A liquid drop placed on a vibrating diaphragm will burst into a fine spray of smaller secondary droplets if it is driven at the proper frequency and amplitude. The process begins when capillary waves appear on the free surface of the drop and then grow in amplitude and complexity as the acceleration amplitude of the diaphragm is slowly increased from zero. When the acceleration of the diaphragm rises above a well-defined critical value, small secondary droplets begin to be ejected from the free-surface wave crests. Then, quite suddenly, the entire volume of the drop is ejected from the vibrating diaphragm in the form of a spray. This event is the result of an interaction between the fluid dynamical process of droplet ejection and the vibrational dynamics of the diaphragm. During droplet ejection, the effective mass of the drop–diaphragm system decreases and the resonance frequency of the system increases. If the initial forcing frequency is above the resonance frequency of the system, droplet ejection causes the system to move closer to resonance, which in turn causes more vigorous vibration and faster droplet ejection. This ultimately leads to drop bursting. In this paper, the basic phenomenon of vibration-induced drop atomization and drop bursting will be introduced, demonstrated, and characterized. Experimental results and a simple mathematical model of the process will be presented and used to explain the basic physics of the system.

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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The mechanisms of droplet formation that take place during vibration-induced drop atomization are investigated experimentally. Droplet ejection results from the breakup of transient liquid spikes that form following the localized collapse of free-surface waves. Breakup typically begins with capillary pinch-off of a droplet from the tip of the spike and can be followed by additional pinch-offs of satellite droplets if the corresponding capillary number is sufficiently small (e.g., in low-viscosity liquids). If the capillary number is increased (e.g., in viscous liquids), breakup first occurs near the base of the spike, with or without subsequent breakup of the detached, thread-like spike. The formation of these detached threads is governed by a breakup mechanism that is separated from the tip-dominated capillary pinch-off mechanism by an order of magnitude in terms of dimensionless driving frequency f*. The dependence of breakup time and unbroken spike length on fluid and driving parameters is established over a broad range of dimensionless driving frequencies (10−3<f*<1). It is also shown that the droplet-ejection acceleration threshold âc of low-viscosity liquids depends on the dimensionless drop diameter d̂. Moreover, in the limit d̂⩾20, the droplet-ejection threshold becomes independent of d̂ (âc≈4). This limit state is described by a scaling equivalent to that of Goodridge, Shi, and Lathrop [Phys. Rev. Lett. 76, 1824 (1996)] derived for the onset of droplet ejection from Faraday waves. It is shown in the present study that the acceleration threshold in this limit scales like ac∼f4∕3(σ∕ρ)1∕3.

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