Hydrodynamic interaction with super-hydrophobic surfaces

Abstract

Patterned surfaces with large effective slip lengths, such as super-hydrophobic surfaces containing trapped gas bubbles, have the potential to reduce hydrodynamic drag. Based on lubrication theory, we analyze an approach of a hydrophilic disk to such a surface. The drag force is predicted analytically and formulated in terms of a correction function to the Reynolds equation, which is shown to be the harmonic mean of corrections expressed through effective slip lengths in the two principal (fastest and slowest) orthogonal directions. The reduction of drag is especially pronounced for a thin (compared to texture period) gap. It is not really sensitive to the pattern geometry, but depends strongly on the fraction of the gas phase and local slip length at the gas area.

20 pages, 7 figures

References in corpus (9)

• Slippage of water past superhydrophobic carbon nanotube forests in microchannels
• A note on the effective slip properties for microchannel flows with ultra-hydrophobic surfaces
• Slip flow over structured surfaces with entrapped microbubbles
• Geometric transition in friction for flow over a bubble mattress
• Effective slip over superhydrophobic surfaces in thin channels
• Effective slip in pressure-driven flow past super-hydrophobic stripes
• Direct measurements of hydrophobic slippage using double-focus fluorescence cross-correlation
• Capillary bridging and long-range attractive forces in a mean-field approach
• Dynamics of the spontaneous breakdown of superhydrophobicity

Cited by in corpus (8)

• Wetting, roughness and flow boundary conditions
• Tensorial slip of super-hydrophobic channels
• Effective slip boundary conditions for arbitrary one-dimensional surfaces
• Drag force on a sphere moving towards an anisotropic super-hydrophobic plane
• Anisotropic flow in striped superhydrophobic channels
• Flow in channels with superhydrophobic trapezoidal textures
• Effective slippage on superhydrophobic trapezoidal grooves
• Lattice-Boltzmann simulations of the drag force on a sphere approaching a superhydrophobic striped plane