Superhydrophobicity and Effective Hydrodynamic Slippage

We examine an idealized superhydrophobic surface in the Cassie state sketched in Fig. 2.7b, where a liquid slab lies on top of the surface roughness. The liquid-gas interface is assumed to be flat with no meniscus curvature, so the modeled superhydrophobic surface appears as a perfectly smooth with a pattern of boundary conditions. In the simpIiFied description the latter are taken as no 

Finally, for the sake of brevity we focus next only on the canonical microfluidic geometry, where the fluid is confined between flat plates, and only on the asymmetric case, where one (upper) surface is smooth hydrophilic and another (lower) represents a superhydrophobic wall in the Cassie state. Such a configuration is relevant for various setups, where the alignment of opposite textures is inconvenient or difficult. We also restrict the discussion by a pressure-driven flow governed by the Stokes equations  

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The power of the tensor formalism and the concept of effective slippage have then been demonstrated by exact solutions for two other potential applications optimization of transverse flow and anal3Aical results for hydrodynamic resistance to the approach of two surfaces. These examples demonstrate that properly designed superhydrophobic surfaces could generate a very strong transverse flow and significantly reduce the so-called "viscous adhesion." Finally, we have discussed how superhydrophobic surfaces could amplify electro kinetic pumping in microfluidic devices. 

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