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Instability and symmetry breaking of surfactant films over an air bubble

Published online by Cambridge University Press:  09 December 2022

Xingyi Shi Open the ORCID record for Xingyi Shi [Opens in a new window] ,
Gerald G. Fuller  and
Eric S.G. Shaqfeh
Xingyi Shi
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
Gerald G. Fuller
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
Eric S.G. Shaqfeh*
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: esgs@stanford.edu
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Abstract

We examine the asymmetric flows of aqueous surfactant films over an air bubble. A thin film is formed by raising an equilibrated air bubble through an aqueous solution of Triton X-100 (0.01 mM, below critical micelle concentration). Due to the advection generated by the squeezing motion, the initially uniformly distributed surfactants redistribute and, thus, generate an axisymmetric surface tension gradient that drives a Marangoni flow. The external forcing of raising the bubble also creates an axisymmetric dimpled film with a radial thickness variation that reaches its minimum at the rim of the dimple. The curvature in the film thickness generates an axisymmetric capillary pressure driven flow. When the apex of the bubble has penetrated the initially flat air-solution interface, the rising bubble is stopped and the resulting flow demonstrates symmetry breaking both in the experiment and in the parameter matched numerical simulation. Linear stability analysis reveals the mechanism behind the disturbance growth. It is found that the most dangerous azimuthal wavenumber scales linearly with the ratio of the rim radius to the radial width of significant radial pressure and surface tension gradients after stopping the bubble. Finally, we compare this instability to the previously studied surfactant spreading induced fingering phenomenon (Warner, Craster & Matar, Phys. Fluids, vol. 16, issue 8, 2004, pp. 2933–2951).

JFM classification

Low-Reynolds-number flows: Lubrication theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 953 , 25 December 2022 , A26
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Atasi, O., Legendre, D., Haut, B., Zenit, R. & Scheid, B. 2020 Lifetime of surface bubbles in surfactant solutions. Langmuir 36 (27), 7749–7764.CrossRefGoogle ScholarPubMed
Balay, S., et al. 2019 PETSc users manual. http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdfGoogle Scholar
Barakat, J.M. 2018 Microhydrodynamics of vesicles in channel flow. PhD thesis. Stanford University.Google Scholar
Bhamla, M.S., Chai, C., Alvarez-Valenzuela, M., Tajuelo, J. & Fuller, G.G. 2017 Interfacial mechanisms for stability of surfactant-laden films. PLoS One 12 (5), e0175753.CrossRefGoogle ScholarPubMed
Borkowski, M., Kosior, D. & Zawala, J. 2020 Effect of initial adsorption coverage and dynamic adsorption layer formation at bubble surface in stability of single foam films. Colloids Surf. (A) 589, 124446.CrossRefGoogle Scholar
Champougny, L., Roché, M., Drenckhan, W. & Rio, E. 2016 Life and death of not so “bare” bubbles. Soft Matt. 12 (24), 5276–5284.CrossRefGoogle ScholarPubMed
Chang, C. & Franses, E.I. 1995 Adsorption dynamics of surfactants at the air/water interface: a critical review of mathematical models, data, and mechanisms. Colloids Surf. (A) 100, 1–45.CrossRefGoogle Scholar
Chatzigiannakis, E., Jaensson, N. & Vermant, J. 2021 Thin liquid films: where hydrodynamics, capillarity, surface stresses, and intermolecular forces meet. Curr. Opin. Colloid Interface Sci. 53, 101441.CrossRefGoogle Scholar
Cunliffe, M., Engel, A., Frka, S., Gašparović, B., Guitart, C., Murrell, J.C., Salter, M., Stolle, C., Upstill-Goddard, R. & Wurl, O. 2013 Sea surface microlayers: a unified physicochemical and biological perspective of the air–ocean interface. Prog. Oceanogr. 109, 104–116.CrossRefGoogle Scholar
Dave, D. & Ghaly, A.E. 2011 Remediation technologies for marine oil spills: a critical review and comparative analysis. Am. J. Environ. Sci. 7 (5), 423–440.CrossRefGoogle Scholar
Frostad, J.M., Tammaro, D., Santollani, L., de Araujo, S.B. & Fuller, G.G. 2016 Dynamic fluid-film interferometry as a predictor of bulk foam properties. Soft Matt. 12 (46), 9266–9279.CrossRefGoogle ScholarPubMed
Gros, A., Bussonnière, A., Nath, S. & Cantat, I. 2021 Marginal regeneration in a horizontal film: instability growth law in the nonlinear regime. Phys. Rev. Fluids 6 (2), 024004.CrossRefGoogle Scholar
Hellgren, A., Weissenborn, P. & Holmberg, K. 1999 Surfactants in water-borne paints. Prog. Org. Coat. 35 (1–4), 79–87.CrossRefGoogle Scholar
Hermans, E., Bhamla, M.S., Kao, P., Fuller, G.G. & Vermant, J. 2015 Lung surfactants and different contributions to thin film stability. Soft Matt. 11 (41), 8048–8057.CrossRefGoogle ScholarPubMed
Jensen, O.E. & Naire, S. 2006 The spreading and stability of a surfactant-laden drop on a prewetted substrate. J. Fluid Mech. 554, 5–24.CrossRefGoogle Scholar
Joye, J. 1994 Mechanisms of symmetric and asymmetric drainage of foam films. PhD thesis, Rice University.CrossRefGoogle Scholar
Lhuissier, H. & Villermaux, E. 2012 Bursting bubble aerosols. J. Fluid Mech. 696, 5–44.CrossRefGoogle Scholar
Lin, S., McKeigue, K. & Maldarelli, C. 1990 Diffusion-controlled surfactant adsorption studied by pendant drop digitization. AIChE J. 36 (12), 1785–1795.CrossRefGoogle Scholar
Miguet, J., Pasquet, M., Rouyer, F., Fang, Y. & Rio, E. 2021 Marginal regeneration-induced drainage of surface bubbles. Phys. Rev. Fluids 6 (10), L101601.CrossRefGoogle Scholar
Ochoa, C., Gao, S., Srivastava, S. & Sharma, V. 2021 Foam film stratification studies probe intermicellar interactions. Proc. Natl Acad. Sci. USA 118 (25), e2024805118.CrossRefGoogle ScholarPubMed
Pigeonneau, F. & Sellier, A. 2011 Low-Reynolds-number gravity-driven migration and deformation of bubbles near a free surface. Phys. Fluids 23 (9), 092102.CrossRefGoogle Scholar
Poulain, S., Villermaux, E. & Bourouiba, L. 2018 Ageing and burst of surface bubbles. J. Fluid Mech. 851, 636–671.CrossRefGoogle Scholar
Shen, A.Q., Gleason, B., McKinley, G.H. & Stone, H.A. 2002 Fiber coating with surfactant solutions. Phys. Fluids 14 (11), 4055–4068.CrossRefGoogle Scholar
Shi, X., Fuller, G.G. & Shaqfeh, E.S.G. 2020 Oscillatory spontaneous dimpling in evaporating curved thin films. J. Fluid Mech. 889, A25.CrossRefGoogle Scholar
Shi, X., Rodríguez-Hakim, M., Shaqfeh, E.S.G. & Fuller, G.G. 2021 Instability and symmetry breaking in binary evaporating thin films over a solid spherical dome. J. Fluid Mech. 915, A45.CrossRefGoogle Scholar
Stubenrauch, C. & Von Klitzing, R. 2003 Disjoining pressure in thin liquid foam and emulsion films—new concepts and perspectives. J. Phys.: Condens. Matter 15 (27), R1197.Google Scholar
Tagawa, Y., Takagi, S. & Matsumoto, Y. 2014 Surfactant effect on path instability of a rising bubble. J. Fluid Mech. 738, 124–142.CrossRefGoogle Scholar
Warner, M.R.E., Craster, R.V. & Matar, O.K. 2004 Fingering phenomena created by a soluble surfactant deposition on a thin liquid film. Phys. Fluids 16 (8), 2933–2951.CrossRefGoogle Scholar
Zasadzinski, J.A., Ding, J., Warriner, H.E., Bringezu, F. & Waring, A.J. 2001 The physics and physiology of lung surfactants. Curr. Opin. Colloid Interface Sci. 6 (5–6), 506–513.CrossRefGoogle Scholar