Suscripción a Biblioteca: Guest
Portal Digitalde Biblioteca Digital eLibros Revistas Referencias y Libros de Ponencias Colecciones
Interfacial Phenomena and Heat Transfer
ESCI SJR: 0.258 SNIP: 0.574 CiteScore™: 0.8

ISSN Imprimir: 2169-2785
ISSN En Línea: 2167-857X

Interfacial Phenomena and Heat Transfer

DOI: 10.1615/InterfacPhenomHeatTransfer.2019031147
pages 255-268


Alexey A. Alabuzhev
Institute of Continuous Media Mechanics UB RAS, Perm, Russia, 614013 or Perm StateUniversity, Perm, Russia, 614990


We consider the oscillations of an oblate gas bubble in the vibrational field with the emphasis placed on the interplay between the bubble compressibility and the contact line motion. The bubble is surrounded by an incompressible fluid and is bounded in the axial direction by two parallel solid surfaces. The velocity of the contact line is assumed to be proportional to the deviation of the contact angle from the equilibrium value. The proportionality coefficients (Hocking parameter) are different for each plate. The frequencies and damping rates of the bubble eigenmodes are studied as a function of the problem parameters. The frequency of the volume (breathing) mode of free oscillations can vanish in a certain interval of the values of the Hocking parameter. This frequency significantly depends on the gas pressure, giving rise to double response: when the external frequency is close to the eigenfrequencies of both the volume and shape modes and when the unlimited growth of the amplitude occurs irrespective of the Hocking parameter. The radial pulsations become small with increase in the gas pressure and the bubble behavior is consistent with the dynamics of an incompressible drop. Different Hocking parameters determine different damping rates, but dissipation in the whole system is determined by their total contribution.


  1. Alabuzhev, A., Behavior of a Cylindrical Bubble under Vibrations, Comput. Continuum Mech, vol. 7, no. 2, pp. 151-161,2014. DOI: 10.7242/1999-6691/2014.7.2.16.

  2. Alabuzhev, A., Axisymmetric Oscillations of a Cylindrical Droplet with a Moving Contact Line, J. Appl. Mech. Tech. Phys, vol. 57, no. 6, pp. 1006-1015,2016. DOI: 10.1134/S0021894416060079.

  3. Alabuzhev, A., Influence of Heterogeneous Plates on the Axisymmetrical Oscillations of a Cylindrical Drop, Micrograv. Sci. Technol., vol. 30, no. 1, pp. 25-32,2018. DOI: 10.1007/s12217-017-9571-8.

  4. Alabuzhev, A.A. and Kashina, M.A., Influence of Surface Properties on Axisymmetric Oscillations of an Oblate Drop in an Alternating Electric Field, Radiophys. Quantum Electron., vol. 61, no. 8, pp. 589-602,2019. DOI: 10.1007/s11141-019-09919-4.

  5. Alabuzhev, A.A. and Kaysina, M.I., The Axisymmetric Oscillations of a Cylindrical Bubble in a Liquid Bounded Volume with Free Deformable Interface, J Phys.: Conf. Series, vol. 929, p. 012106,2017. DOI: 10.1088/1742-6596/929/1/012106.

  6. Alabuzhev, A.A. and Lyubimov, D.V., Effect of the Contact-Line Dynamics on the Natural Oscillations of a Cylindrical Droplet, J. Appl. Mech. Tech. Phys., vol. 48, no. 5, pp. 686-693,2007. DOI: 10.1007/s10808-007-0088-6.

  7. Alabuzhev, A.A. and Shklyaev, S., Emission of Acoustic Waves by Nonlinear Drop Oscillations, Phys. Fluids, vol. 19, no. 4, p. 047102,2007. DOI: 10.1063/1.2718492.

  8. Benilov, E.S., Stability of a Liquid Bridge under Vibration, Phys. Rev. E, vol. 93, p. 063118, 2016. DOI: 10.1103/Phys-RevE.93.063118.

  9. Borcia, R., Borcia, I.D., Bestehorn, M., Varlamova, O., Hoefner, K., and Reif, J., Drop Behavior Influenced by the Correlation Length on Noisy Surfaces, Langmuir, vol. 35, no. 4, pp. 928-934,2019. DOI: 10.1021/acs.langmuir.8b03878.

  10. Borkar, A. and Tsamopoulos, J., Boundary Layer Analysis of the Dynamics of Axisymmetric Capillary Bridges, Phys. Fluids A: FluidDynam., vol. 3, no. 12, pp. 2866-2874,1991. DOI: 10.1063/1.857832.

  11. Fayzrakhmanova, I. and Straube, A., Stick-Slip Dynamics of an Oscillated Sessile Drop, Phys. Fluids, vol. 21, no. 7, p. 072104, 2009. DOI: 10.1063/1.3174446.

  12. Fayzrakhmanova, I.S., Straube, A.V., and Shklyaev, S., Bubble Dynamics Atop an Oscillating Substrate: Interplay of Compressibility and Contact Angle Hysteresis, Phys. Fluids, vol. 23,no. 10,p. 102105,2011. DOI: 10.1063/1.3650280.

  13. Gatapova, E.Y., Kirichenko, E.O., Bai, B., and Kabov, O.A., Interaction of Impacting Water Drop with a Heated Surface and Breakup into Microdrops, Interf. Phenom. Heat Transf, vol. 6, no. 1, pp. 75-88,2018.

  14. Hocking, L.M., The Damping of Capillary-Gravity Waves at a Rigid Boundary, J. Fluid Mech., vol. 179, pp. 253-266,1987a.

  15. Hocking, L.M., Waves Produced by a Vertically Oscillating Plate, J. Fluid Mech., vol. 179, pp. 267-281,1987b.

  16. Kashina, M.A. and Alabuzhev, A.A., The Dynamics of Oblate Drop between Heterogeneous Plates under Alternating Electric Field, Micrograv. Sci. Technol, vol. 30, no. 1,pp. 11-17,2018. DOI: 10.1007/s12217-017-9569-2.

  17. Klimenko,L. and Lyubimov, D., Surfactant Effect on the Average Flow Generation near Curved Interface, Micrograv. Sci. Technol., vol. 30, no. 1,pp. 77-84,2018. DOI: 10.1007/s12217-017-9577-2.

  18. Klimenko, L.S. and Lyubimov, D.V., Generation of an Average Flow by a Pulsating Stream near a Curved Free Surface, Fluid Dynam, vol. 47, no. 1, pp. 26-36,2012. DOI: 10.1134/S0015462812010048.

  19. Lezhnin, S.I., Alekseev, M.V., Vozhakov, I., and Pribaturin, N.A., Simulating Dynamic Processes in Vapor-Drop Medium at Non-Equilibrium Phase Transitions, Interf. Phenom. Heat Transf., vol. 6, no. 1, pp. 1-10,2018.

  20. Miles, J., The Capillary Boundary Layer for Standing Waves, J Fluid Mech, vol. 222, pp. 197-205, 1991. DOI: 10.1017/S0022112091001052.

  21. Pukhnachev, V.V. and Semenova, I.B., Model Problem of Instantaneous Motion of a Three-Phase Contact Line, J. Appl. Mech. Tech. Phys, vol. 40, no. 4, pp. 594-603,1999. DOI: 10.1007/BF02468433.

  22. Shklyaev, S. and Straube, A.V., Linear Oscillations of a Compressible Hemispherical Bubble on a Solid Substrate, Phys. Fluids, vol. 20, no. 5, p. 052102,2008. DOI: 10.1063/1.2918728.

  23. Tsvelodub, O.Y. and Arkhipov, D.G., Simulation of Nonlinear Waves on the Surface of a Thin Fluid Film Moving under the Action of Turbulent Gas Flow, J. Appl. Mech. Tech. Phys, vol. 58, no. 4, pp. 619-628,2017. DOI: 10.1134/S0021894417040058.

  24. Voinov, O.V., Hydrodynamics of Wetting, Fluid Dynam, vol. 11, no. 5, pp. 714-721,1976. DOI: 10.1007/BF01012963.

  25. Vozhakov, I.S., Arkhipov, D.G., and Tsvelodub, O.Y., Simulating Nonlinear Waves on the Surface of Thin Liquid Film Entrained by Turbulent Gas Flow, Thermophys. Aeromech., vol. 22, no. 2, pp. 191-202,2015. DOI: 10.1134/S0869864315020067.

  26. Xia, Y. and Steen, P.H., Moving Contact-Line Mobility Measured, J. Fluid Mech, vol. 841, pp. 767-783, 2018. DOI: 10.1017/jfm.2018.105.

  27. Zhang, L. and Thiessen, D.B., Capillary-Wave Scattering from an Infinitesimal Barrier and Dissipation at Dynamic Contact Lines, J. Fluid Mech, vol. 719, pp. 295-313,2013. DOI: 10.1017/jfm.2013.5.

Articles with similar content:

International Journal of Fluid Mechanics Research, Vol.46, 2019, issue 2
Ananth Pai S., Shaligram Tiwari, Sundararajan Thirumalachari, Mihir Sen
Regulation of the Dynamics of a Carrying Body Using the Cycloidal Damper of Forced Oscillations with Dry Friction
Journal of Automation and Information Sciences, Vol.34, 2002, issue 2
Victor P. Legeza
Liquid Filtration in a Microcirculatory Cell of the Plant Leaf: A Lumped Parameter Model
International Journal of Fluid Mechanics Research, Vol.34, 2007, issue 6
N. N. Kizilova
Telecommunications and Radio Engineering, Vol.73, 2014, issue 5
I. V. Fedorin, A. A. Bulgakov
4th Thermal and Fluids Engineering Conference, Vol.17, 2019, issue
Raunak Bardia, Mario F. Trujillo