Effective slip over superhydrophobic surfaces in thin channels

Abstract

Superhydrophobic surfaces reduce drag by combining hydrophobicity and roughness to trap gas bubbles in a micro- and nanoscopic texture. Recent work has focused on specific cases, such as striped grooves or arrays of pillars, with limited theoretical guidance. Here, we consider the experimentally relevant limit of thin channels and obtain rigorous bounds on the effective slip length for any two-component (e.g. low-slip and high-slip) texture with given area fractions. Among all anisotropic textures, parallel stripes attain the largest (or smallest) possible slip in a straight, thin channel for parallel (or perpendicular) orientation with respect to the mean flow. For isotropic (e.g. chessboard or random) textures, the Hashin-Strikman conditions further constrain the effective slip. These results provide a framework for the rational design of superhydrophobic surfaces.

4+ pages

References in corpus (9)

• Slippage of water past superhydrophobic carbon nanotube forests in microchannels
• Slip behavior in liquid films on surfaces of patterned wettability: Comparison between continuum and molecular dynamics simulations
• Dynamics of simple liquids at heterogeneous surfaces : Molecular Dynamics simulations and hydrodynamic description
• Giant amplification of interfacially driven transport by hydrodynamic slip: diffusio-osmosis and beyond
• A note on the effective slip properties for microchannel flows with ultra-hydrophobic surfaces
• Superstability of Surface Nanobubbles
• Slip flow over structured surfaces with entrapped microbubbles
• Tensorial hydrodynamic slip
• Mesoscopic modeling of heterogeneous boundary conditions for microchannel flows

Cited by in corpus (33)

• Effective slip in pressure-driven flow past super-hydrophobic stripes
• Wetting, roughness and flow boundary conditions
• Effective slip boundary conditions for arbitrary periodic surfaces: The surface mobility tensor
• Anisotropic electro-osmotic flow over super-hydrophobic surfaces
• Random-roughness hydrodynamic boundary conditions
• Tensorial slip of super-hydrophobic channels
• Effective slip boundary conditions for arbitrary one-dimensional surfaces
• Do liquid drops roll or slide on inclined surfaces?
• Molecular diffusion and slip boundary conditions at smooth surfaces with periodic and random nanoscale textures
• Transverse flow in thin superhydrophobic channels
• Contact Angle Hysteresis on Superhydrophobic Stripes
• The relationship between induced fluid structure and boundary slip in nanoscale polymer films
• Drag force on a sphere moving towards an anisotropic super-hydrophobic plane
• Scaling laws for slippage on superhydrophobic fractal surfaces
• Anisotropic flow in striped superhydrophobic channels
• Regularization of the slip length divergence in water nanoflows by inhomogeneities at the Angstrom scale
• Effective slip-length tensor for a flow over weakly slipping stripes
• Inertial migration of neutrally-buoyant particles in superhydrophobic channels
• Flow past superhydrophobic surfaces with cosine variation in local slip length
• Hydrodynamic interaction with super-hydrophobic surfaces
• Flows and mixing in channels with misaligned superhydrophobic walls
• A boundary condition with adjustable slip length for Lattice Boltzmann simulations
• A single parameter can predict surfactant impairment of superhydrophobic drag reduction
• Flow in channels with superhydrophobic trapezoidal textures
• Elastic deformations driven by non-uniform lubrication flows
• Giant Slip at Liquid-Liquid Interfaces Using Hydrophobic Ball Bearings
• Studying Flow Close to an Interface by Total Internal Reflection Fluorescence Cross Correlation Spectroscopy: Quantitative Data Analysis
• Effective slippage on superhydrophobic trapezoidal grooves
• Lattice-Boltzmann simulations of the drag force on a sphere approaching a superhydrophobic striped plane
• Growth morphology and symmetry selection of interfacial instabilities in anisotropic environments
• Advective superdiffusion in superhydrophobic microchannels
• Close-contact melting on hydrophobic textured surfaces: Confinement and meniscus effects
• A Lattice Boltzmann study of flow along patterned surfaces and through channels with alternating slip length