Stretching behaviour of large polymeric and Newtonian liquid bridges in plateau simulation

Kröger, Roland; Berg, Simon van den; Delgado, Antonio; Rath, H. J.

doi:10.1016/0377-0257(92)80069-a

Cited by 45 publications

(34 citation statements)

References 5 publications

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“…The dynamical shapes are therefore closer to cylindrical shapes than Delaunay's. This observation has already been made by Kroger et al (1992) who performed stretching experiments on large bridges in a neutral buoyancy tank. They noticed that 'increasing inertia, friction and flow resistance (.…”

Section: Theoretical Studysupporting

confidence: 58%

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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Section: Theoretical Studysupporting

confidence: 58%

Forced dynamics of a short viscous liquid bridge

2014

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“…The axisymmetric and non-axisymmetric oscillations of liquid bridges were theoretically investigated by Sanz et al 25,26 . Later studies investigated the effects of finite viscosity on the dynamics of liquid bridges under different conditions, including forced oscillations 27,28 and stretching 6,29 . The latter studies showed that even at modest elongation rates of 0.1 s -1 , instantaneous bridge shapes deviate considerably from equilibrium profiles and the limiting length can significantly exceed the critical length of a static bridge at its limit of stability.…”

Section: Introductionmentioning

confidence: 99%

A Combined Experimental and Numerical Modeling Study of the Deformation and Rupture of Axisymmetric Liquid Bridges under Coaxial Stretching

Zhuang

2015

Langmuir

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Abstract:The deformation and rupture of axisymmetric liquid bridges being stretched between two fully wetted coaxial disks are studied experimentally and theoretically. We numerically solve the time-dependent Navier-Stokes equations while tracking the deformation of the liquid-air interface using the Arbitrary Lagrangian-Eulerian (ALE) moving mesh method to fully account for the effects of inertia and viscous forces on bridge dynamics. The effects of the stretching velocity, liquid properties, and liquid volume on the dynamics of liquid bridges are systematically investigated to provide direct experimental validation of our numerical model for stretching velocities as high as 3 m/s. The Ohnesorge number (Oh) of liquid bridges is a primary factor governing the dynamics of liquid bridge rupture, especially the dependence of the rupture distance on the stretching velocity. The rupture distance generally increases with the stretching velocity, far in excess of the static stability limit. For bridges with low Ohnesorge numbers, however, the rupture distance stay nearly constant or decreases with the stretching velocity within certain velocity windows due to the relative rupture position switching and the thread shape change. Our work provides an experimentally validated modeling approach and experimental data to help establish foundation for systematic further studies and applications of liquid bridges.

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“…The conservation equations are derived from the principle of conservation of mass, the principle of balance of linear momentum, and the principle of balance of energy. extensional rheometers have been developed in the past [19][20][21][22][23][24][25][26]. We plan on investigating the use of AFM as a micro/nano-extensional rheometer, and as a starting point in this study, we investigate the effect of different velocity profiles on pulling a viscoelastic fluid sample placed between two flat surfaces.…”

Section: Fiber Formation Simulationsmentioning

confidence: 99%

Three-dimensional nanoscale manipulation and manufacturing using proximal probes: controlled pulling of polymer micro/nanofibers

Nain

Goldman

Sitti

2004

IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004

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Besides imaging and characterization, proximal probes are proposed to be used as three-dimensional (3D) nanoscale manipulation and manufacturing tools in this paper. We propose 3D oanascate pulling of liquid polymer micro/nanofibers by precise positioning of Atomic Force Microscope (AFM) nanoprobes and control of polymer solidification. An AFM probe is used to pull or extrude thermoset and thermoplastic polymers precisely to fabricate 3D polymer nano-fiber structures.A liquid polymer fiber bridge between the probe tip and a substrate is maintained when pulling the probe from the surface with controlled speed and position. We present results of our pulling experiments in vertical, horizontal and arbitrary 3D pulling directions for Poly(methyl methacrylate): PMMA polymer fibers. Force-distance curves obtained using AFM for PMMA samples at different scan rates are presented. A preliminary study showing the effect of velocity profile on pulling liquid bridges using POLYFLOW" is presented.

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Stretching behaviour of large polymeric and Newtonian liquid bridges in plateau simulation

Cited by 45 publications

References 5 publications

Forced dynamics of a short viscous liquid bridge

Forced dynamics of a short viscous liquid bridge

A Combined Experimental and Numerical Modeling Study of the Deformation and Rupture of Axisymmetric Liquid Bridges under Coaxial Stretching

Three-dimensional nanoscale manipulation and manufacturing using proximal probes: controlled pulling of polymer micro/nanofibers

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