Stability of initially slow viscous jets driven by gravity

Sauter, Ulrich; Buggisch, Hans

doi:10.1017/s002211200500412x

Cited by 51 publications

(79 citation statements)

References 29 publications

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“…Sauter & Buggisch 2005). Since the phenomena we will describe result from a dynamics which integrates over distances much larger than the jet initial radius, we use here (2.8) as a good approximation of the base flow everywhere.…”

Section: Base Flowmentioning

confidence: 99%

“…More precisely, we do not consider the global transition that leads to dripping and which has been studied elsewhere (Le Dizès 1997;Sauter & Buggisch 2005;Rubio-Rubio et al 2013). We are interested in the growth of the perturbations that give rise to the formation of droplets far away from the nozzle.…”

Section: Perturbationsmentioning

confidence: 99%

“…This amounts to calculate the maximum spatial gain that perturbations can exhibit at a given downstream location. For this purpose, we will consider two situations: (a) Fluctuations are mainly present at the nozzle as in laboratory experiments where the jet nozzle is vibrated for instance (Sauter & Buggisch 2005). In that case, we are interested in the spatial gain at z f of perturbations generated at the nozzle z = 0.…”

Section: Perturbationsmentioning

confidence: 99%

“…That question has been envisaged in the very viscous limit by Tomotika (1936), for the particular case where u increases linearly with z by Frankel & Weihs (1985, and more recently by Senchenko & Bohr (2005), Sauter & Buggisch (2005) and Javadi et al (2013) for a gravitationally accelerated jet.…”

Section: Introductionmentioning

confidence: 99%

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Capillary jet breakup by noise amplification

Dizès

Villermaux

2016

J. Fluid Mech.

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A liquid jet falling by gravity ultimately destabilizes by capillary forces. Accelerating as it falls, the jet thins and stretches, causing the capillary instability to develop on a spatially varying substrate. We discuss quantitatively the interplay between instability growth, jet thinning and longitudinal stretching for two kinds of perturbations, either solely introduced at the jet nozzle exit, or affecting the jet all along its length. The analysis is conducted for any values of the liquid properties for sufficiently large flow rate. In all cases, we determine the net gain of the most dangerous perturbation for all downstream distances, thus predicting the jet length, the wavelength at breakup and the resulting droplet size.

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Section: Base Flowmentioning

confidence: 99%

Section: Perturbationsmentioning

confidence: 99%

Section: Perturbationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Capillary jet breakup by noise amplification

Dizès

Villermaux

2016

J. Fluid Mech.

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“…Among them is the natural stretching encountered by a capillary jet falling under gravity. This simple configuration has been analysed in detail by Cheong & Howes (2004) and Sauter & Buggisch (2013) among others. The stretching that the jet experiences as it falls is believed to be responsible for the delay in break-up (Tomotika 1936).…”

Section: Introductionmentioning

confidence: 99%

Forced dynamics of a short viscous liquid bridge

2014

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The dynamics of an axisymmetric liquid bridge of a fluid of density ρ, viscosity µ and surface tension σ held between two co-axial disks of equal radius e is studied when one disk is slowly moved with a velocity U(t). The analysis is performed using a one-dimensional model for thin bridges. We consider attached boundary conditions (the contact line is fixed to the boundary of the disk), neglect gravity and limit our analysis to short bridges such that there exists a stable equilibrium shape. This equilibrium is a Delaunay curve characterized by the two geometric parameters 0 = V 0 /(πe 3 ) and S = (πe 2 )/V 0 , where V 0 is the volume of fluid and the length of the bridge. Our objective is to analyse the departure of the dynamical solution from the static Delaunay shape as a function of 0 , S, the Ohnesorge number Oh = µ/ √ ρσ e, and the instantaneous velocity U(t) and acceleration ∂ t U (non-dimensionalized using e and σ /ρ) of the disk. Using a perturbation theory for small velocity and acceleration, we show that (i) a non-homogeneous velocity field proportional to U(t) and independent of Oh is present within the bridge; (ii) the area correction to the equilibrium shape can be written as U 2 A i + U Oh A v + ∂ t UA a where A i , A v and A a are functions of 0 and S only. The characteristics of the velocity field and the shape corrections are analysed in detail. For the case of a cylinder (S = 1), explicit expressions are derived and used to provide some insight into the break-up that the deformation would induce. The asymptotic results are validated and tested by direct numerical simulations when the velocity is constant and when it oscillates. For the constant velocity case, we demonstrate that the theory provides a very good estimate of the dynamics for a large range of parameters. However, a systematic departure is observed for very small Oh due to the persistence of free eigenmodes excited during the transient. These same eigenmodes also limit the applicability of the theory to oscillating bridges with large oscillating periods. Finally, the perturbation theory is applied to the cylindrical solution of Frankel & Weihs (J. Fluid Mech., vol. 155 (1985), pp. 289-307) obtained for constant velocity U when the contact lines are allowed to move. We show that it can be used to compute the correction associated with acceleration. Finally, the effect of gravity is discussed and shown to modify the equilibrium shape but not the main results obtained from the perturbation theory.

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Draw ratio enhancement in nonisothermal melt spinning

Suman

Kumar

2009

AIChE Journal

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in Wiley InterScience (www.interscience.wiley.com).Nonisothermal melt spinning of materials having a step-like viscosity variation with temperature is studied in this work. A set of nonlinear equations is used to describe the fiber behavior and to obtain the draw ratio, the square of the ratio of the fiber diameter at the entrance to that at the exit of the fiber-spinning device. The fluid-flow equation is based on a slender-jet approximation, and external heating and cooling have been accounted for with a one-dimensional model in order to obtain the fiber temperature and viscosity along the fiber length. The model is similar to that used by Wylie et al. (J Fluid Mech. 2007;570:1-16) but accounts for inertia, shear stress at the fiber surface, surface tension, gravity, cooling, and larger heating rates. Steadystate analysis reveals that the draw ratio increases with an increase in the pulling force, passes through a maximum, and then starts increasing again, resulting in three possible pulling forces for the same draw ratio. However, linear stability analysis reveals that depending on the strength of heating and/or cooling, at most two of the steady states are stable. The stability analysis also predicts complicated oscillatory and nonoscillatory dynamical behavior as the pulling force varies. Nonlinear simulations reveal that an unstable system always tends to limit-cycle behavior. Systems predicted as stable by the linear stability analysis are also stable for large-amplitude perturbations. External heating is found to dramatically enhance the draw ratio of the melt-spinning process. The addition of a cooling section suppresses the draw ratio, but this can be compensated for with a higher heating strength.

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Stability of initially slow viscous jets driven by gravity

Cited by 51 publications

References 29 publications

Capillary jet breakup by noise amplification

Capillary jet breakup by noise amplification

Forced dynamics of a short viscous liquid bridge

Draw ratio enhancement in nonisothermal melt spinning

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