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Capillary bridges between a plane and a cylindrical wall

Published online by Cambridge University Press:  14 May 2015

Etienne Reyssat
Etienne Reyssat*
Affiliation:
PMMH, CNRS UMR 7636 - ESPCI - UPMC Université Paris 6 - UPD Université Paris 7, 10 rue Vauquelin, 75005 Paris, France
*
†Email address for correspondence: etienne.reyssat@espci.fr
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Abstract

We report experimental, theoretical and numerical results on the shapes of liquid menisci connecting a planar boundary and the surface of a horizontal cylinder placed above. The gradient of confinement traps the wetting drops in the most confined regions, which promotes their elongation along the line of smallest gap between the walls. The experimental shapes of these stretched capillary bridges are shown to be in good quantitative agreement with the numerical solution of the equation describing their contour. In particular, we show that the measured shapes are better described when taking into account the correction resulting from the coupling of in-plane and transverse interfacial curvatures calculated by Park & Homsy (J. Fluid Mech., vol. 139, 1984, pp. 291–308) over thirty years ago.

JFM classification

Drops and Bubbles: Drops and Bubbles Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Liquid bridges

Information

Type
Rapids
Information
Journal of Fluid Mechanics , Volume 773 , 25 June 2015 , R1
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Copyright
© 2015 Cambridge University Press 

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References

Ajaev, V. S. & Homsy, G. M. 2006 Modeling shapes and dynamics of confined bubbles. Annu. Rev. Fluid Mech. 38 (1), 277–307.Google Scholar
Al-Housseiny, T. T., Tsai, P. A. & Stone, H. A. 2012 Control of interfacial instabilities using flow geometry. Nat. Phys. 8 (10), 747–750.Google Scholar
Anjos, P. H. A. & Miranda, J. A. 2014 Influence of wetting on fingering patterns in lifting Hele-Shaw flows. Soft Matt. 10 (38), 7459–7467.Google Scholar
Bensimon, D., Kadanoff, L. P., Liang, S., Shraiman, B. I. & Tang, C. 1986 Viscous flows in two dimensions. Rev. Mod. Phys. 58 (4), 977–999.Google Scholar
Bonn, D., Eggers, J., Indekeu, J., Meunier, J. & Rolley, E. 2009 Wetting and spreading. Rev. Mod. Phys. 81 (2), 739–805.CrossRefGoogle Scholar
Butt, H.-J. & Kappl, M. 2009 Normal capillary forces. Adv. Colloid Interface Sci. 146 (1–2), 48–60.Google Scholar
Delaunay, C. 1841 Sur la surface de révolution dont la courbure moyenne est constante. J. Math. Pure Appl. 6, 309–314.Google Scholar
Eichelsdoerfer, D. J., Brown, K. A. & Mirkin, C. A. 2014 Capillary bridge rupture in dip-pen nanolithography. Soft Matt. 10 (30), 5603–5608.CrossRefGoogle ScholarPubMed
Federle, W., Riehle, M., Curtis, A. S. G. & Full, R. J. 2002 An integrative study of insect adhesion: mechanics and wet adhesion of pretarsal pads in ants. Integr. Compar. Biol. 42, 1100–1106.Google Scholar
de Gennes, P.-G. 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57 (3), 827–863.Google Scholar
de Gennes, P.-G., Brochard-Wyart, F. & Quéré, D. 2004 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls and Waves. Springer.Google Scholar
Geoffroy, S., Plouraboué, F., Prat, M. & Amyot, O.2006 Quasi-static liquid–air drainage in narrow channels with variations in the gap. J. Colloid Interface Sci. 294, 165–175.Google Scholar
Gondret, P. & Rabaud, M. 1997 Shear instability of two-fluid parallel flow in a Hele-Shaw cell. Phys. Fluids 9 (11), 3267–3274.Google Scholar
Limat, L. 1992 Imperfect Hele-Shaw cell: a model for statics and dynamics of the interface perturbed by an isolated wettability defect. C. R. Acad. Sci. Paris 2 314, 1011–1016.Google Scholar
Melrose, J. C. 1966 Model calculations for capillary condensation. AIChE J. 12 (5), 986–994.Google Scholar
Mitarai, N. & Nori, F. 2006 Wet granular materials. Adv. Phys. 55 (1–2), 1–45.Google Scholar
Nagel, M., Brun, P.-T. & Gallaire, F. 2014 A numerical study of droplet trapping in microfluidic devices. Phys. Fluids 26 (3), 032002.Google Scholar
Park, C.-W. & Homsy, G. M. 1984 Two-phase displacement in Hele-Shaw cells: theory. J. Fluid Mech. 139, 291–308.Google Scholar
Paterson, A. 1996 Mouillage de surfaces hétérogènes: cellule de Hele-Shaw imparfaite. Ann. Phys. 21 (4), 337–436.Google Scholar
Paterson, A., Fermigier, M., Jenffer, P. & Limat, L. 1995 Wetting on heterogeneous surfaces: experiments in an imperfect Hele-Shaw cell. Phys. Rev. E 51 (2), 1291–1298.Google Scholar
Plouraboué, F. & Hinch, E. J. 2002 Kelvin–Helmholtz instability in a Hele-Shaw cell. Phys. Fluids 14 (3), 922–929.Google Scholar
Rabaud, M. 1994 Dynamiques interfaciales dans l’instabilité de l’imprimeur. Ann. Phys. France 19, 659–690.Google Scholar
Rabaud, M., Couder, Y. & Michalland, S. 1991 Wavelength selection and transients in the one-dimensional array of cells of the printer’s instability. Eur. J. Mech. (B/Fluids) 10, 253–260.Google Scholar
Roman, B. & Bico, J. 2010 Elasto-capillarity: deforming an elastic structure with a liquid droplet. J. Phys.: Condens. Matter 22, 493101.Google Scholar
Saffman, P. G. & Taylor, G. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245 (1242), 312–329.Google Scholar
Sauvage, P., Argentina, M., Drappier, J., Senden, T., Siméon, J. & Di Meglio, J.-M. 2011 An elasto-hydrodynamical model of friction for the locomotion of Caenorhabditis elegans . J. Biomech. 44, 1117–1122.Google Scholar