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Coating of a textured solid

Published online by Cambridge University Press:  16 February 2011

JACOPO SEIWERT ,
CHRISTOPHE CLANET  and
DAVID QUÉRÉ
JACOPO SEIWERT
Affiliation:
Physique et Mécanique des Milieux Hétérogènes, UMR 7636 du CNRS, ESPCI, 75005 Paris, France Ladhyx, UMR 7646 du CNRS, École Polytechnique, 91128 Palaiseau CEDEX, France
CHRISTOPHE CLANET
Affiliation:
Physique et Mécanique des Milieux Hétérogènes, UMR 7636 du CNRS, ESPCI, 75005 Paris, France Ladhyx, UMR 7646 du CNRS, École Polytechnique, 91128 Palaiseau CEDEX, France
DAVID QUÉRÉ*
Affiliation:
Physique et Mécanique des Milieux Hétérogènes, UMR 7636 du CNRS, ESPCI, 75005 Paris, France Ladhyx, UMR 7646 du CNRS, École Polytechnique, 91128 Palaiseau CEDEX, France
*
†Email address for correspondence: david.quere@espci.fr
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Abstract

We discuss how a solid textured with well-defined micropillars entrains a film when extracted out of a bath of wetting liquid. At low withdrawal velocity V, it is shown experimentally that the film exactly fills the gap between the pillars; its thickness hd is independent of V and corresponds to the pillar height hp. At larger velocity, hd slowly increases with V and tends towards the Landau–Levich–Derjaguin (LLD) thickness hLLD observed on a flat solid. We model the entrainment by adapting the LLD theory to a double layer consisting of liquid trapped inside the texture and covered by a free film. This model allows us to understand quantitatively our different observations and to predict the transition between hp and hLLD.

JFM classification

Materials Processing Flows: Coating Interfacial Flows (free surface): Interfacial Flows (free surface) Low-Reynolds-number flows: Lubrication theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 669 , 25 February 2011 , pp. 55 - 63
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Afanasiev, K., Munch, A. & Wagner, B. 2007 Landau–Levich problem for non-Newtonian liquids. Phys. Rev. E 76, 036307.CrossRefGoogle ScholarPubMed
Aradian, A., Raphael, E. & de Gennes, P. G. 2000 Dewetting on porous media with aspiration. Eur. Phys. J. E 2, 367–376.CrossRefGoogle Scholar
Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207.Google Scholar
Bretherton, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166–188.CrossRefGoogle Scholar
Callies, M., Chen, Y., Marty, F., Pépin, A. & Quéré, D. 2005 Microfabricated textured surfaces for super-hydrophobicity investigations. Microelectron. Engng 78–79, 100–105.CrossRefGoogle Scholar
Cazabat, A. M. & Cohen-Stuart, M. A. C. 1986 Dynamics of wetting: effects of surface roughness. J. Phys. Chem. 90, 5845–5849.CrossRefGoogle Scholar
Chen, J. D. 1986 Measuring the film thickness surrounding a bubble inside a capillary. J. Colloid Interface Sci. 109, 341–349.Google Scholar
Courbin, L., Denieul, E., Dressaire, E., Roper, M., Ajdari, A. & Stone, H. A. 2007 Imbibition by polygonal spreading on microdecorated surfaces. Nature Mater. 6, 661–664.CrossRefGoogle ScholarPubMed
Derjaguin, B. 1943 Thickness of liquid layer adhering to walls of vessels on their emptying and the theory of photo- and motion-picture film coating. Dokl. Acad. Sci. USSR 39, 13–19.Google Scholar
Devauchelle, O., Josserand, C. & Zaleski, S. 2007 Forced dewetting on porous media. J. Fluid Mech. 574, 343–364.CrossRefGoogle Scholar
Hasimoto, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 317–328.CrossRefGoogle Scholar
Ishino, C., Reyssat, M., Reyssat, E., Okumura, K. & Quéré, D. 2007 Wicking within forest of micro-pillars. EPL 79, 56005.Google Scholar
Jäger, W. & Mikelic, A. 2000 On the interface boundary condition by Beavers, Joseph and Saffman. SIAM J. Appl. Mech. 60, 1111–1127.Google Scholar
Krechetnikov, R. & Homsy, G. M. 2005 Experimental study of substrate roughness and surfactant effects on the Landau–Levich law. Phys. Fluids 17, 102108.Google Scholar
Landau, L. & Levich, V. 1942 Dragging of a liquid by a moving plate. Acta Physicochim. USSR 17, 42–54.Google Scholar
Maleki, M., Reyssat, M., Restagno, F., Quéré, D. & Clanet, C. 2011 Landau–Levich menisci. J. Colloid Interface Sci. 354, 359–363.Google Scholar
McHale, G., Shirtcliffe, N. J., Aqil, S., Perry, C. C. & Newton, M. I. 2004 Topography driven spreading. Phys. Rev. Lett. 93, 036102.CrossRefGoogle ScholarPubMed
Ramdane, O. O. & Quéré, D. 1997 The thickening factor in Marangoni coating. Langmuir 13, 2911–2916.Google Scholar
Savva, N., Kalliadasis, S. & Pavliotis, G. A. 2010 Two-dimensional droplet spreading over random topographical substrates. Phys. Rev. Lett. 104, 084501.CrossRefGoogle ScholarPubMed
Shen, A. Q., Gleason, B., McKinley, G. H. & Stone, H. A. 2002 Fiber coating with surfactant solutions. Phys. Fluids 14, 4055–4068.CrossRefGoogle Scholar
Snoeijer, J. H., Delon, G., Fermigier, M. & Andreotti, B. 2006 Avoided critical behavior in dynamically forced wetting. Phys. Rev. Lett. 96, 174504.CrossRefGoogle ScholarPubMed