Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-02-09T13:49:33.176Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics of a sessile drop in forced vibration

Published online by Cambridge University Press:  31 August 2007

BOJAN VUKASINOVIC ,
MARC K. SMITH  and
ARI GLEZER
BOJAN VUKASINOVIC
Affiliation:
Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA
MARC K. SMITH
Affiliation:
Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA
ARI GLEZER
Affiliation:
Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The interfacial dynamics of a sessile water drop was investigated experimentally. The low-viscosity drop was forced by an underlying diaphragm driven vertically by a piezoelectric actuator. This high-frequency forcing produced very low diaphragm displacements, even at high acceleration amplitudes. As the driving amplitude was increased from zero, the drop exhibited several transitions to states of increasing spatio-temporal complexity. The first state of the forced drop consisted of harmonic axisymmetric standing waves that were present for even the smallest diaphragm motion. Wave modes up to 14 were observed an compared to theoretical results. As the forcing amplitude increased above a critical value, a parametrically driven instability occurred that resulted in the appearance of subharmonic azimuthal waves along the contact line. The critical accelerations and the resulting wavenumbers of the azimuthal waves were documented. For larger values of the forcing amplitude, the subharmonic azimuthal waves coupled with the harmonic axisymmetric waves to produce a striking new lattice-like wave pattern. With a further increase in the forcing amplitude, the lattice mode disappeared and the interface evolved into a highly disordered state, dominated by subharmonic wave motion. The characteristics of the lattice and pre-ejection modes were documented with phase-locked measurements and spectral analysis. Finally, as the forcing amplitude increased above another critical value, the interface broke up via droplet ejection from individual wave crests.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 587 , 25 September 2007 , pp. 395 - 423
Copyright
Copyright © Cambridge University Press 2007

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

REFERENCES

Basaran, O. A. 1992 Nonlinear oscillations of viscous liquid drops. J. Fluid Mech. 241, 169–198.CrossRefGoogle Scholar
Basaran, O. A. & DePaoli, D. W. 1994 Nonlinear oscillations of pendant drops. Phys. Fluid. 6, 2923–2943.CrossRefGoogle Scholar
Benjamin, T. B. & Ursell, F. 1954 The stability of the plane free surface of a liquid in vertical periodic motion. Proc. R. Soc. Lond. A 225, 505–515.Google Scholar
Besson, T., Edwards, W. S. & Tuckerman, L. S. 1996 Two-frequency parametric excitation of surface waves. Phys. Rev. E 54, 507–513.Google ScholarPubMed
Cabeza, C., Negreira, C., Schifino, A. C. & Gibiat, V. 2000 Experimental determination of point localized time correlation and power spectrum in a Faraday experiment. Intl J. Bifur. Chao. 10, 2233–2244.CrossRefGoogle Scholar
Christiansen, B., Alstrom, P. & Levinsen, M. T. 1995 Dissipation and ordering in capillary waves at high aspect ratios. J. Fluid Mech. 291, 323–341.CrossRefGoogle Scholar
Crum, L. A. & Roy, R. A. 1994 Sonoluminescence. Science, 266, 233–234.CrossRefGoogle ScholarPubMed
DePaoli, D. W., Feng, J. Q., Basaran, O. A. & Scott, T. C. 1995 Hysteresis in forced oscillations of pendant drops. Phys. Fluid. 7, 1181–1183.CrossRefGoogle Scholar
Douady, S. 1990 Experimental study of the Faraday instability. J. Fluid Mech. 221, 383–409.CrossRefGoogle Scholar
Edwards, W. S. & Fauve, S. 1994 Patterns and quasi-patterns in the Faraday experiment. J. Fluid Mech. 278, 123–148.CrossRefGoogle Scholar
Faraday, M. 1831 On a peculiar class of acoustical figures, and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Phil. Trans. R. Soc. Lond. 121, 299–340.Google Scholar
Ganán, A. & Barrero, A. 1990 Free oscillations of liquid captive drops. Microgravity Sci. Technol. 3, 70–86.Google Scholar
Gluckman, B. J., Arnold, C. B. & Gollub, J. P. 1995 Statistical studies of chaotic wave patterns. Phys. Rev. E 51, 1128–1147.Google ScholarPubMed
Gollub, J. P. & Langer, J. S. 1999 Pattern formation in nonequilibrium physics. Rev. Mod. Phys. 71, 396–403.CrossRefGoogle Scholar
Henderson, D. M. 1998 Effects of surfactants on Faraday-wave dynamics. J. Fluid Mech. 365, 89–107.CrossRefGoogle Scholar
Henderson, D. M. & Miles, J. W. 1994 Surface-wave damping in a circular cylinder with a fixed contact line. J. Fluid Mech. 275, 285–299.CrossRefGoogle Scholar
Hocking, L. M. 1987 The damping of capillary–gravity waves at a rigid boundary. J. Fluid Mech. 179, 253–266.CrossRefGoogle Scholar
James, A., Vukasinovic, B., Smith, M. K. & Glezer, A. 2003 a Vibration-induced drop atomization and bursting. J. Fluid Mech. 476, 1–28.CrossRefGoogle Scholar
James, A., Smith, M. K. & Glezer, A. 2003 b Vibration-induced drop atomization and the numerical simulation of low-frequency single-droplet ejection. J. Fluid Mech. 476, 29–62.CrossRefGoogle Scholar
Kumar, K. 1996 Linear theory of Faraday instability in viscous liquids. Proc. R. Soc. Lond. A 452, 1113–1126.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.Google Scholar
Landau, L. & Lifshitz, E. M. 1987 Fluid Mechanics. 2nd edn, Pergamon.Google Scholar
Lee, C. P., Anilkumar, A. V. & Wang, T. G. 1991 Static shape and instability of an acoustically levitated drop. Phys. Fluid. 3, 2497–2515.CrossRefGoogle Scholar
Leissa, A. W. & Chern, Y. T. 1992 Approximate analysis of the forced vibration response of plates. J. Vib. Acousts Trans. ASM. 114, 106–111.CrossRefGoogle Scholar
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.Google Scholar
Lundgren, T. S. & Mansour, N. N. 1988 Oscillations of drops in zero gravity with weak viscous effects. J. Fluid Mech. 194, 479–510.CrossRefGoogle Scholar
Lyubimov, D. V., Lyubimova, T. P. & Shklyaev, S. V. 2006 Behaviour of a drop on an oscillating solid plate. Phys. Fluid. 18, 012101.CrossRefGoogle Scholar
Mesquita, O. N., Kane, S. & Gollub, J. P. 1992 Transport by capillary waves: fluctuating Stokes drift. Phys. Rev. A 45, 3700–3705.CrossRefGoogle ScholarPubMed
Miles, J. W. 1967 Surface-wave damping in closed basins. Proc. R. Soc. Lond. A 297, 459–475.Google Scholar
Miles, J. W. 1984 Nonlinear Faraday resonance. J. Fluid Mech. 146, 285–302.CrossRefGoogle Scholar
Miles, J. W. 1991 The capillary boundary layer for standing waves. J. Fluid Mech. 222, 197– 205.CrossRefGoogle Scholar
Miles, J. & Henderson, D. 1990 Parametrically forced surface waves. Annu. Rev. Fluid Mech. 22, 143–165.CrossRefGoogle Scholar
Noblin, X., Buguin, A. Brochard-Wyart, F. 2004 Vibrated sessile drops: transition between pinned and mobile contact line oscillations. Eur. Phys. J. E 14, 395–404.Google ScholarPubMed
Noblin, X., Buguin, A. & Brochard-Wyart, F. 2005 Triplon modes of puddles. Phys. Rev. Lett. 94, 166102.CrossRefGoogle ScholarPubMed
Perlin, M. & Schultz, W. W. 2000 Capillary effects on surface waves. Annu. Rev. Fluid Mech. 32, 241–274.CrossRefGoogle Scholar
Pratt, W. K. 1978 Digital Image Processing. John Wiley.Google Scholar
Prosperetti, A. 1980 Free oscillations of drops and bubbles: the initial-value problem. J. Fluid Mech. 100, 333–347.CrossRefGoogle Scholar
Prosperetti, A. & Oguz, H. N. 1993 Impact of drops on liquid surfaces and the underwater noise of rain. Annu. Rev. Fluid Mech. 25, 577–602.CrossRefGoogle Scholar
Range, K., Smith, M. K., & Glezer, A. 1998 An experimental investigation of vibration-induced single droplet ejection. Fifty-First Meeting of the American Physical Society – Division of Fluid Dynamics, Philadelphia, PA, November 22–24.Google Scholar
Rayleigh, Lord 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. A 29, 71–97.Google Scholar
Rodot, H., Bisch, C. & Lasek, A. 1979 Zero-gravity simulation of liquids in contact with a solid surface. Acta Astronaut. 6, 1083–1092.CrossRefGoogle Scholar
Siekmann, J. & Schilling, U. 1989 On the vibrations of an inviscid liquid droplet contacting a solid wall in a low-gravity environment. Appl. Microgravity Technol. 2, 17–26.Google Scholar
Simonelli, F. & Gollub, J. P. 1989 Surface wave mode interactions: effects of symmetry and degeneracy. J. Fluid Mech. 199, 471–494.CrossRefGoogle Scholar
Strani, M. & Sabetta, F. 1984 Free vibrations of a drop in partial contact with a solid support. J. Fluid Mech. 141, 233–247.CrossRefGoogle Scholar
Strani, M. & Sabetta, F. 1988 Viscous oscillations of a supported drop in an immiscible fluid. J. Fluid Mech. 189, 397–421.CrossRefGoogle Scholar
Trinh, E. & Wang, T. G. 1982 Large-amplitude free and driven drop-shape oscillations: experimental observations. J. Fluid Mech. 122, 315–338.CrossRefGoogle 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.CrossRefGoogle Scholar
Tsamopoulos, J. H. & Brown, R. A. 1983 Nonlinear oscillations of inviscid drops and bubbles. J. Fluid Mech. 127, 519–537.CrossRefGoogle Scholar
Vukasinovic, B. 2002 Vibration-induced droplet atomization. PhD thesis, Georgia Institute of Technology.Google Scholar
Vukasinovic, B., Smith, M. K. & Glezer, A. 2007 Mechanisms of free-surface breakup in vibration-induced liquid atomization. Phys. Fluid. 19, 012104.CrossRefGoogle Scholar
Wilkes, E. D. & Basaran, O. A. 1997 Forced oscillations of pendant (sessile) drops. Phys. Fluid. 9, 1512–1528.CrossRefGoogle Scholar
Wilkes, E. D. & Basaran, O. A. 1999 Hysteretic response of supported drops during forced oscillations. J. Fluid Mech. 393, 333–356.CrossRefGoogle Scholar