Skip to main content

Dynamics of a sessile drop in forced vibration


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.

Hide All
Basaran, O. A. 1992 Nonlinear oscillations of viscous liquid drops. J. Fluid Mech. 241, 169198.
Basaran, O. A. & DePaoli, D. W. 1994 Nonlinear oscillations of pendant drops. Phys. Fluid. 6, 29232943.
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, 505515.
Besson, T., Edwards, W. S. & Tuckerman, L. S. 1996 Two-frequency parametric excitation of surface waves. Phys. Rev. E 54, 507513.
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, 22332244.
Christiansen, B., Alstrom, P. & Levinsen, M. T. 1995 Dissipation and ordering in capillary waves at high aspect ratios. J. Fluid Mech. 291, 323341.
Crum, L. A. & Roy, R. A. 1994 Sonoluminescence. Science, 266, 233234.
DePaoli, D. W., Feng, J. Q., Basaran, O. A. & Scott, T. C. 1995 Hysteresis in forced oscillations of pendant drops. Phys. Fluid. 7, 11811183.
Douady, S. 1990 Experimental study of the Faraday instability. J. Fluid Mech. 221, 383409.
Edwards, W. S. & Fauve, S. 1994 Patterns and quasi-patterns in the Faraday experiment. J. Fluid Mech. 278, 123148.
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, 299340.
Ganán, A. & Barrero, A. 1990 Free oscillations of liquid captive drops. Microgravity Sci. Technol. 3, 7086.
Gluckman, B. J., Arnold, C. B. & Gollub, J. P. 1995 Statistical studies of chaotic wave patterns. Phys. Rev. E 51, 11281147.
Gollub, J. P. & Langer, J. S. 1999 Pattern formation in nonequilibrium physics. Rev. Mod. Phys. 71, 396403.
Henderson, D. M. 1998 Effects of surfactants on Faraday-wave dynamics. J. Fluid Mech. 365, 89107.
Henderson, D. M. & Miles, J. W. 1994 Surface-wave damping in a circular cylinder with a fixed contact line. J. Fluid Mech. 275, 285299.
Hocking, L. M. 1987 The damping of capillary–gravity waves at a rigid boundary. J. Fluid Mech. 179, 253266.
James, A., Vukasinovic, B., Smith, M. K. & Glezer, A. 2003 a Vibration-induced drop atomization and bursting. J. Fluid Mech. 476, 128.
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, 2962.
Kumar, K. 1996 Linear theory of Faraday instability in viscous liquids. Proc. R. Soc. Lond. A 452, 11131126.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Landau, L. & Lifshitz, E. M. 1987 Fluid Mechanics. 2nd edn, Pergamon.
Lee, C. P., Anilkumar, A. V. & Wang, T. G. 1991 Static shape and instability of an acoustically levitated drop. Phys. Fluid. 3, 24972515.
Leissa, A. W. & Chern, Y. T. 1992 Approximate analysis of the forced vibration response of plates. J. Vib. Acousts Trans. ASM. 114, 106111.
Lighthill, M. J. 1978 Waves in Fluids. Cambridge University Press.
Lundgren, T. S. & Mansour, N. N. 1988 Oscillations of drops in zero gravity with weak viscous effects. J. Fluid Mech. 194, 479510.
Lyubimov, D. V., Lyubimova, T. P. & Shklyaev, S. V. 2006 Behaviour of a drop on an oscillating solid plate. Phys. Fluid. 18, 012101.
Mesquita, O. N., Kane, S. & Gollub, J. P. 1992 Transport by capillary waves: fluctuating Stokes drift. Phys. Rev. A 45, 37003705.
Miles, J. W. 1967 Surface-wave damping in closed basins. Proc. R. Soc. Lond. A 297, 459475.
Miles, J. W. 1984 Nonlinear Faraday resonance. J. Fluid Mech. 146, 285302.
Miles, J. W. 1991 The capillary boundary layer for standing waves. J. Fluid Mech. 222, 197– 205.
Miles, J. & Henderson, D. 1990 Parametrically forced surface waves. Annu. Rev. Fluid Mech. 22, 143165.
Noblin, X., Buguin, A. Brochard-Wyart, F. 2004 Vibrated sessile drops: transition between pinned and mobile contact line oscillations. Eur. Phys. J. E 14, 395404.
Noblin, X., Buguin, A. & Brochard-Wyart, F. 2005 Triplon modes of puddles. Phys. Rev. Lett. 94, 166102.
Perlin, M. & Schultz, W. W. 2000 Capillary effects on surface waves. Annu. Rev. Fluid Mech. 32, 241274.
Pratt, W. K. 1978 Digital Image Processing. John Wiley.
Prosperetti, A. 1980 Free oscillations of drops and bubbles: the initial-value problem. J. Fluid Mech. 100, 333347.
Prosperetti, A. & Oguz, H. N. 1993 Impact of drops on liquid surfaces and the underwater noise of rain. Annu. Rev. Fluid Mech. 25, 577602.
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 2224.
Rayleigh, Lord 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. A 29, 7197.
Rodot, H., Bisch, C. & Lasek, A. 1979 Zero-gravity simulation of liquids in contact with a solid surface. Acta Astronaut. 6, 10831092.
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, 1726.
Simonelli, F. & Gollub, J. P. 1989 Surface wave mode interactions: effects of symmetry and degeneracy. J. Fluid Mech. 199, 471494.
Strani, M. & Sabetta, F. 1984 Free vibrations of a drop in partial contact with a solid support. J. Fluid Mech. 141, 233247.
Strani, M. & Sabetta, F. 1988 Viscous oscillations of a supported drop in an immiscible fluid. J. Fluid Mech. 189, 397421.
Trinh, E. & Wang, T. G. 1982 Large-amplitude free and driven drop-shape oscillations: experimental observations. J. Fluid Mech. 122, 315338.
Trinh, E., Zwern, A. & Wang, T. G. 1982 An experimental study of small-amplitude drop oscillations in immiscible liquid systems. J. Fluid Mech. 115, 453474.
Tsamopoulos, J. H. & Brown, R. A. 1983 Nonlinear oscillations of inviscid drops and bubbles. J. Fluid Mech. 127, 519537.
Vukasinovic, B. 2002 Vibration-induced droplet atomization. PhD thesis, Georgia Institute of Technology.
Vukasinovic, B., Smith, M. K. & Glezer, A. 2007 Mechanisms of free-surface breakup in vibration-induced liquid atomization. Phys. Fluid. 19, 012104.
Wilkes, E. D. & Basaran, O. A. 1997 Forced oscillations of pendant (sessile) drops. Phys. Fluid. 9, 15121528.
Wilkes, E. D. & Basaran, O. A. 1999 Hysteretic response of supported drops during forced oscillations. J. Fluid Mech. 393, 333356.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed