Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-20T05:21:55.405Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental and theoretical investigation of large-amplitude oscillations of liquid droplets

Published online by Cambridge University Press:  26 April 2006

E. Becker ,
W. J. Hiller  and
T. A. Kowalewski
E. Becker
Affiliation:
Max-Planck-Institut für Strömungsforschung, Bunsenstrasse 10, 3400 Göttingen. Germany
W. J. Hiller
Affiliation:
Max-Planck-Institut für Strömungsforschung, Bunsenstrasse 10, 3400 Göttingen. Germany
T. A. Kowalewski
Affiliation:
Max-Planck-Institut für Strömungsforschung, Bunsenstrasse 10, 3400 Göttingen. Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

Finite-amplitude, axially symmetric oscillations of small (0.2 mm) liquid droplets in a gaseous environment are studied, both experimentally and theoretically. When the amplitude of natural oscillations of the fundamental mode exceeds approximately 10% of the droplet radius, typical nonlinear effects like the dependence of the oscillation frequency on the amplitude, the asymmetry of the oscillation amplitude, and the interaction between modes are observed. As the amplitude decreases due to viscous damping, the oscillation frequency and the amplitude decay factor reach their asymptotical values predicted by linear theory. The initial behaviour of the droplet is described quite satisfactorily by a proposed nonlinear inviscid theoretical model.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 231 , October 1991 , pp. 189 - 210
Copyright
© 1991 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

Brosa, U. 1988 Strongly dissipative modes. Unpublished paper, Universität Marburg.
Brosa, U., Grossmann, S., Müller, A. & Becker, E. 1989 Nuclear scission. Nucl. Phys. A 502, 423c–442c.Google Scholar
Chandrasekhar, S. 1959 The oscillations of a viscous liquid globe. Proc. Lond. Math. Soc. 9, 141–149.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability, pp. 466–477. Clarendon.
Chaudhary, K. C. & Maxworthy, T. 1980 The nonlinear capillary instability of a liquid jet. Part 3. Experiments on satellite drop formation and control. J. Fluid Mech. 96, 287–297.Google Scholar
Dürr, H. M. & Siekmann, J. 1987 Numerical studies of fluid oscillation problems by boundary integral techniques. Acta Astr. 15, 859–864.Google Scholar
Fehlberg, E. 1970 Klassische Runge—Kutta—Fromeln vierter und niedriger Ordnung mit Schrittweitenkontrolle und ihre Anwendung auf Wärmeleitungsprobleme. Computing (Wien) 6, 61–71.Google Scholar
Hiller, W. J. & Kowalewski, T. A. 1989a Surface tension measurements by the oscillating droplet method. Phys. Chem. Hydrodyn. 11, 103–112.Google Scholar
Hiller, W. J. & Kowalewski, T. A. 1989b Application of the frame transfer charge-coupled device for high speed imaging. Opt. Engng 28, 197–200.Google Scholar
Hiller, W. J., Kowalewski, T. A. & Stasicki, B. 1989 High speed image recording. Laser Optoelektronic 21, 64–68 (in German).Google Scholar
Lamb, H. 1932 Hydrodynamics, 6th edn, pp. 473–475. Cambridge University Press.
Lundgren, T. S. & Mansour, N. N. 1988 Oscillation of drops in zero gravity with weak viscous effects. J. Fluid Mech. 194, 479–510.Google Scholar
Miller, C. A. & Scriven, L. E. 1968 The oscillation of a fluid droplet immersed in another fluid. J. Fluid Mech. 32, 417–435.Google Scholar
Natarajan, E. & Brown, R. A. 1987 Third-order resonance effect and the nonlinear stability of drop oscillation. J. Fluid Mech. 183, 95–121.Google Scholar
Prosperetti, A. 1977 Viscous effects on perturbed spherical flows. Q. Appl. Maths 35, 339–352.Google Scholar
Prosperetti, A. 1980a Normal-mode analysis for the oscillations of a viscous liquid drop immersed in another liquid. J. Méc. 19, 149–182.Google Scholar
Prosperetti, A. 1980b Free oscillations of drops and bubbles: the initial-value problem. J. Fluid Mech. 100, 333–347.Google Scholar
Rayleigh, Lord 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. Maths 18, 86–89.Google Scholar
Sommerfeld, A. 1978 Theoretische Physik. Mechanik der deformierbaren Medien. vol. III. $12. Thun-Frankfurt/M: Harri Deutsch.
Stasicki, B., Hiller, W. J. & Meier, G. E. A. 1990 A light pulse generator for high speed photography using semiconductor devices as a light source. Opt. Engng 29, 821–827.Google Scholar
Stoer, J. 1972 Einführung in die Numerische Mathematik I, chap. 2. Springer.
Strani, M. & Sabetta, F. 1988 Viscous oscillations of a supported drop in an immiscible fluid. J. Fluid Mech. 189, 397–421.Google Scholar
Trinh, E. H., Marston, P. L. & Robey, J. L. 1987 Acoustic measurement of the surface tension of levitated drops. J. Colloid Interface Sci. 124, 95–103.Google Scholar
Trinh, E. & Wang, T. G. 1982 Large-amplitude free and driven drop-shape oscillations: experimental observations. J. Fluid Mech. 122, 315–338.Google Scholar
Tsamopoulos, J. A. & Brown, R. A. 1983 Nonlinear oscillations of inviscid drops and bubbles. J. Fluid Mech. 127, 519–537.Google Scholar
Valentine, R. S., Sather, N. F. & Heideger, W. J. 1965 The motion of drops in various media. Chem. Engng Sci. 20, 719–728.Google Scholar