The role of capillary waves in two-fluid atomization

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Abstract
A mechanistic study of two-fluid atomization has been carried out using a new spray technique called ultrasound-modulated two-fluid (UMTF) atomization. This technique is based on resonance between the liquid capillary waves generated by ultrasound and those generated by high-velocity air. Specifically, capillary waves are established on the surface of a liquid jet as it issues from a coaxial two-fluid atomizer, the nozzle tip of which vibrates at the same frequency as the ultrasound while the frequency of the capillary waves is only half of the ultrasound frequency. As these capillary waves travel downstream in the direction of air flow, their amplitude is further amplified by the air flowing around them. Atomization occurs when the wave amplitude becomes too great to maintain wave stability; the resulting drop sizes are proportional to the wavelength of the resonant capillary waves which is determined by the harmonic frequency of the ultrasound in accordance with the Kelvin equation. Theoretical calculations of the amplitude growth rate are based on two models of temporal instability of wind-generated capillary waves: Taylor’s dispersion relation and Jeffreys’ one-parameter (sheltering factor) model. Good agreements between the theoretical predictions by these models and the experimental results of how drop-size and size distributions are influenced by air velocity and surface tension led to the conclusion that Taylor-mode breakup of capillary waves plays a very important role in two-fluid atomization. Furthermore, all peak drop diameters can be accounted for by the harmonic frequencies of the ultrasound. Hence, it is further concluded that secondary atomization is negligible in co-flow two-fluid atomization of a water jet at air velocities up to 170 m/s and air-to-water mass ratio up to 5.6. In addition, uniform drops with diameters predetermined by the ultrasound frequency can be accomplished by adjusting the air velocity.

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