Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Contactless rheology of finite-size air-water interfaces

Vincent Bertin1,2,*, Zaicheng Zhang1,*, Rodolphe Boisgard1, Christine Grauby-Heywang1, Elie Raphaël2, Thomas Salez1,3,†, and Abdelhamid Maali1,‡

  • 1Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33405 Talence, France
  • 2UMR CNRS Gulliver 7083, ESPCI Paris, PSL Research University, 75005 Paris, France
  • 3Global Station for Soft Matter, Global Institution for Collaborative Research and Education, Hokkaido University, Sapporo, Hokkaido 060-0808, Japan

  • *These authors contributed equally to this paper.
  • †thomas.salez@u-bordeaux.fr
  • ‡abdelhamid.maali@u-bordeaux.fr

Phys. Rev. Research 3, L032007 – Published 8 July, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L032007

Abstract

We present contactless atomic force microscopy measurements of the hydrodynamic interactions between an oscillating sphere and a bubble in water at the microscale. The size of the bubble is found to have a significant effect on the response due to the long-range capillary deformation of the air-water interface. To rationalize the experimental data, we develop a viscocapillary lubrication model accounting for the finite-size effect. The comparison between experiments and theory allows us to measure the air-water surface tension, without contact and with the volume of liquid down to tens of microliters, paving the way toward robust contactless tensiometry of polluted air-water interfaces.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (57)

  1. P.-G. De Gennes, F. Brochard-Wyart, and D. Quéré, Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves (Springer Science & Business Media, New York, 2013).
  2. A. Marchand, J. H. Weijs, J. H. Snoeijer, and B. Andreotti, Why is surface tension a force parallel to the interface? Am. J. Phys. 79, 999 (2011).
  3. P.-G. De Gennes, Wetting: statics and dynamics, Rev. Mod. Phys. 57, 827 (1985).
  4. D. Bonn, J. Eggers, J. Indekeu, J. Meunier, and E. Rolley, Wetting and spreading, Rev. Mod. Phys. 81, 739 (2009).
  5. A. Oron, S. H. Davis, and S. G. Bankoff, Long-scale evolution of thin liquid films, Rev. Mod. Phys. 69, 931 (1997).
  6. R. V. Craster and O. K. Matar, Dynamics and stability of thin liquid films, Rev. Mod. Phys. 81, 1131 (2009).
  7. D. Langevin, Rheology of adsorbed surfactant monolayers at fluid surfaces, Annu. Rev. Fluid Mech. 46, 47 (2014).
  8. J. D. Berry, M. J. Neeson, R. R. Dagastine, D. Y. Chan, and R. F. Tabor, Measurement of surface and interfacial tension using pendant drop tensiometry, J. Colloid Interface Sci. 454, 226 (2015).
  9. J. Drelich, C. Fang, and C. White, Measurement of interfacial tension in fluid-fluid systems, in Encyclopedia of Surface and Colloid Science, edited by A. T. Hubbard (Marcel Dekker, Inc., New York, 2002), pp. 3152–3166.
  10. G. L. Gaines, Insoluble Monolayers at Liquid-gas Interfaces (Interscience, New York, 1966).
  11. S. Reynaert, C. F. Brooks, P. Moldenaers, J. Vermant, and G. G. Fuller, Analysis of the magnetic rod interfacial stress rheometer, J. Rheol. 52, 261 (2008).
  12. D. K. Schwartz, C. M. Knobler, and R. Bruinsma, Direct Observation of Langmuir Monolayer Flow Through a Channel, Phys. Rev. Lett. 73, 2841 (1994).
  13. R. Miller, V. B. Fainerman, J. Krägel, and G. Loglio, Surface rheology of adsorbed surfactants and proteins, Curr. Opin. Colloid Interface Sci. 2, 578 (1997).
  14. P. Erni, P. Fischer, E. J. Windhab, V. Kusnezov, H. Stettin, and J. Läuger, Stress- and strain-controlled measurements of interfacial shear viscosity and viscoelasticity at liquid/liquid and gas/liquid interfaces, Rev. Sci. Instrum. 74, 4916 (2003).
  15. F. Ortega, H. Ritacco, and R. G. Rubio, Interfacial microrheology: particle tracking and related techniques, Curr. Opin. Colloid Interface Sci. 15, 237 (2010).
  16. J. R. Samaniuk and J. Vermant, Micro and macrorheology at fluid-fluid interfaces, Soft matter 10, 7023 (2014).
  17. M. H. Lee, C. P. Lapointe, D. H. Reich, K. J. Stebe, and R. L. Leheny, Interfacial hydrodynamic drag on nanowires embedded in thin oil films and protein layers, Langmuir 25, 7976 (2009).
  18. V. Bergeron and D. Langevin, Monolayer Spreading of Polydimethylsiloxane Oil on Surfactant Solutions, Phys. Rev. Lett. 76, 3152 (1996).
  19. A. Yeung, T. Dabros, and J. Masliyah, Dissipative interfaces and departures from the young- laplace equation, Langmuir 13, 6597 (1997).
  20. M. Leser, S. Acquistapace, A. Cagna, A. Makievski, and R. Miller, Limits of oscillation frequencies in drop and bubble shape tensiometry, Colloids Surf., A 261, 25 (2005).
  21. F. Ravera, G. Loglio, and V. I. Kovalchuk, Interfacial dilational rheology by oscillating bubble/drop methods, Curr. Opin. Colloid Interface Sci. 15, 217 (2010).
  22. A. Yeung and L. Zhang, Shear effects in interfacial rheology and their implications on oscillating pendant drop experiments, Langmuir 22, 693 (2006).
  23. D. Langevin et al., Light Scattering by Liquid Surfaces and Complementary Techniques (Dekker, New York, 1992).
  24. J. C. Earnshaw, Surface light scattering: a methodological review, Appl. Opt. 36, 7583 (1997).
  25. R. Miller, J. K. Ferri, A. Javadi, J. Krägel, N. Mucic, and R. Wüstneck, Rheology of interfacial layers, Colloid Polym. Sci. 288, 937 (2010).
  26. A. Shmyrov, A. Mizev, A. Shmyrova, and I. Mizeva, Capillary wave method: An alternative approach to wave excitation and to wave profile reconstruction, Phys. Fluids 31, 012101 (2019).
  27. F. Monroy and D. Langevin, Direct Experimental Observation of the Crossover from Capillary to Elastic Surface Waves on Soft Gels, Phys. Rev. Lett. 81, 3167 (1998).
  28. I. U. Vakarelski, J. Lee, R. R. Dagastine, D. Y. Chan, G. W. Stevens, and F. Grieser, Bubble colloidal afm probes formed from ultrasonically generated bubbles, Langmuir 24, 603 (2008).
  29. I. U. Vakarelski, R. Manica, X. Tang, S. J. O'Shea, G. W. Stevens, F. Grieser, R. R. Dagastine, and D. Y. Chan, Dynamic interactions between microbubbles in water, Proc. Natl. Acad. Sci. (USA) 107, 11177 (2010).
  30. R. R. Dagastine, R. Manica, S. L. Carnie, D. Chan, G. W. Stevens, and F. Grieser, Dynamic forces between two deformable oil droplets in water, Science 313, 210 (2006).
  31. D. Y. Chan, E. Klaseboer, and R. Manica, Film drainage and coalescence between deformable drops and bubbles, Soft Matter 7, 2235 (2011).
  32. R. F. Tabor, F. Grieser, R. R. Dagastine, and D. Y. Chan, Measurement and analysis of forces in bubble and droplet systems using afm, J. Colloid Interface Sci. 371, 1 (2012).
  33. S. Ecke, M. Preuss, and H.-J. Butt, Microsphere tensiometry to measure advancing and receding contact angles on individual particles, J. Adhes. Sci. Technol. 13, 1181 (1999).
  34. X. Xiong, S. Guo, Z. Xu, P. Sheng, and P. Tong, Development of an atomic-force-microscope-based hanging-fiber rheometer for interfacial microrheology, Phys. Rev. E 80, 061604 (2009).
  35. M. Delmas, M. Monthioux, and T. Ondarçuhu, Contact Angle Hysteresis at the Nanometer Scale, Phys. Rev. Lett. 106, 136102 (2011).
  36. S. Guo, M. Gao, X. Xiong, Y. J. Wang, X. Wang, P. Sheng, and P. Tong, Direct Measurement of Friction of a Fluctuating Contact Line, Phys. Rev. Lett. 111, 026101 (2013).
  37. J. Dupré de Baubigny, M. Benzaquen, L. Fabié, M. Delmas, J.-P. Aimé, M. Legros, and T. Ondarçuhu, Shape and effective spring constant of liquid interfaces probed at the nanometer scale: Finite size effects, Langmuir 31, 9790 (2015).
  38. C. Mortagne, K. Lippera, P. Tordjeman, M. Benzaquen, and T. Ondarçuhu, Dynamics of anchored oscillating nanomenisci, Phys. Rev. Fluids 2, 102201(R) (2017).
  39. O. Manor, I. U. Vakarelski, G. W. Stevens, F. Grieser, R. R. Dagastine, and D. Y. Chan, Dynamic forces between bubbles and surfaces and hydrodynamic boundary conditions, Langmuir 24, 11533 (2008).
  40. A. Maali, R. Boisgard, H. Chraibi, Z. Zhang, H. Kellay, and A. Würger, Viscoelastic Drag Forces and Crossover from No-Slip to Slip Boundary Conditions for Flow Near Air-Water Interfaces, Phys. Rev. Lett. 118, 084501 (2017).
  41. Y. Wang, B. Zeng, H. T. Alem, Z. Zhang, E. Charlaix, and A. Maali, Viscocapillary response of gas bubbles probed by thermal noise atomic force measurement, Langmuir 34, 1371 (2018).
  42. A. Steinberger, C. Cottin-Bizonne, P. Kleimann, and E. Charlaix, High friction on a bubble mattress, Nat. Mater. 6, 665 (2007).
  43. S. Leroy and E. Charlaix, Hydrodynamic interactions for the measurement of thin film elastic properties, J. Fluid Mech. 674, 389 (2011).
  44. S. Leroy, A. Steinberger, C. Cottin-Bizonne, F. Restagno, L. Léger, and É. Charlaix, Hydrodynamic Interaction Between a Spherical Particle and an Elastic Surface: A Gentle Probe for Soft Thin Films, Phys. Rev. Lett. 108, 264501 (2012).
  45. R. Villey, E. Martinot, C. Cottin-Bizonne, M. Phaner-Goutorbe, L. Léger, F. Restagno, and E. Charlaix, Effect of Surface Elasticity on the Rheology of Nanometric Liquids, Phys. Rev. Lett. 111, 215701 (2013).
  46. D. Guan, C. Barraud, E. Charlaix, and P. Tong, Noncontact viscoelastic measurement of polymer thin films in a liquid medium using long-needle atomic force microscopy, Langmuir 33, 1385 (2017).
  47. D. Guan, E. Charlaix, R. Z. Qi, and P. Tong, Noncontact Viscoelastic Imaging of Living Cells Using a Long-Needle Atomic Force Microscope with Dual-Frequency Modulation, Phys. Rev. Appl. 8, 044010 (2017).
  48. Z. Zhang, V. Bertin, M. Arshad, E. Raphaël, T. Salez, and A. Maali, Direct Measurement of the Elastohydrodynamic Lift Force at the Nanoscale, Phys. Rev. Lett. 124, 054502 (2020).
  49. A. Maali and R. Boisgard, Precise damping and stiffness extraction in acoustic driven cantilever in liquid, J. Appl. Phys. 114, 144302 (2013).
  50. O. Reynolds, IV. On the theory of lubrication and its application to Mr. Beauchamp tower's experiments, including an experimental determination of the viscosity of olive oil, Philos. Trans. R. Soc. London 177, 157 (1886).
  51. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L032007 for further technical details on the theoretical model and experiments.
  52. V. S. Craig and C. Neto, In situ calibration of colloid probe cantilevers in force microscopy: hydrodynamic drag on a sphere approaching a wall, Langmuir 17, 6018 (2001).
  53. J. M. Skotheim and L. Mahadevan, Soft lubrication: The elastohydrodynamics of nonconforming and conforming contacts, Phys. Fluids 17, 092101 (2005).
  54. B. Saintyves, T. Jules, T. Salez, and L. Mahadevan, Self-sustained lift and low friction via soft lubrication, Proc. Natl. Acad. Sci. (USA) 113, 5847 (2016).
  55. Y. Moroi, K. Motomura, and R. Matuura, The critical micelle concentration of sodium dodecyl sulfate-bivalent metal dodecyl sulfate mixtures in aqueous solutions, J. Colloid Interface Sci. 46, 111 (1974).
  56. E. Fuguet, C. Ràfols, M. Rosés, and E. Bosch, Critical micelle concentration of surfactants in aqueous buffered and unbuffered systems, Anal. Chim. Acta 548, 95 (2005).
  57. K. Joshi and J. F. Gilchrist, Effect of added surfactant on convective assembly of monosized microspheres, Appl. Phys. Lett. 116, 083702 (2020).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation