Threshold Dynamics of Singular Gravity-Capillary Waves

Goodridge, Christopher L.; Shi, W.; Lathrop, Daniel P.

doi:10.1103/physrevlett.77.4692

Cited by 15 publications

(25 citation statements)

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“…Jiang, Perlin & Schultz (1998) and Jiang, Ting, Perlin & Schultz (1996) demonstrated the breaking scenario of parametrically forced two-dimensional gravity waves. Goodridge, Shi & Lathrop (1996); Goodridge, Tao Shi, Hentschel & Lathrop (1997) and Goodridge, Hentschel & Lathrop (1999) determined the drop ejection threshold acceleration for capillary waves in water and glycerin-water mixtures up to driving frequencies of 100 Hz, but did not investigate the wave pattern at large ǫ. The critical driving acceleration for the onset of drop ejection given by Goodridge et al (1996Goodridge et al ( , 1997Goodridge et al ( , 1999 is…”

Section: Introductionmentioning

confidence: 99%

Evolution and breaking of parametrically forced capillary waves in a circular cylinder

Puthenveettil

Hopfinger

2009

J. Fluid Mech.

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We present results on parametrically forced capillary waves in a circular cylinder, obtained in the limit of large fluid depth, using two low-viscosity liquids whose surface tensions differ by an order of magnitude. The evolution of the wave patterns from the instability to the wave-breaking threshold is investigated in a forcing frequency range (f= ω/2π = 25–100 Hz) that is around the crossover frequency (ωot) from gravity to capillary waves (ωot/2≤ω/2≤4ωot). As expected, near the instability threshold the wave pattern depends on the container geometry, but as the forcing amplitude is increased the wave pattern becomes random, and the wall effects are insignificant. Near breaking, the distribution of random wavelengths can be fitted by a Gaussian. A new gravity–capillary scaling is introduced that is more appropriate, than the usual viscous scaling, for low-viscosity fluids and forcing frequencies <103Hz. In terms of these scales, a criterion is derived to predict the crossover from capillary- to gravity-dominated breaking. A wave-breaking model is developed that gives the relation between the container and the wave accelerations in agreement with experiments. The measured drop size distribution of the ejected drops above the breaking threshold is well approximated by a gamma distribution. The mean drop diameter is proportional to the wavelength determined from the dispersion relation; this wavelength is also close to the most likely wavelength of the random waves at drop ejection. The dimensionless drop ejection rate is shown to have a cubic power law dependence on the dimensionless excess acceleration ε′dan inertial–gravitational ligament formation model is consistent with such a power law.

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Section: Introductionmentioning

confidence: 99%

Evolution and breaking of parametrically forced capillary waves in a circular cylinder

Puthenveettil

Hopfinger

2009

J. Fluid Mech.

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“…Sorokin (1957) observed droplet ejection experimentally. Goodridge, Shi & Lathrop (1996) performed experiments in which a layer of liquid was oscillated vertically and droplets were ejected from the liquid surface. The forcing amplitude threshold for droplet ejection was measured.…”

Section: Introductionmentioning

confidence: 99%

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

2003

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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 forcing 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.

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“…In Figure 3, the angle at the contact line can be used for representing the balance of forces resulting from intermolecular forces between solid, liquid and gas phases. The tangential component of the resulting force at the contact line (F R ) is shown in Equation (13). In static equilibrium, Equation (13) leads to the well-known Young-Laplace equation as given in Equation (14).…”

Section: Contact Line Treatmentmentioning

confidence: 99%

“…The given static contact angle is represented by 0 , and is the present contact angle at an instant. In this approach, the force at the contact line is obtained by plugging Equation (14) into Equation (13). This contact line force in Equation (15) accelerates or decelerates flow fields, and makes the present contact angle ( ) approach the prescribed static contact angle ( 0 ) asymptotically.…”

Section: Contact Line Treatmentmentioning

confidence: 99%

Interfacial flow computations using adaptive Eulerian–Lagrangian method for spacecraft applications

Sim

Shyy

2010

Numerical Methods in Fluids

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SUMMARY Understanding the interfacial dynamics and fluid physics associated with the operation of spacecraft is important for scientific as well as engineering purposes. To help address the issues associated with moving boundaries, interfacial dynamics, and spatial‐temporal variations in time and length scales, a 3‐D adaptive Eulerian–Lagrangian method is extended and further developed. The stationary (Eulerian) Cartesian grid is adopted to resolve the fluid flow, and the marker‐based triangulated moving (Lagrangian) surface meshes are utilized to treat the phase boundary. The key concepts and numerical procedures, along with the selected interfacial flow problems are presented. Specifically, the liquid fuel draining dynamics in different flow regimes, and the liquid surface stability under vertically oscillating gravitational acceleration are investigated. Direct assessment of experimental measurement and scaling analysis is made to highlight the computational performance of the present approach as well as the key fluid physics influenced by the given flow parameters. Copyright © 2010 John Wiley & Sons, Ltd.

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Threshold Dynamics of Singular Gravity-Capillary Waves

Abstract: A factor of 2p was inadvertently omitted in Eq. (3), which should read a c 2.39͑v͞2p͒ 4͞3 ͑s͞r͒ 1͞3 .(4692 0031-9007͞96͞77(22)͞4692(1)$10.00

Cited by 15 publications

References 0 publications

Evolution and breaking of parametrically forced capillary waves in a circular cylinder

Evolution and breaking of parametrically forced capillary waves in a circular cylinder

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

Interfacial flow computations using adaptive Eulerian–Lagrangian method for spacecraft applications

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