Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-28T20:30:46.291Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics of elastocapillary rise

Published online by Cambridge University Press:  24 May 2011

CAMILLE DUPRAT ,
JEFFREY M. ARISTOFF  and
HOWARD A. STONE
CAMILLE DUPRAT*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
JEFFREY M. ARISTOFF
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
HOWARD A. STONE
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We present the results of a combined experimental and theoretical investigation of the surface-tension-driven coalescence of flexible structures. Specifically, we consider the dynamics of the rise of a wetting liquid between flexible sheets that are clamped at their upper ends. As the elasticity of the sheets is progressively increased, we observe a systematic deviation from the classical diffusive-like behaviour: the time to reach equilibrium increases dramatically and the departure from classical rise occurs sooner, trends that we elucidate via scaling analyses. Three distinct temporal regimes are identified and subsequently explored by developing a theoretical model based on lubrication theory and the linear theory of plates. The resulting free-boundary problem is solved numerically and good agreement is obtained with experiments.

JFM classification

Interfacial Flows (free surface): Capillary flows Low-Reynolds-number flows: Lubrication theory Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 679 , 25 July 2011 , pp. 641 - 654
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Andrade, J. D., King, R. N. & Gregonis, D. E. 1979 Surface characterization of poly (hydroxyethyl methacrylate) and related polymers. J. Polym. Sci.: Polym. Symp. 66, 313–336.Google Scholar
Aristoff, J. M., Duprat, C. & Stone, H. A. 2011 Elastocapillary imbibition. Inter. J. Nonlinear Mech. 46, 648–656.CrossRefGoogle Scholar
Bell, J. M. & Cameron, F. K. 1906 The flow of liquids through capillary spaces. J. Phys. Chem. 10, 658–674.CrossRefGoogle Scholar
Bico, J., Roman, B., Moulin, L. & Boudaoud, A. 2004 Elastocapillary coalescence in wet hair. Nature 432, 690.CrossRefGoogle ScholarPubMed
de Boer, M. P. & Michalske, T. A. 1999 Accurate method for determining adhesion of cantilever beams. J. Appl. Phys. 86, 817–827.CrossRefGoogle Scholar
Eisner, T. & Aneshansley, D. J. 2000 Defense by foot adhesion in a beetle (hemisphaerota cyanea). PNAS 97, 6568–6573.CrossRefGoogle Scholar
Fortes, M. A. 1984 Deformation of solid surfaces due to capillary forces. J. Colloid Interface Sci. 100, 17–26.CrossRefGoogle Scholar
Guyon, E., Hulin, J.-P. & Petit, L. 2001 Physical Hydrodynamics. Oxford University Press.CrossRefGoogle Scholar
Hoffman, R. L. 1975 A study of the advancing interface: 1. Interface shape in liquid-gas systems. Phys. Rev. E 50, 228–241.Google Scholar
van Honschoten, J. W., Escalante, M., Tas, N. R., Jansen, H. V. & Elwenspoek, M. 2007 Elastocapillary filling of deformable nanochannels. J. Appl. Phys. 101, 094310.CrossRefGoogle Scholar
Hosoi, A. E. & Mahadevan, L. 2004 Peeling, healing, and bursting in a lubricated elastic sheet. Phys. Rev. Lett. 93, 137802.CrossRefGoogle Scholar
Huang, J., Juszkiewicz, M., de Jeu, W. H., Cerda, E., Emrick, T., Menon, N. & Russell, T. P. 2007 Capillary wrinkling of floating thin polymer films. Science 317, 650–653.CrossRefGoogle ScholarPubMed
Kim, Ho-Young & Mahadevan, L. 2006 Capillary rise between elastic sheets. J. Fluid Mech. 548, 141–150.CrossRefGoogle Scholar
Lester, G. R. 1961 Contact angles of liquids at deformable solid surfaces. J. Colloid Sci. 16, 315–326.CrossRefGoogle Scholar
Mastrangelo, C. H. & Hsu, C. H. 1993 Mechanical stability and adhesion of microstructures under capillary forces. J. Microelectromech. Syst. 2, 33–55.CrossRefGoogle Scholar
Pericet-Camara, R., Best, A., Butt, H.-J. & Bonaccurso, E. 2008 Effect of capillary pressure and surface tension on the deformation of elastic surfaces by sessile liquid microdrops: An experimental investigation. Langmuir 24, 10565–10568.CrossRefGoogle ScholarPubMed
Pokroy, B., Kang, S. H., Mahadevan, L. & Aizenberg, J. 2009 Self-organization of a mesoscale bristle into ordered, hierarchical helical assemblies. Science 323, 237–240.CrossRefGoogle ScholarPubMed
Py, C., Reverdy, P., Doppler, L., Bico, J., Roman, B. & Baroud, C. N. 2007 Capillary origami: spontaneous wrapping of a droplet with an elastic sheet. Phys. Rev. Lett. 98, 156103.CrossRefGoogle ScholarPubMed
Quere, D. 1997 Inertial capillarity. Europhys. Lett. 39, 533–538.CrossRefGoogle Scholar
Reyssat, M., Courbin, L., Reyssat, E. & Stone, H. A. 2008 Imbibition in geometries with axial variation. J. Fluid Mech. 615, 335–344.CrossRefGoogle Scholar
Siddique, J. I., Anderson, D. M. & Bondarev, A. 2009 Capillary rise of a liquid into a deformable porous material. Phys. Fluids 21, 013106.CrossRefGoogle Scholar
Tanner, L. H. 1979 The spreading of silicone oil drops on horizontal surfaces. J. Phys. D: Appl. Phys. 12, 1473.CrossRefGoogle Scholar
Warren, P. B. 2004 Late stage kinetics for various wicking and spreading problems. Phys. Rev. E 69, 041601.Google ScholarPubMed