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Vibration-induced drop atomization and the numerical simulation of low-frequency single-droplet ejection

ASHLEY J. JAMES, MARC K. SMITH, ARI GLEZER

2003
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Journal of Fluid Mechanics
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Vibration-induced droplet ejection is a novel way to create a spray. In this method, a liquid drop is placed on a vertically vibrating solid surface. The vibration leads to the formation of waves on the free surface. Secondary droplets break off from the wave crests when the forcing amplitude is above a critical value. When the forcing frequency is small, only low-order axisymmetric wave modes are excited, and a single secondary droplet is ejected from the tip of the primary drop. When the
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... ng frequency is high, many high-order non-axisymmetric modes are excited, the motion is chaotic, and numerous small secondary droplets are ejected simultaneously from across the surface of the primary drop. In both frequency regimes a crater may form that collapses to create a liquid spike from which droplet ejection occurs. An axisymmetric, incompressible, Navier-Stokes solver was developed to simulate the low-frequency ejection process. A volume-of-fluid method was used to track the free surface, with surface tension incorporated using the continuum-surface-force method. A time sequence of the simulated interface shape compared favourably with an experimental sequence. The dynamics of the droplet ejection process was investigated, and the conditions under which ejection occurs and the effect of the system parameters on the process were determined. the volume of the ejected droplet, the velocity of the ejected droplet, and the time at which ejection occurred are presented in § 4. The threshold forcing amplitude, above which ejection occurs, is discussed in § 5. Conclusions are presented in § 6. Computational method An axisymmetric, Navier-Stokes solver, based on a projection method, was designed to simulate the transient fluid mechanics of low-frequency, vibration-induced, droplet ejection. In the volume-of-fluid method, a volume fraction, F, is defined in each cell as the fraction of the cell volume that contains liquid. The volume fraction is convected with the flow to track the interface. The equations are solved in both the liquid drop and the surrounding gas. Surface tension is incorporated using the continuum-surfaceforce (CSF) method. In this method, surface-tension forces are included directly in the momentum equation. The majority of previous work using the VOF and CSF methods is in Cartesian geometry, but Beris et al. (1996) successfully used these methods in an axisymmetric geometry to study jet break-up. The axisymmetric governing equations are written in a reference frame that oscillates with the solid base. The equations are non-dimensionalized using a length scale that is the cube root of the drop volume, V. The velocity scale is σ/ρ L V 1/3 , the time scale is ρ L V/σ, and the pressure scale is σ/V 1/3 . The dimensionless density, ρ, and viscosity, µ, are scaled on the liquid properties, denoted by a subscript L. Gas properties are denoted by a subscript G. The surface tension coefficient is σ. After non-dimensionalization, the governing equations are

doi:10.1017/s0022112002002860
fatcat:xgcy5toisbahzenytoo5g6o4sm