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  • Journal of Fluid Mechanics, Volume 666
  • January 2011, pp. 554-572

The motion, stability and breakup of a stretching liquid bridge with a receding contact line

  • BIAN QIAN (a1) and KENNETH S. BREUER (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112010004611
  • Published online: 06 January 2011
Abstract

The complex behaviour of drop deposition on a hydrophobic surface is considered by looking at a model problem in which the evolution of a constant-volume liquid bridge is studied as the bridge is stretched. The bridge is pinned with a fixed diameter at the upper contact point, but the contact line at the lower attachment point is free to move on a smooth substrate. Experiments indicate that initially, as the bridge is stretched, the lower contact line slowly retreats inward. However, at a critical radius, the bridge becomes unstable, and the contact line accelerates dramatically, moving inward very quickly. The bridge subsequently pinches off, and a small droplet is left on the substrate. A quasi-static analysis, using the Young–Laplace equation, is used to accurately predict the shape of the bridge during the initial bridge evolution, including the initial onset of the slow contact line retraction. A stability analysis is used to predict the onset of pinch-off, and a one-dimensional dynamical equation, coupled with a Tanner law for the dynamic contact angle, is used to model the rapid pinch-off behaviour. Excellent agreement between numerical predictions and experiments is found throughout the bridge evolution, and the importance of the dynamic contact line model is demonstrated.

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Corresponding author
Email address for correspondence: kbreuer@brown.edu
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D. G. A. L. Aarts , H. N. W. Lekkerkerker , H. Guo , G. H. Wegdam & D. Bonn 2005 Hydrodynamics of droplet coalescence. Phys. Rev. Lett. 95, 164503.

J. C. Bird , S. Mandre & H. A. Stone 2008 Short-time dynamics of partial wetting. Phys. Rev. Lett. 100, 234501.

D. Bonn , J. Eggers , J. Indekeu , J. Meunier & E. Rolley 2009 Wetting and spreading. Rev. Mod. Phys. 81, 739805.

S. Deladi , N. R. Tas , J. W. Berenschot , G. J. M. Krijnen , M. J. de Boer , J. H. de Boer , M. Peter & M. C. Elwenspoek 2004 Micromachined fountain pen for atomic force microscope-based nanopatterning. Appl. Phys. Lett. 85, 53615363.

S. Dodds , M. da Silveira Carvalho & S. Kumar 2009 Stretching and slipping of liquid bridges near plates and cavities. Phys. Fluids 21, 092103.

V. E. B. Dussan , 1979 On the spreading of liquid on the solid surfaces: static and dynamic contact lines. Annu. Rev. Fluid Mech. 11, 371400.

J. Eggers 1993 Universal pinching of 3D axisymmetric free-surface flow. Phys. Rev. Lett. 71, 34583460.




R. D. Gillette & D. C. Dyson 1971 Stability of fluid interfaces of revolution between equal solid circular plates. Chem. Engng J. 2, 4454.

D. S. Ginger , H. Zhang & C. A. Mirkin 2004 The evolution of dip-pen nanolithography. Angew. Chem. 43, 3045.

Y. C. Liao , E. I. Franses & O. A. Basaran 2006 Deformation and breakup of a stretching liquid bridge covered with an insoluble surfactant monolayer. Phys. Fluids 18, 022101.

G. C. Mason 1970 An experimental determination of the stable length of cylindrical liquid bubbles. J. Colloid Interface Sci. 32, 172176.

J. Meseguer 1984 Stability of slender, axisymmetric liquid bridges between unequal disks. J. Cryst. Growth 67, 141143.


N. Moldovan , K.-H. Kim & H. D. Espinosa 2006 Design and fabrication of a novel microfluidic nanoprobe. J. Microelectromech. Syst. 15, 204213.

A. D. Myshkis , V. G. Babskii , N. D. Slobozhanin , L. A. Kopachevskii & A. D. Tyuptsov 1987 Low-Gravity Fluid Mechanics. Springer.

A. Oron , S. H. Davis & S. G. Bankoff 1997 Long scale evolution of thin liquid films. Rev. Mod. Phys. 69, 931980.


J. M. Perales , J. Meseguer & I. Martinez 1991 Minimum volume stability limits for axisymmetric liquid bridges subject to steady axial acceleration. J. Cryst. Growth 110, 855861.

B. Qian , M. Loureiro , D. A. Gagnon , A. Tripathi & K. S. Breuer 2009 Micron-scale droplet deposition on a hydrophobic surface using a retreating syringe. Phys. Rev. Lett. 102, 164502.

M. J. Russo & P. H. Steen 1986 Instability of rotund capillary bridges to general disturbances, experiment and theory. J. Colloid Interface Sci. 113, 154163.

A. Sanz & I. Martinez 1983 Minimum volume for a liquid bridge between equal disks. J. Colloid Interface Sci. 93, 235240.

L. A. Slobozhanin & J. I. D. Alexander 1998 Combined effect of disk inequality and axial gravity on axisymmetric liquid bridge stability. Phys. Fluids 10, 24732488.

L. A. Slobozhanin , J. I. D. Alexander & A. H. Resnick 1997 Bifurcation of the equilibrium states of a weightless liquid bridge. Phys. Fluids 9, 18931905.

L. A. Slobozhanin & J. M. Perales 1993 Stability of liquid bridges between equal disks in an axial gravity field. Phys. Fluids A 5, 13051314.

L. H. Tanner 1979 The spreading of silicone oil drops on horizontal surfaces. J. Phys. D: Appl. Phys. 12, 14731484.


W. Villanueva , J. Sjödahl , M. Stjernström , J. Roeraade & G. Amberg 2007 Microdroplet deposition under a liquid medium. Langmuir 23, 11711177.


O. E. Yildirim & O. A. Basaran 2001 Deformation and breakup of stretching bridges of Newtonian and shear-thinning liquids: comparison of one- and two-dimensional models. Chem. Engng Sci. 56, 211233.


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