Drop Formation from a Liquid Jet: A Linear One-dimensional Analysis Considered as a Boundary Value Problem

Pimbley, W. T.

doi:10.1147/rd.202.0148

Cited by 60 publications

(30 citation statements)

References 6 publications

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“…To understand their significance, one has to consider the full problem in halfspace, with boundary conditions at the nozzle. This was attempted in a series of papers (Pimbley, 1976;Bogy 1978aBogy , 1978bBogy , 1979b, which correctly analyzed the problem for large Weber numbers. However, the authors failed to notice the absolute instability later found by Leib and Goldstein (1986) for small ␤.…”

Section: B Spatial Instabilitymentioning

confidence: 99%

“…This allowed him to look at the nonuniformity of breakup and to estimate the size of satellite drops. Lee's equations were further investigated (Pimbley, 1976;Pimbley and Lee, 1977) to study satellite behavior. The fundamental problem with Lee's equations is, however, that viscosity will become important in the process of pinching, regardless of how small.…”

Section: One-dimensional Approximationsmentioning

confidence: 99%

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Nonlinear dynamics and breakup of free-surface flows

1997

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Surface-tension-driven flows and, in particular, their tendency to decay spontaneously into drops have long fascinated naturalists, the earliest systematic experiments dating back to the beginning of the 19th century. Linear stability theory governs the onset of breakup and was developed by Rayleigh, Plateau, and Maxwell. However, only recently has attention turned to the nonlinear behavior in the vicinity of the singular point where a drop separates. The increased attention is due to a number of recent and increasingly refined experiments, as well as to a host of technological applications, ranging from printing to mixing and fiber spinning. The description of drop separation becomes possible because jet motion turns out to be effectively governed by one-dimensional equations, which still contain most of the richness of the original dynamics. In addition, an attraction for physicists lies in the fact that the separation singularity is governed by universal scaling laws, which constitute an asymptotic solution of the Navier-Stokes equation before and after breakup. The Navier-Stokes equation is thus continued uniquely through the singularity. At high viscosities, a series of noise-driven instabilities has been observed, which are a nested superposition of singularities of the same universal form. At low viscosities, there is rich scaling behavior in addition to aesthetically pleasing breakup patterns driven by capillary waves. The author reviews the theoretical development of this field alongside recent experimental work, and outlines unsolved problems. [S0034-6861(97)00303-6] CONTENTS

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Section: B Spatial Instabilitymentioning

confidence: 99%

Section: One-dimensional Approximationsmentioning

confidence: 99%

Nonlinear dynamics and breakup of free-surface flows

1997

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“…By application of the continuity principle to a control volume bounded by two contiguous cross-sections and the corresponding interface, the following result is obtained: Before pursuing the matter further, it would be pertinent to introduce some considerations on the assumption of the unidimensionality of the problem. This assumption is well justified in capillary jets whenever the ratio of the disturbance wavelength to the undisturbed radius of the jet is large (Pimbley 1976;Pimbley & Lee 1977). In the liquid bridge, a typical wavelength perturbation is determined by the bridge length, and the abovementioned ratio is of the order of twice the slenderness A, which is bounded from above by the value A = n.…”

Section: One-dimensional Slice Inviscid Modelmentioning

confidence: 99%

The breaking of axisymmetric slender liquid bridges

Meseguer

1983

J. Fluid Mech.

121

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Liquids held by surface tension forces can bridge the gap between two solid bodies placed not too far apart from each other. The equilibrium conditions and stability criteria for static, cylindrical liquid bridges are well known. However, the behaviour of an unstable liquid bridge, regarding both its transition toward breaking and the resulting configuration, is a matter for discussion. The dynamical problem of axisymmetric rupture of a long liquid bridge anchored at two equal coaxial disks is treated in this paper through the adoption of one-dimensional theories which are widely used in capillary jet problems.

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“…The classical breakup driven by the Rayleigh mechanism [19] is caused by the amplification of shape defects due to surface tension effect. Unlike the classical breakup, the forced breakup that is influenced by the discharge velocity modulation based on the Pimbley's theoretical analysis [20] is dominantly caused by the periodical inertial dynamics of the liquid jet. While in the case of passive modulation, where especially acoustic resonance is employed [21], [22], relatively small depth of modulation is achieved and technically significant increase in erosive effects has not been proven yet, significant progress has been achieved using methods of an active flow modulation around the nozzle.…”

Section: Experience With Generating Pulsed Liquid Jet Gathered So Farmentioning

confidence: 99%

Pulsed water jet generated by pulse multiplication

2016

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Original scientific paper First theoretical papers, summarizing the high mechanical energy cumulation when high-speed drops impact on the solid surface as a result of the water hammer effect, have been known since 1960's. Heymann has demonstrated that pressure maximum during the impact of a spherical drop of a liquid is several times higher than the presupposed maximum for the classical waterhammer effect. The mentioned maximum pressure exceeds the stagnation pressure of the continuous jet several times over. When developing devices for pulsed jet generation, a new generalization of the classical water hammer theory for high pressures has been introduced. Based on this a new patented principle of "pulse multiplication" has been formulated. The pulse multiplier is the source of high-pressure pulses with 100 % depth of modulation of discharge velocity of a liquid jet. It enables to significantly increase the jet disintegration effect without addition of abrasives.Keywords: high-pressure pulses; pulse intensifier; pulsed water jet; water hammer effect Pulsirajući vodeni mlaz dobiven multiplikacijom impulsaIzvorni znanstveni članak Prvi teorijski radovi, koji su opisivali stvaranje velike količine mehaničke energije kad kapljice velike brzine udare u čvrstu površinu kao rezultat hidrauličkog udara, poznati su još od 1960-tih. Heymann je pokazao da je maksimalni tlak kod udara loptaste kapljice tekučine nekoliko puta veći od pretpostavljenog maksimalnog u slučaju klasičnog hidrauličkog udara. Spomenuti maksimalni tlak nekoliko je puta veći od tlaka kontinuiranog mlaza u stanju mirovanja. Kod stvaranja uređaja za generiranje pulsirajućeg mlaza, za visoke je tlakove uvedena nova generalizacija klasične teorije hidrauličkog udara. Na tom je temelju zasnovan novi patentirani princip "multiplikacije impulsa". Multiplikator impulsa je izvor visokotlačnih impulsa sa 100 % dubinom modulacije izlazne brzine tekućeg mlaza. Omogućuje značajno povećanje dezintegracijskog učinka mlaza bez dodavanja abraziva.Ključne riječi: pojačavač impulsa; pulsirajući vodeni mlaz; rezultat hidrauličkog udara; visokotlačni impulsi

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Drop Formation from a Liquid Jet: A Linear One-dimensional Analysis Considered as a Boundary Value Problem

Cited by 60 publications

References 6 publications

Nonlinear dynamics and breakup of free-surface flows

Nonlinear dynamics and breakup of free-surface flows

The breaking of axisymmetric slender liquid bridges

Pulsed water jet generated by pulse multiplication

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