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

References in corpus (15)

• 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
• A note on the effective slip properties for microchannel flows with ultra-hydrophobic surfaces
• Tensorial hydrodynamic slip
• Effective slip over superhydrophobic surfaces in thin channels
• Effective slip in pressure-driven flow past super-hydrophobic stripes
• Effective slip boundary conditions for arbitrary periodic surfaces: The surface mobility tensor
• Hydrodynamic friction of fakir-like super-hydrophobic surfaces
• Anisotropic electro-osmotic flow over super-hydrophobic surfaces
• Electro-osmosis on anisotropic super-hydrophobic surfaces
• Tensorial slip of super-hydrophobic channels
• Molecular diffusion and slip boundary conditions at smooth surfaces with periodic and random nanoscale textures
• Drag force on a sphere moving towards an anisotropic super-hydrophobic plane
• Scaling laws for slippage on superhydrophobic fractal surfaces
• Hydrodynamic interaction with super-hydrophobic surfaces

Cited by in corpus (14)

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• A theory for the slip and drag of superhydrophobic surfaces with surfactant
• Effective slip-length tensor for a flow over weakly slipping stripes
• 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