The breaking of axisymmetric slender liquid bridges

Meseguer, José

doi:10.1017/s0022112083001019

Cited by 119 publications

(98 citation statements)

References 15 publications

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“…Apart from an equation of motion for h, we now have two equations for the expansion coefficients of the velocity field, v 0 (z, t) and v 2 (z, t). Those equations, although readily written down, are considerably more complicated than (17), (18) and require new numerical methods. Therefore, we consider it a study all of its own which should be investigated separately.…”

Section: Discussionmentioning

confidence: 99%

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Drop formation in a one-dimensional approximation of the Navier–Stokes equation

1994

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We consider the viscous motion of a thin, axisymmetric column of fluid with a free surface. A one-dimensional equation of motion for the velocity and the radius is derived from the Navier-Stokes equation. We compare with recent experiments on the breakup of a liquid jet and on the bifurcation of a drop suspended from an orifice. The equations form singularities as the fluid neck is pinching off. The nature of the singularities is investigated in detail.

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Section: Discussionmentioning

confidence: 99%

“…The physical pressure (11) also carries contributions from the shear stress. This should be born in mind when we refer to v and p in (17), (18) as "velocity" and "pressure".…”

Section: The Equations Of Motionmentioning

confidence: 99%

Drop formation in a one-dimensional approximation of the Navier–Stokes equation

1994

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“…In the case of a linear system (as it is well known from random process theory [9]) the mean level of a stationary random perturbation is transmitted through the system as a constant signal; that is, the superposed random perturbation does not affect the relation MLI/MLO = 7/(0) between the mean level input (MLI) and the mean level output (MLO), H(u) being the transfer function which is characterized by the static response H(0) (already known for almost cylindrical liquid bridges in a reasonable number of cases [6,7,[10][11][12][13][14]) and the resonance frequencies w [3,4]. This principle can be used to describe the dynamics of a liquid bridge, which can be considered as a linear system provided the interface deforma- tions are small enough.…”

Section: Breaking Sequencesmentioning

confidence: 99%

“…As published elsewhere [3][4][5][6], concerning liquid bridge breakage, the most suitable result to be experimentally checked is the partial volume (defined as the ratio of the volume of the larger drop appearing after liquid bridge breakage to the whole liquid column volume), because the partial volume depends mainly on variables which can be easily controlled and experimentally measured (volume of the liquid column and the slenderness A = …”

Section: Introductionmentioning

confidence: 99%

Liquid bridge breakages aboard spacelab-d1

Meseguer¹,

Sanz²,

Lopez³

1986

Journal of Crystal Growth

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The study of the stability of long liquid columns under microgravity was the purpose of one of the experiments carried out aboard Spacelab-Dl. In this paper a preliminary analysis of this experiment, mainly concerning the different liquid column breakages, is presented, As shown in the paper, the behaviour, both static and dynamic, of long liquid bridges can be accurately predicted by using available theoretical models.

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“…This model has a long history which goes back to Saint Venant and Cosserat (see, for instance Bogy 1978;Meseguer 1983). It has been tested and validated in numerous studies (see for instance Eggers & Dupont 1994;Ramos, Garcia & Valverde 1999;Ambravaneswaran, Wilkes & Basaran 2002).…”

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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The breaking of axisymmetric slender liquid bridges

Cited by 119 publications

References 15 publications

Drop formation in a one-dimensional approximation of the Navier–Stokes equation

Drop formation in a one-dimensional approximation of the Navier–Stokes equation

Liquid bridge breakages aboard spacelab-d1

Forced dynamics of a short viscous liquid bridge

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