Effective slip boundary conditions for arbitrary one-dimensional surfaces

Abstract

In many applications it is advantageous to construct effective slip boundary conditions, which could fully characterize flow over patterned surfaces. Here we focus on laminar shear flows over smooth anisotropic surfaces with arbitrary scalar slip $b(y)$, varying in only one direction. We derive general expressions for eigenvalues of the effective slip-length tensor, and show that the transverse component is equal to a half of the longitudinal one with twice larger local slip, $2b(y)$. A remarkable corollary of this relation is that the flow along any direction of the 1D surface can be easily determined, once the longitudinal component of the effective slip tensor is found from the known spatially nonuniform scalar slip.

10 pages, 2 figures, submitted to J. Fluid Mech

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• A note on the effective slip properties for microchannel flows with ultra-hydrophobic surfaces
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• Flow past superhydrophobic surfaces with cosine variation in local slip length
• Electrokinetic Instability near Charge-Selective Hydrophobic Surfaces
• A single parameter can predict surfactant impairment of superhydrophobic drag reduction
• Flow in channels with superhydrophobic trapezoidal textures
• Flow-driven collapse of lubricant-infused surfaces
• Effective slippage on superhydrophobic trapezoidal grooves
• Linear stability of slip pipe flow
• Lattice-Boltzmann simulations of the drag force on a sphere approaching a superhydrophobic striped plane
• Hydrodynamic radius approximation for spherical particles suspended in a viscous fluid: influence of particle internal structure and boundary
• Close-contact melting on hydrophobic textured surfaces: Confinement and meniscus effects