The non-linear break-up of an inviscid liquid jet using the spatial-instability method

Busker, DP; Lamers, Apgg Anton; Nieuwenhuizen, JK

doi:10.1016/0009-2509(89)85074-2

Cited by 9 publications

(3 citation statements)

References 15 publications

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“…The fine structure at the point of breakup, including necking and satellite formation under both jetting and low-velocity dripping conditions (where jets do not form but pendant shapes emerge, neck and detach from a nozzle), has been the subject of several further experimental studies (Pimbley & Lee 1977;Chaudhary & Maxworthy 1980b;Peregrine, Shoker & Symon 1990;Vassallo & Ashgriz 1991;Basaran & Zhang 1995;Kowalewski 1996;Clanet & Lasheras 1999). Theoretical efforts, including a series of weakly nonlinear (Wang 1968;Yuen 1968;Nayfeh 1970;Lafrance 1975;Chaudhary & Redekopp 1980;Busker, Lamers & Nieuwenhuizen 1989), fully nonlinear numerical (Mansour & Lundgren 1990;Tjahjadi, Stone & Ottino 1992;Zhang & Stone 1997;Zhang 1999) and nonlinear one-dimensional or slender body studies (Lee 1974;Pimbley 1976;Bogy 1978;Bogy, Shine & Talke 1980;Bousfield & Denn 1987;Wilson 1988;Ting & Keller 1990;Eggers 1993;Schulkes 1993;Eggers & Dupont 1994;Bechtel, Carlson & Forest 1995;Eggers 1995;Brenner et al 1997), have captured some of the details of the breakup.…”

Section: Introductionmentioning

confidence: 99%

Temporal instability of compound threads and jets

et al. 2000

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Compound threads and jets consist of a core liquid surrounded by an annulus of a second immiscible liquid. Capillary forces derived from axisymmetric disturbances in the circumferential curvatures of the two interfaces destabilize cylindrical base states of compound threads and jets (with inner and outer radii R1 and aR1 respectively). The capillary instability causes breakup into drops; the presence of the annular phase allows both the annular- and core-phase properties to influence the drop size. Of technological interest is breakup where the core snaps first, and then the annulus. This results in compound drops. With jets, this pattern can form composite particles, or if the annular fluid is evaporatively removed, single drops whose size is modulated by both fluids.This paper is a study of the linear temporal instability of compound threads and jets to understand how annular fluid properties control drop size in jet breakup, and to determine conditions which favour compound drop formation. The temporal dispersion equation is solved numerically for non-dimensional annular thicknesses a of order one, and analytically for thin annuli (a – 1 = ε [Lt ] 1) by asymptotic expansion in ε. There are two temporally growing modes: a stretching mode, unstable for wavelengths greater than the undisturbed inner circumference 2πR1, in which the two interfaces grow in phase; and a squeezing mode, unstable for wavelengths greater than 2πaR1, which grows exactly out of phase. Growth rates are always real, indicating that in jetting configurations disturbances convect downstream with the base velocity. For order-one thicknesses, the growth rate of the stretching mode is higher for the entire range of system parameters examined. The drop size scales with the wavenumber of the maximally growing wave (kmax). We find that for the dominant stretching mode and a = 2, variations from 0.1 to 10 in the ratios of the annulus to core viscosity, or the tension of the outer surface to that of the inner interface, can result in changes in kmax by a factor of approximately 2. However, for these changes in the system ratios, the growth rate (smax) and the ratio of the amplitude of the outer to the inner interface (Amax) for the fastest growing wave only change marginally, with Amax near one. The system appears most sensitive to the ratio of the density of the annulus to the core fluid. For a variation between 0.1 and 10, kmax again changes by a factor of 2, but Amax and smax vary more significantly with large amplitude ratios for low density ratios. The amplitude ratio of the stretching mode at the maximally growing wave (Amax) indicates whether the film or core will break first. When this ratio is near one, linear theory predicts that the core breaks with the annulus intact, forming compound drops. Except for low values of the density ratio, our results indicate that most system conditions promote compound drop formation.For thin annuli, the growth rate disparity between modes becomes even greater. In the limit ε → 0, the squeezing growth rate is roughly proportional to ε2 while the stretching mode growth rate is roughly proportional to ε0 and asymptotes to a single jet with radius R1 and tension equal to the sum of the two tensions. Thus, in this limit the growth rate and kmax are independent of the film density and viscosity. The amplitude ratio of the stretching mode becomes equal to one for all wavenumbers; so thin films break as compound drops. Our results compare favourably with previously published measurements on unstable waves in compound jets.

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Section: Introductionmentioning

confidence: 99%

Temporal instability of compound threads and jets

et al. 2000

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“…They observed that disturbances on the jet surface can grow in space rather than with time, where k is assumed to be complex, while ω is purely imaginary. According to Busker, Lamers, and Nieuwenhuizen, 35 the spatial instability can better describe the physical process of the liquid jet breakup. Spatial instability can also be used to simulate satellite formation before or after the main droplet formation based on the disturbance amplitude.…”

Section: B Spatial Instability Analysismentioning

confidence: 99%

Absolute instability of free-falling viscoelastic liquid jets with surfactants

Alhushaybari

Uddin

2020

Physics of Fluids

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Where a licence is displayed above, please note the terms and conditions of the licence govern your use of this document. When citing, please reference the published version. Take down policy While the University of Birmingham exercises care and attention in making items available there are rare occasions when an item has been uploaded in error or has been deemed to be commercially or otherwise sensitive.

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“…They observed that disturbances on the jet surface can grow in space rather than with time, where k is assumed to be complex, while ω is purely imaginary. According to Busker, Lamers, and Nieuwenhuizen, 40 the spatial instability can better describe the physical process of the liquid jet breakup. Spatial instability can also be used to simulate satellite formation before or after the main droplet formation based on the disturbance amplitude.…”

Section: B Spatial Instability Analysismentioning

confidence: 99%

Convective and absolute instability of viscoelastic liquid jets in the presence of gravity

Alhushaybari

Uddin

2019

Physics of Fluids

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The convective and absolute instability of a viscoelastic liquid jet falling under gravity is examined for axisymmetrical disturbances. We use the upper-convected Maxwell model to provide a mathematical description of the dynamics of a viscoelastic liquid jet. An asymptotic approach, based on the slenderness of the jet, is used to obtain the steady state solutions. By considering traveling wave modes, we derive a dispersion relation relating the frequency to the wavenumber of disturbances which is then solved numerically using the Newton-Raphson method. We show the effect of changing a number of dimensionless parameters, including the Froude number, on convective and absolute instability. In this work, we use a mapping technique developed by Kupfer, Bers, and Ram ["The cusp map in the complex-frequency plane for absolute instabilities," Phys. Fluids 30, 3075-3082 (1987)] to find the cusp point in the complex frequency plane and its corresponding saddle point (the pinch point) in the complex wavenumber plane for absolute instability. The convective/absolute instability boundary is identified for various parameter regimes.

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The non-linear break-up of an inviscid liquid jet using the spatial-instability method

Cited by 9 publications

References 15 publications

Temporal instability of compound threads and jets

Temporal instability of compound threads and jets

Absolute instability of free-falling viscoelastic liquid jets with surfactants

Convective and absolute instability of viscoelastic liquid jets in the presence of gravity

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