Dynamics of a sessile drop in forced vibration

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.

Using laser Doppler vibrometry to measure capillary surface waves on fluid-fluid interfaces

“…6,7 Although others have tried controlling the appearance of such waves 8,9 or have considered more complex excitation schemes, 10 the difficulty of accurately measuring the characteristics of the wave while adequately controlling the boundary conditions has limited researchers to work on frequencies of at most a few thousand of hertz. 11 However, there are many practical applications of such capillary waves driven at far higher frequencies-a few to even several hundreds of megahertz-from the production of nanoparticles 12,13 to pulmonary drug delivery 14,15 via atomization, a process believed to occur due to Faraday wave instabilities driven to eventually eject droplets with a size roughly corresponding to one-half the wavelength of the capillary wave. 16 Therefore, by increasing the excitation frequency, f, the capillary wavelength and therefore the droplet size, d, is reduced according to d ϳ f −2/3 .…”

Footprint geometry and sessile drop resonance

“…For both, typical observables are mode shapes [11,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], resonance frequencies [11,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], and the evolution of surface waves with forcing amplitude [18,23,[29][30][31][33][34][35]. The free surface waves oscillate at the forcing frequency (harmonically) when the forcing acceleration is low.…”

“…The free surface waves oscillate at the forcing frequency (harmonically) when the forcing acceleration is low. However, an elevated acceleration triggers modes which oscillate at half the forcing frequency [15,18,19,21,[30][31][32], called half-frequency subharmonic modes.…”

“…This has been identified as a parametric response, often modeled by the Mathieu-Hill equation [15,18,19,25,31,32,36,37]. These common features apparently imply that resonance of drops and Faraday waves are closely related, although they have been separate studies in the literature mostly.…”

Bubble dynamics atop an oscillating substrate: Interplay of compressibility and contact angle hysteresis

“…[1][2][3][4][5][6][7] While the ability to predict the contact line motion and, therefore, to control the wetting processes is generally important for technological applications, 8,9 these setups can also be used to manipulate small droplets over surfaces. [10][11][12] Instead of substrate vibrations, oscillations of drops and bubbles can be induced by electrowetting, see Refs.…”