Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T18:42:16.292Z Has data issue: false hasContentIssue false
  • English
  • Français

Coupled vibrations of a meniscus and liquid films

Published online by Cambridge University Press:  22 December 2015

Jacopo Seiwert ,
Juliette Pierre  and
Benjamin Dollet
Jacopo Seiwert
Affiliation:
Institut de Physique de Rennes, UMR 6251 CNRS/Université Rennes 1, Campus Beaulieu, Bâtiment 11A, 35042 Rennes Cedex, France
Juliette Pierre
Affiliation:
Institut de Physique de Rennes, UMR 6251 CNRS/Université Rennes 1, Campus Beaulieu, Bâtiment 11A, 35042 Rennes Cedex, France
Benjamin Dollet*
Affiliation:
Institut de Physique de Rennes, UMR 6251 CNRS/Université Rennes 1, Campus Beaulieu, Bâtiment 11A, 35042 Rennes Cedex, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the vibration properties of a circular horizontal film that is bounded by a meniscus (or Plateau border) and suspended between two catenary films. The suspending films act as capillary springs, and the system is thus free to oscillate around its equilibrium position. We study its free and forced oscillations. In our experiments, we track simultaneously the positions of the Plateau border and the film. The model that we present predicts the eigenfrequency of the system and its resonance characteristics (in forced oscillations). In particular, we show that the dynamics of both the Plateau border and the film have to be taken into account in order to provide an accurate prediction of the oscillation frequency.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
Papers
Information
Journal of Fluid Mechanics , Volume 788 , 10 February 2016 , pp. 183 - 208
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Afenchenko, V. O., Ezersky, A. B., Kiyashko, S. V., Rabinovich, M. I. & Weidman, P. D. 1998 The generation of two-dimensional vortices by transverse oscillation of a soap film. Phys. Fluids 10, 390–399.CrossRefGoogle Scholar
Besson, S. & Debrégeas, G. 2007 Static and dynamics of adhesion between two soap bubbles. Eur. Phys. J. E 24, 109–117.CrossRefGoogle ScholarPubMed
Boudaoud, A., Couder, Y. & Ben Amar, M. 1999 Self-adaptation in vibrating soap films. Phys. Rev. Lett. 82, 3847–3850.CrossRefGoogle Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166–188.CrossRefGoogle Scholar
Britan, A., Liverts, M. & Ben-Dor, G. 2009 Mitigation of sound waves by wet aqueous foams. Colloids Surf. A 344, 48–55.CrossRefGoogle Scholar
Cantat, I. 2013 Liquid meniscus friction on a wet plate: bubbles, lamellae, and foams. Phys. Fluids 25, 031303.CrossRefGoogle Scholar
Chaigne, A. & Kergomard, J. 2008 Acoustique des instruments de musique. Belin.Google Scholar
Cohen, A., Fraysse, N., Rajchenbach, J., Argentina, M., Bouret, Y. & Raufaste, C. 2014 Inertial mass transport and capillary hydraulic jump in a liquid foam microchannel. Phys. Rev. Lett. 112, 218303.CrossRefGoogle Scholar
Cohen, A., Fraysse, N. & Raufaste, C.2015 High amplitude vibration of a liquid foam microchannel (in preparation).Google Scholar
Cohen-Addad, S., Höhler, R. & Pitois, O. 2013 Flow in foams and flowing foams. Annu. Rev. Fluid Mech. 45, 241–267.CrossRefGoogle Scholar
Couder, Y., Chomaz, J. M. & Rabaud, M. 1989 On the hydrodynamics of soap films. Physica D 37, 384–405.CrossRefGoogle Scholar
Del Prete, E., Chinnayya, A., Domergue, L., Hadjadj, A. & Haas, J. F. 2013 Blast wave mitigation by dry aqueous foams. Shock Waves 23, 39–53.CrossRefGoogle Scholar
Denkov, N. D., Subramanian, V., Gurovich, D. & Lips, A. 2005 Wall slip and viscous dissipation in sheared foams: effect of surface mobility. Colloids Surf. A 263, 129–145.CrossRefGoogle Scholar
Dollet, B. & Raufaste, C. 2014 Rheology of aqueous foams. C. R. Physique 15, 731–747.CrossRefGoogle Scholar
Drenckhan, W., Dollet, B., Hutzler, S. & Elias, F. 2008 Soap films under large-amplitude oscillations. Phil. Mag. Lett. 88, 669–677.CrossRefGoogle Scholar
Elias, F., Hutzler, S. & Ferreira, M. S. 2007 Visualization of sound waves using regularly spaced soap films. Eur. J. Phys. 28, 755–765.CrossRefGoogle Scholar
Elias, F., Janiaud, E., Bacri, J. P. & Andreotti, B. 2014 Elasticity of a soap film junction. Phys. Fluids 26, 037101.CrossRefGoogle Scholar
Elias, F., Kaurin, D., Arbogast, L., Leroy, V., Gay, C. & Derec, C. 2015 Propagation of a transverse wave on a Plateau border. EPL (in press).Google Scholar
Goldfarb, I., Orenbakh, Z., Shreiber, I. & Vafina, F. 1997 Sound and weak shock wave propagation in gas–liquid foams. Shock Waves 7, 77–88.CrossRefGoogle Scholar
Hutzler, S., Saadatfar, M., van der Net, A., Weaire, D. & Cox, S. J. 2008 The dynamics of a topological change in a system of soap films. Colloids Surf. A 323, 123–131.CrossRefGoogle Scholar
Joosten, J. G. H. 1984 Spectral analysis of light scattered by liquid films. I. General considerations. J. Chem. Phys. 80, 2363–2382.CrossRefGoogle Scholar
Kann, K. B. 2005 Sound waves in foams. Colloids Surf. A 263, 315–319.CrossRefGoogle Scholar
Kosgodagan Acharige, S., Elias, F. & Derec, C. 2014 Vibrating soap film: origin of the dissipation. Soft Matter 10, 8341–8348.CrossRefGoogle Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.Google Scholar
Landau, L. & Levich, B. 1942 Dragging of a liquid by a moving plate. Acta Physicochim. USSR 17, 42–54.Google Scholar
Landau, L. & Lifchitz, E. 1994 Mécanique des fluides, 3rd edn. Mir–Ellipses.Google Scholar
Landau, L. D. & Lifchitz, E. M. 1969 Mechanics, 2nd edn. Pergamon.Google Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.Google Scholar
Moxon, N. T., Torrance, A. C. & Richardson, S. B. 1988 The attenuation of acoustic signals by aqueous and particulate foams. Appl. Acoust. 24, 193–209.CrossRefGoogle Scholar
Mujica, N. & Fauve, S. 2002 Sound velocity and absorption in a coarsening foam. Phys. Rev. E 66, 021404.CrossRefGoogle Scholar
Mysels, K. J., Shinoda, K. & Frankel, S. 1959 Soap Films: Study of Their Thinning and a Bibliography. Pergamon.Google Scholar
Pierre, J., Dollet, B. & Leroy, V. 2014 Resonant acoustic propagation and negative density in liquid foams. Phys. Rev. Lett. 112, 148307.CrossRefGoogle ScholarPubMed
Pierre, J., Guillermic, R. M., Elias, F., Drenckhan, W. & Leroy, V. 2013 Acoustic characterisation of liquid foams with an impedance tube. Eur. Phys. J. E 36, 113.CrossRefGoogle ScholarPubMed
Rutgers, M. A., Wu, X. I., Bhagavatula, R., Petersen, A. A. & Goldburg, W. I. 1996 Two-dimensional velocity profiles and laminar boundary layers in flowing soap films. Phys. Fluids 8, 2847–2854.CrossRefGoogle Scholar
Salkin, L., Schmit, A., Panizza, P. & Courbin, L. 2014 Influence of boundary conditions on the existence and stability of minimal surfaces of revolution made of soap films. Am. J. Phys. 82, 839–847.CrossRefGoogle Scholar
Schwartz, L. W. & Princen, H. M. 1987 A theory of extensional viscosity for flowing foams and concentrated emulsions. J. Colloid Interface Sci. 118, 201–211.CrossRefGoogle Scholar
Seiwert, J., Dollet, B. & Cantat, I. 2014 Theoretical study of the generation of soap films: role of interfacial visco-elasticity. J. Fluid Mech. 739, 124–142.CrossRefGoogle Scholar
Seiwert, J., Monloubou, M., Dollet, B. & Cantat, I. 2013 Extension of a suspended soap film: a homogeneous dilatation followed by new film extraction. Phys. Rev. Lett. 111, 094501.CrossRefGoogle ScholarPubMed
Sens, P., Marques, C. & Joanny, J. F. 1993 Hydrodynamic modes of viscoelastic soap films. Langmuir 9, 3212–3218.CrossRefGoogle Scholar
Stevenson, P. 2012 Foam Engineering: Fundamental and Applications. Wiley.CrossRefGoogle Scholar
Taylor, G. I. 1959 The dynamics of thin sheets of fluid II. Waves on fluid sheets. Proc. R. Soc. Lond. A 253, 296–312.Google Scholar
Vega, J. M., Higuera, F. J. & Weidman, P. D. 1998 Quasi-steady vortical structures in vertically vibrating soap films. J. Fluid Mech. 372, 213–230.CrossRefGoogle Scholar
Weaire, D. & Hutzler, S. 1999 The Physics of Foams. Clarendon.Google Scholar
Wood, A. B. 1944 A Textbook of Sound. Bell.Google Scholar
Zhang, W. & Stone, H. A. 1998 Oscillatory motions of circular disks and nearly spherical particles in viscous flows. J. Fluid Mech. 367, 329–358.CrossRefGoogle Scholar