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Physics of Fluids / Volume 24 / Issue 1 / ARTICLES / Micro- and Nanofluid Mechanics

Phys. Fluids 24, 012001 (2012); http://dx.doi.org/10.1063/1.3674300 (13 pages)

Scaling laws for slippage on superhydrophobic fractal surfaces

C. Cottin-Bizonne, C. Barentin, and L. Bocquet

LPMCN, Université de Lyon, Université Lyon 1 and CNRS, UMR 5586, F-69622 Villeurbanne, France

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(Received 14 June 2011; accepted 8 December 2011; published online 12 January 2012)

We study the slippage on hierarchical fractal superhydrophobic surfaces and find an unexpected rich behavior for hydrodynamic friction on these surfaces. We develop a scaling law approach for the effective slip length, which is validated by numerical resolution of the hydrodynamic equations. Our results demonstrate that slippage does strongly depend on the fractal dimension and is found to be always smaller on fractal surfaces as compared with surfaces with regular patterns. This shows that in contrast to naive expectations, the value of effective contact angle is not sufficient to infer the amount of slippage on a fractal surface: depending on the underlying geometry of the roughness, strongly superhydrophobic surfaces may, in some cases, be fully inefficient in terms of drag reduction. Finally, our scaling analysis can be directly extended to the study of heat transfer at fractal surfaces, in order to estimate the Kapitsa surface resistance on patterned surfaces, as well as to the question of trapping of diffusing particles by patchy hierarchical surfaces, in the context of chemoreception.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. A SCALING LAW APPROACH
    1. Wettability and contact angle
    2. Slippage on a two scale roughness
    3. Slippage on hierarchical fractal surfaces
    4. Discussion: 1D/2D hierarchical surfaces versus regular surfaces
      1. 1D structures
      2. 2D structures
    5. Alternative scaling law approach in the dilute regime
  3. NUMERICAL RESULTS
    1. Numerical results for slippage over hierarchical 2D structures
    2. Numerical results for slippage over hierarchical 1D structures
  4. CONCLUSION

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KEYWORDS and PACS

Keywords

contact angle, drag reduction, fractals, hydrophobicity, pattern formation, slip flow

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3674300

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    C. Lee, C. H. Choi, and C. J. Kim, “Structured surfaces for a giant liquid slip,” Phys. Rev. Lett. 101, 064501 (2008).

    F. Feuillebois, M. Z. Bazant, and O. I. Vinogradova, “Effective slip over superhydrophobic surfaces in thin channels,” Phys. Rev. Lett. 102, 026001 (2009).

    M. A. Samaha, H. V. Tafreshi, and M. Gad-El-Hak, “Modeling drag reduction and meniscus stability of superhydrophobic surfaces comprised of random roughness,” Phys. Fluids 23, 012001 (2011)PHFLE6000023000001012001000001.

    A. M. Berezhkovskii, Yu. A. Makhnovskii, M. I. Monine, V. Yu. Zitserman, and S. Y. Shvartsman, “Homogenization of boundary conditions on surfaces randomly covered by patches of different sizes and shapes,” J. Chem. Phys. 121, 11390 (2004)JCPSA6000121000022011390000001.


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