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The influence of an insoluble surfactant on capillary oscillations of a bubble in a liquid.

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Title: The influence of an insoluble surfactant on capillary oscillations of a bubble in a liquid.
Authors: Lyubimova, Tatyana1 (AUTHOR) lubimova@psu.ru, Konovalov, Vladimir1,2 (AUTHOR), Borzenko, Evgeny2,3 (AUTHOR), Nepomnyashchy, Alexander1,3 (AUTHOR)
Source: Journal of Fluid Mechanics. 11/10/2025, Vol. 1022, p1-28. 28p.
Subjects: Surface active agents, Capillary waves, Viscosity, Fluid flow, Elasticity, Liquids, Computer simulation, Energy dissipation
Abstract: This study is devoted to the analysis of capillary oscillations of a gas bubble in a liquid with an insoluble surfactant adsorbed on the surface. The influence of the Gibbs elasticity, the viscosities of the liquid and gas, as well as the shear and dilatational surface viscosities, on the damping of free oscillations is examined. Dependences of the frequency shift and the damping rate on the parameters of the problem are determined. In the limit of small viscosities and neglecting the surfactant surface diffusion, a simplified dispersion relation is obtained, which includes finite parameters of surface viscosities and Gibbs elasticity. From this relation, conditions are identified under which the damping of capillary oscillations can occur with a small frequency. Numerical solutions of the full dispersion relation demonstrate that a non-oscillatory regime is impossible for the considered configuration. An additional mode associated with Gibbs elasticity is discovered, characterized as a rule by low natural frequency and damping rate. Approximate relations for the complex natural frequency of bubble oscillations in a low-viscosity liquid in the presence of a surfactant are derived, including an estimate of the contribution of the gas inside the bubble to viscous dissipation. An original Lagrangian–Eulerian method is proposed and used to perform direct numerical simulations based on the full nonlinear Navier–Stokes equations and natural boundary conditions at the interface, accounting for shear and dilatational viscosities. The numerical data on the damping process confirm the results of the linear theory. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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Header DbId: egs
DbLabel: Engineering Source
An: 189831709
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: The influence of an insoluble surfactant on capillary oscillations of a bubble in a liquid.
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  Data: <searchLink fieldCode="AR" term="%22Lyubimova%2C+Tatyana%22">Lyubimova, Tatyana</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> lubimova@psu.ru</i><br /><searchLink fieldCode="AR" term="%22Konovalov%2C+Vladimir%22">Konovalov, Vladimir</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Borzenko%2C+Evgeny%22">Borzenko, Evgeny</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Nepomnyashchy%2C+Alexander%22">Nepomnyashchy, Alexander</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Fluid+Mechanics%22">Journal of Fluid Mechanics</searchLink>. 11/10/2025, Vol. 1022, p1-28. 28p.
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  Data: <searchLink fieldCode="DE" term="%22Surface+active+agents%22">Surface active agents</searchLink><br /><searchLink fieldCode="DE" term="%22Capillary+waves%22">Capillary waves</searchLink><br /><searchLink fieldCode="DE" term="%22Viscosity%22">Viscosity</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid+flow%22">Fluid flow</searchLink><br /><searchLink fieldCode="DE" term="%22Elasticity%22">Elasticity</searchLink><br /><searchLink fieldCode="DE" term="%22Liquids%22">Liquids</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+dissipation%22">Energy dissipation</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This study is devoted to the analysis of capillary oscillations of a gas bubble in a liquid with an insoluble surfactant adsorbed on the surface. The influence of the Gibbs elasticity, the viscosities of the liquid and gas, as well as the shear and dilatational surface viscosities, on the damping of free oscillations is examined. Dependences of the frequency shift and the damping rate on the parameters of the problem are determined. In the limit of small viscosities and neglecting the surfactant surface diffusion, a simplified dispersion relation is obtained, which includes finite parameters of surface viscosities and Gibbs elasticity. From this relation, conditions are identified under which the damping of capillary oscillations can occur with a small frequency. Numerical solutions of the full dispersion relation demonstrate that a non-oscillatory regime is impossible for the considered configuration. An additional mode associated with Gibbs elasticity is discovered, characterized as a rule by low natural frequency and damping rate. Approximate relations for the complex natural frequency of bubble oscillations in a low-viscosity liquid in the presence of a surfactant are derived, including an estimate of the contribution of the gas inside the bubble to viscous dissipation. An original Lagrangian–Eulerian method is proposed and used to perform direct numerical simulations based on the full nonlinear Navier–Stokes equations and natural boundary conditions at the interface, accounting for shear and dilatational viscosities. The numerical data on the damping process confirm the results of the linear theory. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1017/jfm.2025.10793
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      – Code: eng
        Text: English
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        PageCount: 28
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      – SubjectFull: Surface active agents
        Type: general
      – SubjectFull: Capillary waves
        Type: general
      – SubjectFull: Viscosity
        Type: general
      – SubjectFull: Fluid flow
        Type: general
      – SubjectFull: Elasticity
        Type: general
      – SubjectFull: Liquids
        Type: general
      – SubjectFull: Computer simulation
        Type: general
      – SubjectFull: Energy dissipation
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    Titles:
      – TitleFull: The influence of an insoluble surfactant on capillary oscillations of a bubble in a liquid.
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            NameFull: Lyubimova, Tatyana
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            NameFull: Konovalov, Vladimir
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            NameFull: Borzenko, Evgeny
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            NameFull: Nepomnyashchy, Alexander
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            – D: 10
              M: 11
              Text: 11/10/2025
              Type: published
              Y: 2025
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              Value: 1022
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