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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.

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L. Landau & E. M. Lifshitz 1987 Fluid Mechanics. 2nd edn, Pergamon.

A. W. Leissa & Y. T. Chern 1992 Approximate analysis of the forced vibration response of plates. J. Vib. Acousts Trans. ASM. 114, 106111.

D. V. Lyubimov , T. P. Lyubimova & S. V. Shklyaev 2006 Behaviour of a drop on an oscillating solid plate. Phys. Fluid. 18, 012101.

J. Miles & D. Henderson 1990 Parametrically forced surface waves. Annu. Rev. Fluid Mech. 22, 143165.

M. Perlin & W. W. Schultz 2000 Capillary effects on surface waves. Annu. Rev. Fluid Mech. 32, 241274.

Lord Rayleigh 1879 On the capillary phenomena of jets. Proc. R. Soc. Lond. A 29, 7197.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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