Review Reports - Dilational Rheology of Fluid/Fluid Interfaces: Foundations and Tools

Round 1

Reviewer 1 Report

REVIEW REPORT:

This is a nice paper that compiles and explains the theory on rheology of interfaces. The paper may be published, since it will be of interest to many research scientists in this area. My comments are listed below, but I have two major points that I would like the authors to address. The first point: I recommend the authors to expand their explanations on the theories (for example see points 4,5) - this is because I expect this paper to be used as a reference by many people and it would prove useful to them if the definitions and explanations are provided in detail. The second point: since this is a review paper, it must include a comprehensive list of references, and should cite recent works on the topic and related applications. Some examples include the application of interfacial rheology in bubble dynamics and droplet dynamics (Zhong et al, A model for bubble dynamics in a protein solution in Journal of Fluid Mechanics, Vol. 935, 2022 and Chen et al, Phase-dependent surfactant transport on the microscale: interfacial tension and droplet coalescence, Langmuir, 36(49), 2020). Including a range of references will make this paper more rigid and thorough. For example, the text by Gade, titled “Marine Surface Films - Chemical Characteristics, Influence on Air-Sea Interactions and Remote Sensing” is a classic collection of many notable works on the effects of interfacial processes on wave motion.

1. Please provide a comprehensive list of all areas where interfacial rheology can play a role. I understand that you have sort of spread out the information across several pages, but a comprehensive list upfront - may be in the form of a table in Section 1 (along with necessary references for reading up on the specific applications) would make the reader more interested in your work, and get you more readers.

2. Figure 1 is first mentioned at the end of p.1, whereas it is placed in p.3. I would recommend moving figure 1 to p.2.

3. The paper is missing some important citations to some classic works, such as: Manikantan, H.; Squires, T. M. Surfactant Dynamics: Hidden Variables Controlling Fluid Flows. Journal of Fluid Mechanics, 2020, 892, 1−115.

4. Please provide more information in lines 100 to 102, where you talk about the restorations by interfacial tension gradients. Specifically, please provide some background on how these gradients are produced, and how they restore the deformations. May be just explain it here, rather than in line 132, where you talk about Marangoni stresses.

5. I would recommend giving more information in line 111 - what is the coupling that you are referring to here? And, what do the real and imaginary components of the viscoelastic moduli represent?

6. Somewhere around Eq. (2), I would recommend citing the classic papers such as the one by Stone and Leal, The effects of surfactants on drop deformation and breakup, Published in JFM (1990). This is because this paper clearly explains the meaning of the surface gradient operator, and the physical significance of the Scriven model.

7. Line 161: Please provide some information on J, the dilation compliance, for the benefit of rookies in this field. I noticed later that it is explained briefly in line 376. But maybe add a pointer in line 161.

8. I guess it would be good to include a small explanation on “diffusivity” in lines 175-176.

9. I am curious to know what can be the typical values of the complex modulus, E, defined in Eq. (8,9). Maybe it would be good to include a small table with some numbers for E corresponding to different types of interfaces, so that readers can get to know the typical order of magnitude of the complex E.

10. Figure 2 looks little out of focus in its present state. Could you please improve the clarity, and make is sharp?

11. In Section 4.1.1.d (lines 339-350), the authors talk about measuring the interfacial properties through wave damping. There it would be appropriate to cite the following: Characterization of capillary waves: A review and a new optical method, published in the Physics of Fluids by Slavchov et al Vol 33(10), 101303 (2021); and Damping rate measurements and predictions for gravity waves in an air–oil–water system, published in Physics of Fluids by Rajan et al - Vol 34(2), 022113 (2022); Using Faraday Waves to Measure Interfacial Tension, published by au et al in Langmuir 2020, 36, 21, 5872–5879 2020; Effects of surfactants on Faraday-wave dynamics, published by Henderson in Journal of Fluid Mechanics, 365(12), pp. 89-107, 1998; A study of wheat storage protein monolayers by Faraday wave damping published by Henderson et al in Langmuir, 7(11), p.2731, 1991; The dynamics of waves at the interface between a viscoelastic coating and a fluid flow by Duncan et al in Journal of Fluid mechanics, Vol 158, 1985; and other relevant references available in these papers.

12. With respect to wave damping, can the authors comment on how things might change if the interface is not sharp, and happens to be a thick region, rather than monomolecular? A review of related literature in this are might be useful. For example, see “wave damping by a thin layer of viscous fluid” published by Jenkins et al in Physics of Fluids, 1997, and other related papers in this area.

13. Lines 347-349, when you talk about the longitudinal waves, it is perhaps appropriate to cite the following works: A laboratory study of longitudinal waves in surfactant films in a water wave tank published in JGR: Oceans by Duncan et al in 2007; and Dissipation of interfacial marangoni waves and their resonance with capillary-gravity waves, published in International Journal of Engineering Science by Rajan et al - Vol. 154 (2020). Another paper by same group, solutions of a comprehensive dispersion relation for waves at the elastic interface of two viscous fluids, published in European Journal of Mechanics, Vol. 89, 2021, for a fluid-fluid interface, highlights the limiting cases considering both transverse and longitudinal waves. Also see the paper, Attenuation of monochromatic surface waves due to the presence of an inextensible cover published by Sutherland et al in Wave Motion, 68, pp.88-96, 2017, which analyses wave damping for large values of elasticities. The results are in tune with Eq (23), the dispersion relation for surface waves, which shows how the interfacial parameters (tension and elasticity) affect wave motion.

14. Additional works that may be cited in Section 4.1 include: Damping of surface waves due to crude oil/oil emulsion films on water, by Ermakov et al in Marine Pollution Bulletin 146, 206–214 (2019); Resonance damping of gravity-capillary waves on the water surface covered with a surface-active film, by Ermakov in Izvestiya Atmospheric and Oceanic Physics. 39(5), 624–628 (2003); and Laboratory study of the damping of parametric ripples due to surfactant films, by Ermakov in Marine Surface Films (Springer, 2006), pp. 113–128; Resonance damping of gravity-capillary waves on the water surface covered with a surface-active film of finite thickness: A reappraisal, by Ermakov in Physics of Fluids, Vol. 34(9), 2022.

15. In Section 4.2, please cite some seminal works such as The Marangoni wave in ripples on an air-water interface covered by a spreading film by Lombardini et al in IL Nuovo Cimento C, Vol. 5(2), p. 256, in 1982; On the vibration modes of the air-water interface in the presence of surface films by Ghia et al in IL Nuovo Cimento C, Vol. 11(4), p. 305, in 1988; Ripple damping on water surface covered by a spreading film: Theory and experiment by Lombardini et al in IL Nuovo Cimento C, Vol. 8(4), p. 491, in 1985.

16. In section 4.2, I would recommend expanding the description of the difference between soluble and insoluble films by including a discussion on the diffusion coefficient D. What kind of values for D would one expect to see for a soluble film?’

17. In many places, the authors talk about the elasticity and concentration relation, see for example in Equation (6). Is this valid for all concentrations? What happens at critical micelle concentration (CMC)?

18. Could the authors comment on the effects of hysteresis on the measurement of interfacial properties? The book by Stephan Abbot on Surfactant Science deals with isotherms, and interfacial property measurements. Maybe it is a good book to cite here.

19. Some papers that comment on the role of interfacial dynamics on remote sensing applications are as follows: (i) Gade, Byfield, Ermakov, Lavrova, Mitnik, Slicks as indicators for marine processes, In: Oceanography. 26, 2, 2012 (ii) Ermakov, S. A., Sergievskaya, I. A., da Silva, J. C., Kapustin, I. A., Shomina, O. V., Kupaev, A. V., and Molkov, A. A., “Remote sensing of organic films on the water surface using dual co-polarized ship-based X-/C-/S-band radar and TerraSAR-X,” Remote Sensing 10, 1097 (2018).

Author Response

We have extended the text following the recommendation of the reviewer.

Please provide a comprehensive list of all areas where interfacial rheology can play a role. I understand that you have sort of spread out the information across several pages, but a comprehensive list upfront - may be in the form of a table in Section 1 (along with necessary references for reading up on the specific applications) would make the reader more interested in your work, and get you more readers.

We have added the information required by the reviewer in Section 1.

Figure 1 is first mentioned at the end of p.1, whereas it is placed in p.3. I would recommend moving figure 1 to p.2.

We thank to the reviewer for the comment. The reference to Figure 1 at the end of p.1 should not be included in the manuscript, we have removed it from the revised text.

The paper is missing some important citations to some classic works, such as: Manikantan, H.; Squires, T. M. Surfactant Dynamics: Hidden Variables Controlling Fluid Flows. Journal of Fluid Mechanics, 2020, 892, 1−115.

We have included the recommended reference.

Please provide more information in lines 100 to 102, where you talk about the restorations by interfacial tension gradients. Specifically, please provide some background on how these gradients are produced, and how they restore the deformations. May be just explain it here, rather than in line 132, where you talk about Marangoni stresses.

Following the reviewer comment, we have provided additional information in the text.

I would recommend giving more information in line 111 - what is the coupling that you are referring to here? And, what do the real and imaginary components of the viscoelastic moduli represent?

We have included the explanation required by the reviewer.

Somewhere around Eq. (2), I would recommend citing the classic papers such as the one by Stone and Leal, The effects of surfactants on drop deformation and breakup, Published in JFM (1990). This is because this paper clearly explains the meaning of the surface gradient operator, and the physical significance of the Scriven model.

Following the reviewer recommendation, we have included the reference in the text.

Line 161: Please provide some information on J, the dilation compliance, for the benefit of rookies in this field. I noticed later that it is explained briefly in line 376. But maybe add a pointer in line 161.

In Line 161 and equation 4, there were errors that now have been corrected. Mechanical compliance should not be included in this point. We have corrected.

I guess it would be good to include a small explanation on “diffusivity” in lines 175-176.

We have included a brief discussion about the diffusivity.

I am curious to know what can be the typical values of the complex modulus, E, defined in Eq. (8,9). Maybe it would be good to include a small table with some numbers for E corresponding to different types of interfaces, so that readers can get to know the typical order of magnitude of the complex E.

The broad range of interfaces existing makes a very difficult tasks to summarize some characteristics values. Moreover, they depend strongly on the conditions, and the probed frequency. Therefore, we consider that it is not possible to introduce the table suggested by the reviewer.

Figure 2 looks little out of focus in its present state. Could you please improve the clarity, and make is sharp?

We have improved the quality of Figure 2.

In Section 4.1.1.d (lines 339-350), the authors talk about measuring the interfacial properties through wave damping. There it would be appropriate to cite the following: Characterization of capillary waves: A review and a new optical method, published in the Physics of Fluids by Slavchov et al Vol 33(10), 101303 (2021); and Damping rate measurements and predictions for gravity waves in an air–oil–water system, published in Physics of Fluids by Rajan et al - Vol 34(2), 022113 (2022); Using Faraday Waves to Measure Interfacial Tension, published by au et al in Langmuir 2020, 36, 21, 5872–5879 2020; Effects of surfactants on Faraday-wave dynamics, published by Henderson in Journal of Fluid Mechanics, 365(12), pp. 89-107, 1998; A study of wheat storage protein monolayers by Faraday wave damping published by Henderson et al in Langmuir, 7(11), p.2731, 1991; The dynamics of waves at the interface between a viscoelastic coating and a fluid flow by Duncan et al in Journal of Fluid mechanics, Vol 158, 1985; and other relevant references available in these papers.

Following the reviewer recommendation, we have included the cited references and some additional one. Moreover, we have included brief text discussing some aspects of the recommended works.

With respect to wave damping, can the authors comment on how things might change if the interface is not sharp, and happens to be a thick region, rather than monomolecular? A review of related literature in this are might be useful. For example, see “wave damping by a thin layer of viscous fluid” published by Jenkins et al in Physics of Fluids, 1997, and other related papers in this area.

The point raised by the reviewer is very interesting. However, it exceeds the interfacial aspects, and hence we have preferred to avoid the discussion of this specific case in our discussion. However, we have mentioned it in the revised text, including the mentioned reference and some additional one.

Lines 347-349, when you talk about the longitudinal waves, it is perhaps appropriate to cite the following works: A laboratory study of longitudinal waves in surfactant films in a water wave tank published in JGR: Oceans by Duncan et al in 2007; and Dissipation of interfacial marangoni waves and their resonance with capillary-gravity waves, published in International Journal of Engineering Science by Rajan et al - Vol. 154 (2020). Another paper by same group, solutions of a comprehensive dispersion relation for waves at the elastic interface of two viscous fluids, published in European Journal of Mechanics, Vol. 89, 2021, for a fluid-fluid interface, highlights the limiting cases considering both transverse and longitudinal waves. Also see the paper, Attenuation of monochromatic surface waves due to the presence of an inextensible cover published by Sutherland et al in Wave Motion, 68, pp.88-96, 2017, which analyses wave damping for large values of elasticities. The results are in tune with Eq (23), the dispersion relation for surface waves, which shows how the interfacial parameters (tension and elasticity) affect wave motion.

We have included the references

Additional works that may be cited in Section 4.1 include: Damping of surface waves due to crude oil/oil emulsion films on water, by Ermakov et al in Marine Pollution Bulletin 146, 206–214 (2019); Resonance damping of gravity-capillary waves on the water surface covered with a surface-active film, by Ermakov in Izvestiya Atmospheric and Oceanic Physics. 39(5), 624–628 (2003); and Laboratory study of the damping of parametric ripples due to surfactant films, by Ermakov in Marine Surface Films (Springer, 2006), pp. 113–128; Resonance damping of gravity-capillary waves on the water surface covered with a surface-active film of finite thickness: A reappraisal, by Ermakov in Physics of Fluids, Vol. 34(9), 2022.

We have introduced the references cited for the reviewer.

In Section 4.2, please cite some seminal works such as The Marangoni wave in ripples on an air-water interface covered by a spreading film by Lombardini et al in IL Nuovo Cimento C, Vol. 5(2), p. 256, in 1982; On the vibration modes of the air-water interface in the presence of surface films by Ghia et al in IL Nuovo Cimento C, Vol. 11(4), p. 305, in 1988; Ripple damping on water surface covered by a spreading film: Theory and experiment by Lombardini et al in IL Nuovo Cimento C, Vol. 8(4), p. 491, in 1985.

We have introduced the mentioned references in the revised text.

In section 4.2, I would recommend expanding the description of the difference between soluble and insoluble films by including a discussion on the diffusion coefficient D. What kind of values for D would one expect to see for a soluble film?’

We have included some additional points in the text. However, in relation to the values of D, it is impossible to provide a summary of the most relevant values of D because there are many types of systems studies until now in the literature which makes impossible to define characteristic values.

In many places, the authors talk about the elasticity and concentration relation, see for example in Equation (6). Is this valid for all concentrations? What happens at critical micelle concentration (CMC)?

The point raised by the reviewer is interesting but soluble surfactant where the CMC can be defined are only one possible system, and therefore we have preferred to avoid the discussion of specific aspects.

Could the authors comment on the effects of hysteresis on the measurement of interfacial properties? The book by Stephan Abbot on Surfactant Science deals with isotherms, and interfacial property measurements. Maybe it is a good book to cite here.

Hysteresis is not considered because the presence of hysteresis in the evaluation of the rheological properties will destroy all the formalism exploited in the study of the rheological response of fluid/fluid interfaces. Moreover, the presence of hysteresis is avoided for experiments within the linear regime.

Some papers that comment on the role of interfacial dynamics on remote sensing applications are as follows: (i) Gade, Byfield, Ermakov, Lavrova, Mitnik, Slicks as indicators for marine processes, In: Oceanography. 26, 2, 2012 (ii) Ermakov, S. A., Sergievskaya, I. A., da Silva, J. C., Kapustin, I. A., Shomina, O. V., Kupaev, A. V., and Molkov, A. A., “Remote sensing of organic films on the water surface using dual co-polarized ship-based X-/C-/S-band radar and TerraSAR-X,” Remote Sensing 10, 1097 (2018).

We have included the references suggested by the reviewer-

We thank to the reviewers for his/her useful comments, they were very useful for improving the quality of our work.

Reviewer 2 Report

This article provides an updated perspective on the study of the response of fluid/fluid interfaces against dilational stresses. Both available theoretical and experimental strategies for evaluating the dilational properties of fluid/fluid interfaces are overviewed. The chosen subject is of interest from both fundamental and practical points of view. In my opinion, the paper is scientifically sound, provides relevant information, and is clearly well written. I believe it should be published as is.

Author Response

#Reviewer 2

We thank to the reviewer for his/her nice consideration in relation to our paper.

Round 2

Reviewer 1 Report

I do not have any further comments.