Nonlinear breakup of a laminar liquid jet

Lafrance, Pierre

doi:10.1063/1.861168

Cited by 143 publications

(69 citation statements)

References 10 publications

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“…This observation is considered today as the first prediction of the formation of satellite drops. Good agreement of the predictions of his model with experimental results was found for the deviation of the jet surface shape from the single sinusoidal one [9], the satellite drop size [10,11] and the growth rate of the two first nonlinear harmonics for wave numbers less than the fastest growing mode [12]. For larger wave numbers (more precisely, greater than the fastest growing mode), Yuen's model does not predict the formation of satellite drops, even though they are still observed in the experiment [10].…”

supporting

confidence: 58%

Weakly nonlinear instability of a viscous liquid jet

Renoult¹,

Brenn²,

Mutabazi³

2017

Proceedings ILASS–Europe 2017. 28th Conference on Liquid Atomization and Spray Systems

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A weakly nonlinear stability analysis of an axisymmetric viscous liquid jet is performed. The calculation is based on a small-amplitude perturbation method and restricted to second order. Contrary to the inviscid jet and the planar viscous sheet cases studied by Yuen in 1968 [1] and Yang et al. in 2013 [2], respectively, a part of the solution results from a polynomial approximation of Bessel functions. Results on interface shapes for a small wave number and initial perturbation amplitude, four different Ohnesorge numbers, taking into account the approximate part or not, are used to predict the influence of liquid viscosity on satellite drop formation and evaluate the influence of the approximation. It is observed that the liquid viscosity has a retarding effect on satellite drop formation, in agreement with previous experimental and numerical work. In addition, it is found that the approximate terms can be reasonably ignored, providing a simpler viscous weakly nonlinear model for the description of the first nonlinearity growth in liquid jets. The present work replaces the ILASS 2016 paper [3] by the authors on the same subject. KeywordsViscous liquid jet, nonlinear capillary instability, satellite drop formation. IntroductionA liquid jet breaks up forming main and satellite drops. The present work is concerned with the influence of both liquid viscosity and nonlinearities on satellite drop formation. The first linear stability analysis of the capillary instability of a liquid jet in an ambient medium was conducted by Rayleigh [4,5], more than a century ago. In this reference work, the liquid is assumed inviscid and the ambient medium is the vacuum. His analysis shows that, in order to destabilize the jet, the wavelength λ of a varicose surface disturbance must be greater than the circumference of the undeformed circular jet cross section, as observed initially by Savart and Plateau [6,7]. Two associated amplitude growth rates correspond to such an unstable perturbation wavelength, one being the opposite of the other, with the magnitude given by the well-known Rayleigh's linear dispersion relation for the inviscid jet in a vacuum. The effect of liquid viscosity was then investigated by Weber [8], about fifty years later. The generalization of the previous dispersion relation introduces a growth rate and viscosity dependent modified wave number making the dispersion relation transcendental, yet numerically solvable, which is turned into a closed-form expression in the long-wave approximation. Contrary to the inviscid case, there are two different real growth rates with opposite signs for each unstable wavelength, with distinct absolute values below the corresponding inviscid one. This difference leads to dispersion relation curves always lower than the inviscid ones, as expected by the classical damping effect inferred from liquid viscosity. Due to the linearity of the previous analysis, the interaction of disturbances with different wavelengths is not accounted for, and the drops produced by the jet br...

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supporting

confidence: 58%

Weakly nonlinear instability of a viscous liquid jet

Renoult¹,

Brenn²,

Mutabazi³

2017

Proceedings ILASS–Europe 2017. 28th Conference on Liquid Atomization and Spray Systems

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“…The problem was first studied experimentally by Plateau [24] and later theoretically by Lord Rayleigh [25], and is currently referred to as Rayleigh-Plateau (RP) instability. The RP instability has been extensively studied experimentally, theoretically, and numerically [24][25][26][27]. Moreover, the problem is fully axisymmetric and therefore suitable for the validation of our multiphase axisymmetric LBM model.…”

Section: Rayleigh-plateau (Rp) Instabilitymentioning

confidence: 99%

Axisymmetric multiphase lattice Boltzmann method

et al. 2013

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A lattice Boltzmann method for axisymmetric multiphase flows is presented and validated. The method is capable of accurately modeling flows with variable density. We develop the classic Shan-Chen multiphase model [Phys. Rev. E 47, 1815(1993] for axisymmetric flows. The model can be used to efficiently simulate single and multiphase flows. The convergence to the axisymmetric Navier-Stokes equations is demonstrated analytically by means of a Chapmann-Enskog expansion and numerically through several test cases. In particular, the model is benchmarked for its accuracy in reproducing the dynamics of the oscillations of an axially symmetric droplet and on the capillary breakup of a viscous liquid thread. Very good quantitative agreement between the numerical solutions and the analytical results is observed.

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“…It may be noted that Rayleigh's original analysis predicts only the onset of breakup and not the formation of satellite droplets. To predict analytically satellite droplet formation, it has been shown that at least a third-order perturbation analysis of the Navier-Stokes equations (NSE) is needed [36]. Computations based on direct solutions of the NSE also predict the formation of the satellite droplets.…”

Section: Resultsmentioning

confidence: 99%

Lattice Boltzmann model for axisymmetric multiphase flows

2005

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In this paper, a lattice Boltzmann (LB) model is presented for axisymmetric multiphase flows. Source terms are added to a two-dimensional standard lattice Boltzmann equation (LBE) for multiphase flows such that the emergent dynamics can be transformed into the axisymmetric cylindrical coordinate system. The source terms are temporally and spatially dependent and represent the axisymmetric contribution of the order parameter of fluid phases and inertial, viscous and surface tension forces. A model which is effectively explicit and second order is obtained. This is achieved by taking into account the discrete lattice effects in the Chapman-Enskog multiscale analysis, so that the macroscopic axisymmetric mass and momentum equations for multiphase flows are recovered self-consistently. The model is extended to incorporate reduced compressibility effects. Axisymmetric equilibrium drop formation and oscillations, breakup and formation of satellite droplets from viscous liquid cylindrical jets through Rayleigh capillary instability and drop collisions are presented. Comparisons of the computed results with available data show satisfactory agreement.

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Nonlinear breakup of a laminar liquid jet

Cited by 143 publications

References 10 publications

Weakly nonlinear instability of a viscous liquid jet

Weakly nonlinear instability of a viscous liquid jet

Axisymmetric multiphase lattice Boltzmann method

Lattice Boltzmann model for axisymmetric multiphase flows

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