Lines 325-335, Page 14).
At this magnitude Φ, the composite system is completely different than the one of the single liquids.I mean that the systems are not comparable.We could mostly term it bubble and not droplet with a small bubble inside it.
Response: We extend our sincere appreciation to the referee for raising this question and providing your perspective.We understand the concern regarding the presence of a bubble and its impact on the fluid system structure.However, we would like to highlight that the comparison between hollow droplets (HDs) and single-phase droplets (SDs) remains relevant and informative based on the following considerations: Firstly, the objective of our study is to investigate the impact behavior of HDs on superrepellent surfaces and the suppression of rebound.It is worth noting that numerous studies in the literature have conducted comparative investigations between HDs and SDs, highlighting the distinct characteristics and behavior of HDs (References 1-4).
Secondly, we have taken meticulous care in controlling the mass, liquid material, and release height of both HDs and SDs to ensure a direct comparison between the two systems.
This careful control ensures that any observed differences can be attributed to the presence of the bubble in HDs.
Lastly, and most importantly, our research primarily focuses on the bouncing behavior of droplets on super-repellent surfaces, a behavior observed for both SDs and HDs upon impact.
The characteristic parameters such as contact time, maximum spreading radius, contact radius, retraction velocity, and restitution coefficient are essential for describing this behavior and can be measured and compared between the two systems.Therefore, in terms of droplet impact and bouncing behavior, the two systems are directly comparable.It is important to note that for the specific case of droplet rebound studied in our research, SDs can be considered as a special instance of HDs with a fully filled core (Φ = 0).
To address the referee's concern and provide a more comprehensive literature review, we have added a paragraph to the revised manuscript in the 'Introduction' section (Lines 44-54, Pages 2-3).This addition will further emphasize the uniqueness of the rebound suppression behavior and enrich the discussion of HDs in our paper.
You write "N indicates the time of droplet rebound.".Do you mean "N indicates the number of droplet rebounds."? Response: In accordance with the referee's comments, we have revised the figure caption in Lines 511-513, Page 26, as follows: "The dashed line presents the theoretical prediction of the boundary between the two regimes, as calculated using Eq.(4) with a fitting prefactor of C4 = 1/7.N indicates the number of droplet rebounds."5.In the discussion, you claim that you can "suppress the rebound, without altering the droplet composition or surface properties".However, you do significantly change the surface tension of water by adding the stabilising surfactant (SDBS, see my comment in 1 above).I would recommend rephrasing this sentence.
(Bird et al.Nature 2013 and Gauthier et al.Nat.Commun.2015).This needs to be discussed -why decreasing volume does not decrease the contact time for the author's case, as one would expect from Quéré's inertia-capillary scaling (Richard et al.Nature 2002).The increase in the contact time could be quantified as a function of \phi to elaborate on this.