Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-04T18:19:18.912Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear oscillations of inviscid drops and bubbles

Published online by Cambridge University Press:  20 April 2006

John A. Tsamopoulos  and
Robert A. Brown
John A. Tsamopoulos
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
Robert A. Brown
Affiliation:
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139
Get access Rights & Permissions [Opens in a new window]

Abstract

Moderate-amplitude axisymmetric oscillations of incompressible inviscid drops and bubbles are studied using a Poincaré–Lindstedt expansion technique. The corrections to the drop shape and velocity potential caused by mode coupling at second order in amplitude are predicted for two-, three- and four-lobed motions. The frequency of oscillation is found to decrease with the square of the amplitude; this result compares well with experiments and numerical calculations for drops undergoing two-lobed oscillations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 127 , February 1983 , pp. 519 - 537
Copyright
© 1983 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

Alonso, C. T. 1974 The dynamics of colliding and oscillating drops. In Proc. Int. Colloq. on Drops and Bubbles (ed. D. J. Collins, M. S. Plesset & M. M. Saffren). Jet Propulsion Laboratory.
Brink, D. M. & Satchler, G. R. 1968 Angular Momentum, 2nd ed. Clarendon.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Concus, P. 1962 Standing capillary-gravity waves of finite amplitude J. Fluid Mech. 14, 568–576.Google Scholar
Foote, G. B. 1973 A numerical method for studying simple drop behavior: simple oscillation. J. Comp. Phys. 11, 507–530.Google Scholar
Hall, P. & Seminara, G. 1980 Nonlinear oscillations of non-spherical cavitation bubbles in acoustic fields J. Fluid Mech. 101, 423–444.Google Scholar
Joseph, D. D. 1973 Domain perturbations: the higher order theory of infinitesimal water waves. Arch. Rat. Mech. Anal. 51, 295–303.Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th ed. Cambridge University Press.
MACSYMA 1977 Reference Manual. Laboratory of Computer Science, Massachusetts Institute of Technology.
Marston, P. L. 1980 Shape oscillation and static deformation of drops and bubbles driven by modulated radiation stresses: theory. J. Acoust. Soc. Am. 67, 15–26.CrossRefGoogle Scholar
Marston, P. L. & Apfel, R. E. 1979 Acoustically forced shape oscillation of hydrocarbon drops levitated in water J. Colloid Interface Sci. 68, 280–286.Google Scholar
Marston, P. L. & Apfel, R. E. 1980 Quadrapole resonance of drops driven by modulated acoustic radiation pressure: experimental properties. J. Acoust. Soc. Am. 67, 27–37.Google Scholar
Miller, C. A. & Scriven, L. E. 1968 The oscillations of a fluid droplet immersed in another fluid J. Fluid Mech. 32, 417–135.Google Scholar
Nayfeh, A. H. & Mook, D. T. 1979 Nonlinear Oscillations. Wiley-Interscience.
Pavelle, R., Rothstein, M. & Fitch, J. 1981 Computer algebra Sci. Am. 245, 136–152.Google Scholar
Plateau, J. A. F. 1873 Statique Expérimental et Théorique des liquides soumis aux seules forces moléculaires. Gauthier-Villars.
Prosperetti, A. 1980 Normal-mode analysis for the oscillations of a viscous liquid drop in an immiscible liquid J. Méc. 19, 149–182.Google Scholar
Rayleigh, J. W. S. 1879 On the capillary phenomena of jets Proc. R. Soc. Lond. 29, 71–97.Google Scholar
Reid, W. H. 1960 The oscillations of a viscous liquid drop Q. Appl. Math. 18, 86–89.Google Scholar
Rotenberg, M., Bivins, R., Metropolis, N. & Wooten, J. K. 1959 The 3j and 6j Symbols. Technology Press.
Savart, F. 1833 Mémoire sur la constitution des veines liquides lancées par des orifices circulaires en mince paroi Ann. de Chim. 53, 337–386.Google Scholar
Tadjbakhsh, I. & Keller, J. B. 1960 Standing surface waves of finite amplitude J. Fluid Mech. 8, 442–451.Google Scholar
Trinh, E., Zwern, A. & Wang, T. G. 1982 An experimental study of small-amplitude drop oscillations in immiscible liquid systems J. Fluid Mech. 115, 453–474.Google Scholar
Trinh, E. & Wang, T. G. 1982 Large amplitude drop shape oscillations. In Proc. 2nd Int. Colloq. on Drops and Bubbles. JPL Publ. 82–87, Pasadena.
Tsamopoulos, J. A. 1983 Ph.D. thesis, Massachusetts Institute of Technology (in preparation).