publication . Article . Other literature type . Preprint . 2012

Scaling laws for slippage on superhydrophobic fractal surfaces

Catherine BARENTIN;
Open Access
  • Published: 24 Jan 2012 Journal: Physics of Fluids, volume 24, page 12,001 (issn: 1070-6631, eissn: 1089-7666, Copyright policy)
  • Publisher: AIP Publishing
Abstract
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 to 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 ge...
Subjects
free text keywords: Condensed Matter Physics, Scaling, Drag, Slippage, Pattern formation, Fractal dimension, Slip (materials science), Fractal, Physics, Surface finish, Classical mechanics, Condensed Matter - Soft Condensed Matter, Physics - Fluid Dynamics
38 references, page 1 of 3

[1] D., Qu´er´e, “Non-sticking drops”, Rep. Prog. Phys. 68, 2495 (2005).

[2] L. Bocquet and E. Lauga “A smooth future ?”, Nature Mat., 10, 334 (2011).

[3] J. Bico, U. Thiele, and D. Quere, “Wetting of textured surfaces”, Colloids Surf., A, 206, 41 (2002).

[4] A. Lafuma and D. Quere, “Superhydrophobic states,” Nature Mat., 2, 457 (2003).

[5] C. Cottin-Bizonne, J. L. Barrat, L. Bocquet, and E. Charlaix, “Low-friction flows of liquid at nanopatterned interfaces,” Nat. Mater., 2, 237 (2003). [OpenAIRE]

[6] D. Quere, A. Lafuma, and J. Bico, “Slippy and sticky microtextured solids,” Nanotechnology, 14, 1109 (2003). [OpenAIRE]

[7] J. Ou, B. Perot, and J. P. Rothstein, “Laminar drag reduction in microchannels using ultrahydrophobic surfaces,” Phys. Fluids, 16, 4635 (2004). [OpenAIRE]

[8] J. Ou and J. Rothstein, “Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces,” Phys. Fluids, 17, 103606 (2005).

[9] P. Joseph, C. Cottin, J.-M. Benoit, C. Ybert, C. Journet, P. Tabeling, L. Bocquet, “ Slippage of water past superhydrophobic carbon nanotube carpets in microchanels ”, Phys. Rev. Lett. 97 156104 (2006). [OpenAIRE]

[10] C. Lee, C.H. Choi, CJ Kim, “Structured surfaces for a giant liquid slip”, Phys. Rev. Lett. 101 064501 (2008).

[11] S.S. Bahga, O.I. Vinogradova, M.Z. Bazant, “Anisotropic electro-osmotic flow over super-hydrophobic surfaces”, J. Fluid Mech. 644 245 (2010)

[12] C. Duez, C. Ybert, C. Clanet, L. Bocquet, “ Wetting controls separation of inertial flows from solid surfaces”, Phys. Rev. Lett. 104 084503 (2010). [OpenAIRE]

[13] A. Cassie and S. Baxter, “Wettability of porous surfaces”, Trans. Faraday Society, 40, 546 (1944). [OpenAIRE]

[14] J. Philip, “Flows satisfying mixed no-slip and no-shear conditions,” Z Angew Math Phys, 23, 353 (1972); ibid. “Integral properties of flows satisfying mixed no-slip and no-shear conditions”,23, 960 (1972).

[15] E. Lauga and H. A. Stone, “Effective slip in pressuredriven stokes flow,” J. Fluid Mech., 489, 55 (2003).

38 references, page 1 of 3
Abstract
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 to 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 ge...
Subjects
free text keywords: Condensed Matter Physics, Scaling, Drag, Slippage, Pattern formation, Fractal dimension, Slip (materials science), Fractal, Physics, Surface finish, Classical mechanics, Condensed Matter - Soft Condensed Matter, Physics - Fluid Dynamics
38 references, page 1 of 3

[1] D., Qu´er´e, “Non-sticking drops”, Rep. Prog. Phys. 68, 2495 (2005).

[2] L. Bocquet and E. Lauga “A smooth future ?”, Nature Mat., 10, 334 (2011).

[3] J. Bico, U. Thiele, and D. Quere, “Wetting of textured surfaces”, Colloids Surf., A, 206, 41 (2002).

[4] A. Lafuma and D. Quere, “Superhydrophobic states,” Nature Mat., 2, 457 (2003).

[5] C. Cottin-Bizonne, J. L. Barrat, L. Bocquet, and E. Charlaix, “Low-friction flows of liquid at nanopatterned interfaces,” Nat. Mater., 2, 237 (2003). [OpenAIRE]

[6] D. Quere, A. Lafuma, and J. Bico, “Slippy and sticky microtextured solids,” Nanotechnology, 14, 1109 (2003). [OpenAIRE]

[7] J. Ou, B. Perot, and J. P. Rothstein, “Laminar drag reduction in microchannels using ultrahydrophobic surfaces,” Phys. Fluids, 16, 4635 (2004). [OpenAIRE]

[8] J. Ou and J. Rothstein, “Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces,” Phys. Fluids, 17, 103606 (2005).

[9] P. Joseph, C. Cottin, J.-M. Benoit, C. Ybert, C. Journet, P. Tabeling, L. Bocquet, “ Slippage of water past superhydrophobic carbon nanotube carpets in microchanels ”, Phys. Rev. Lett. 97 156104 (2006). [OpenAIRE]

[10] C. Lee, C.H. Choi, CJ Kim, “Structured surfaces for a giant liquid slip”, Phys. Rev. Lett. 101 064501 (2008).

[11] S.S. Bahga, O.I. Vinogradova, M.Z. Bazant, “Anisotropic electro-osmotic flow over super-hydrophobic surfaces”, J. Fluid Mech. 644 245 (2010)

[12] C. Duez, C. Ybert, C. Clanet, L. Bocquet, “ Wetting controls separation of inertial flows from solid surfaces”, Phys. Rev. Lett. 104 084503 (2010). [OpenAIRE]

[13] A. Cassie and S. Baxter, “Wettability of porous surfaces”, Trans. Faraday Society, 40, 546 (1944). [OpenAIRE]

[14] J. Philip, “Flows satisfying mixed no-slip and no-shear conditions,” Z Angew Math Phys, 23, 353 (1972); ibid. “Integral properties of flows satisfying mixed no-slip and no-shear conditions”,23, 960 (1972).

[15] E. Lauga and H. A. Stone, “Effective slip in pressuredriven stokes flow,” J. Fluid Mech., 489, 55 (2003).

38 references, page 1 of 3
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publication . Article . Other literature type . Preprint . 2012

Scaling laws for slippage on superhydrophobic fractal surfaces

Catherine BARENTIN;