Tensorial slip of super-hydrophobic channels

Abstract

We describe a generalization of the tensorial slip boundary condition, originally justified for a thick (compared to texture period) channel, to any channel thickness. The eigenvalues of the effective slip length tensor, however, in general case become dependent on the gap and cannot be viewed as a local property of the surface, being a global characteristic of the channel. To illustrate the use of the tensor formalism we develop a semi-analytical theory of an effective slip in a parallel-plate channel with one super-hydrophobic striped and one hydrophilic surface. Our approach is valid for any local slip at the gas sectors and an arbitrary distance between the plates, ranging from a thick to a thin channel. We then present results of lattice Boltzmann simulations to validate the analysis. Our results may be useful for extracting effective slip tensors from global measurements, such as the permeability of a channel, in experiments or simulations.

arXiv comment12 pages, 7 figures

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Cited by in corpus (16)

• Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state
• Inertial focusing of finite-size particles in microchannels
• Effective slip boundary conditions for arbitrary one-dimensional surfaces
• Anisotropic flow in striped superhydrophobic channels
• Regularization of the slip length divergence in water nanoflows by inhomogeneities at the Angstrom scale
• Correlation between surface topography and slippage: a Molecular Dynamics study
• Inertial migration of neutrally-buoyant particles in superhydrophobic channels
• Effective slip-length tensor for a flow over weakly slipping stripes
• Flow past superhydrophobic surfaces with cosine variation in local slip length
• Flows and mixing in channels with misaligned superhydrophobic walls
• Flow in channels with superhydrophobic trapezoidal textures
• Singular effective slip length for longitudinal flow over a dense bubble mattress
• Boundary conditions at the gas sectors of superhydrophobic grooves
• Effective slippage on superhydrophobic trapezoidal grooves
• Lattice-Boltzmann simulations of the drag force on a sphere approaching a superhydrophobic striped plane
• Advective superdiffusion in superhydrophobic microchannels