One-dimensional linear analysis of the compound jet

Sanz, A.; Meseguer, José

doi:10.1017/s0022112085003093

Cited by 51 publications

(27 citation statements)

References 16 publications

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“…In their temporal analysis, these authors found two spatially unstable modes, stretching and squeezing, similar to those determined in previous studies. 47,48 They reported that the stretching mode yields a higher growth rate s, and thus would dominate the breakup dynamics if linear analysis were valid until pinch-off and the stretching mode were present in the initial perturbation. In their spatial analysis, they showed that the compound jet is unstable for small jet velocities and admits a convectively growing instability for larger velocities.…”

Section: Dynamics Of Compound Jetsmentioning

confidence: 99%

Nonlinear dynamics and breakup of compound jets

2006

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Finite-amplitude deformation and breakup of a compound jet, whose core and shell are both incompressible Newtonian fluids, that is surrounded by a passive gas are analyzed computationally by a temporal analysis. The means is a method of lines algorithm in which the Galerkin/finite element method with elliptic mesh generation is used for spatial discretization and an adaptive finite difference method is employed for time integration. The dynamics are initiated by subjecting the inner and the outer interfaces of a quiescent compound jet to axially periodic perturbations that are either in phase ͑ =0͒ or radians out phase ͑ = ͒, where is the phase shift between the disturbances imposed on the two interfaces. The initial growth rates of disturbances obtained from computations are compared and demonstrated to be in excellent agreement with predictions of linear theory ͓Chauhan et al., J. Fluid Mech. 420, 1 ͑2000͔͒. Computations reveal that recirculating flows occur commonly during the deformation and pinch-off of compound jets, and hence render inapplicable the use of slender-jet type approximations for analyzing the dynamics in such cases. Moreover, as the deformations of one or both of the interfaces of the compound jet grow, the resulting shapes at the incipience of pinch-off are asymmetric and lead to the formation of satellite drops. Calculations are carried out over a wide range of Reynolds numbers of the core fluid, ratios of the viscosity and density of the shell fluid to those of the core fluid, ratio of the surface tension of the outer interface to the interfacial tension of the inner interface, the ratio of the unperturbed radius of the outer cylindrical interface to that of the inner cylindrical interface, wavenumber, and perturbation amplitudes to determine their effects on breakup time and whether both interfaces pinch at the same instant in time to result in the formation of compound drops. Conditions are also identified for which the dynamical response of compound jets subjected to initial perturbations with = 0 differ drastically from those subjected to ones with = .

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Section: Dynamics Of Compound Jetsmentioning

confidence: 99%

Nonlinear dynamics and breakup of compound jets

2006

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“…3, where the four solutions of (22) are shown, of which two are growing modes, which is similar to what is seen for an uniform inviscid compound jet, as found by Sanz and Meseguer. 1 Of the two unstable modes, it is typically assumed that breakup of the jet is caused by the mode with the largest growth rate and throughout this work we will focus our attention on this mode and we refer to it as the most unstable mode. In such a case, it can be seen that there is a value of the wavenumber k, at which the growth rate is maximal-we refer to this value as the most unstable wavenumber and denote it by k max .…”

Section: Resultsmentioning

confidence: 99%

“…6-10, for x = 0, is the same as illustrated in Sanz and Meseguer. 1 Using the results from our temporal instability analysis, we may determine the profile of waves travelling along both the inner and outer interfaces. In order to do this, we first need to evaluate an expression for timet (in Eqs.…”

Section: Resultsmentioning

confidence: 99%

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Temporal instability analysis of inviscid compound jets falling under gravity

et al. 2013

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“…18 There have also been linear stability studies that begin with model onedimensional equations, and perform a linear stability analysis of the simplified system. For example, Sanz and Meseguer 19 consider inviscid compound jets and write down a onedimensional model produced using the ideas of Lee. 20 The model is based on long wave asymptotics and raises certain consistency issues-for a consistent evaluation of such models as well as a comparison of solutions they produce; see Papageorgiou and Orellana.…”

Section: Introductionmentioning

confidence: 99%

Pinchoff and satellite formation in compound viscous threads

Matar

Papageorgiou

2003

Physics of Fluids

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The breakup of viscous compound threads in the presence of insoluble surfactant at both interfaces is investigated. We use asymptotic methods in the limit of long axisymmetric waves to derive a coupled system of five one-dimensional ͑1-D͒ partial differential equations governing the evolution of the outer and inner interfaces, the surfactant concentrations there, and the leading order axial velocity component in the jet. The linear, and nonlinear, stability of these equations is then investigated for a wide range of outer to inner viscosity ratio, m, outer to inner surface tension ratio, ␥, the ratio of initial outer to inner radii, ␣, initial surfactant concentrations at the outer and inner interfaces, ⌫ 1 0 and ⌫ 2 0 , surfactant activities, ␤ 1 and ␤ 2 , and the Schmidt numbers, Sc 1 and Sc 2 , defined as the ratio of the kinematic viscosity to the surfactant surface diffusion coefficient. We also show that if Sc 1 ϭSc 2 , these results are recovered via solution of 1-D evolution equations governing the dynamics of an effective single surfactant covered thread, which are obtained through appropriate rescalings; these rescalings are detailed herein.

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One-dimensional linear analysis of the compound jet

Cited by 51 publications

References 16 publications

Nonlinear dynamics and breakup of compound jets

Nonlinear dynamics and breakup of compound jets

Temporal instability analysis of inviscid compound jets falling under gravity

Pinchoff and satellite formation in compound viscous threads

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