Achieving large slip with superhydrophobic surfaces: Scaling laws for generic geometries

Abstract

We investigate the hydrodynamic friction properties of superhydrophobic surfaces and quantify their superlubricating potential. On such surfaces, the contact of the liquid with the solid roughness is minimal, while most of the interface is a liquid-gas one, resulting in strongly reduced friction. We obtain scaling laws for the effective slip length at the surface in terms of the generic surface characteristics ͑roughness length scale, depth, solid fraction of the interface, etc.͒. These predictions are successfully compared to numerical results in various geometries ͑grooves, posts or holes͒. This approach provides a versatile framework for the description of slip on these composite surfaces. Slip lengths up to 100 m are predicted for an optimized patterned surface.

Superhydrophobic drag reduction in laminar flows: a critical review

“…Analytical models and numerical simulations are useful tools in understanding slip lengths in laminar flows on a few simple surface patterns such as grates (ridges, trenches) (Philip 1972a, b;Lauga and Stone 2003;Belyaev and Vinogradova 2010a;Asmolov and Vinogradova 2012), posts (pillars) (Ybert et al 2007;Davis and Lauga 2010), and holes (Ybert et al 2007;Davis and Lauga 2009a), as shown in Fig. 2.…”

“…Analytical solutions for slip lengths on posts were derived for large gas fractions (i.e., φ g > 0.3) as follows (Davis and Lauga 2010): In case of holes, a logarithmic dependency of slip length on gas fraction was derived analytically (Ybert et al 2007): where A and B are prefactors obtained by numerical simulations. For an example, in the case of circular holes at a gas fraction between 0.25 and 0.78, they were obtained as A = 0.134 and B = −0.023 (Ng and Wang 2010).…”

“…As a result, the slip length on posts increases much more steeply at high gas fraction compared to grates and holes. The different functional expression of slip length on each pattern type can be physically understood using a simple scaling analysis (Ybert et al 2007). According to the scaling analysis, at a high gas fraction, the average slip velocity is scaled as u s ∼ U and the frictional stress is only applied on the solid area as σ w ∼ η(1 − φ g )U/a, where U, η, and a are the far field liquid velocity, liquid viscosity, and the typical size of the solid area, respectively.…”

“…Following early work (Philip 1972a, b), many analytical models about slip lengths on simple SHPo surfaces have been developed (Lauga and Stone 2003;Ybert et al 2007;Sbragaglia and Prosperetti 2007a, b;Davis and Lauga 2009a, b;Feuillebois et al 2009;Belyaev and Vinogradova 2010a, b;Davis and Lauga 2010;Asmolov and Vinogradova 2012;Cottin-Bizonne et al 2012) and corroborated by numerical simulations (Cottin-Bizonne et al 2003Priezjev et al 2005;Hendy and Lund 2007;Biben and Joly 2008;Hyvalouma and Harting 2008;Teo and Khoo 2008;Cheng et al 2009;Wang 2009, 2010;Teo and Khoo 2010). By fabricating near-perfect microstructures in an extremely clean condition, Lee et al (2008) succeeded to measure the slip length as a function of surface features, finally verifying the early theoretical models (Lauga and Stone 2003;Ybert et al 2007) quantitatively and bringing a conclusion to the issue.…”

Using surface force apparatus, diffusion and velocimetry to measure slip lengths

“…Furthermore, recent theoretical predictions and experimental results have pointed to the possibility to create huge (more than 10 mm) slip lengths by the use of composite surfaces (Choi & Kim 2006;Ybert et al 2007). mPIV is a particularly appropriate method to measure the slippage on such surfaces, thanks to its ability to precisely reconstruct the speed profile with a submicrometre resolution, as has already been demonstrated on carbon nanotube-coated surfaces (Joseph et al 2006).…”