Boundary condition for fluid flow: Curved or rough surfaces

Einzel, Dietrich; Panzer, Peter; Liu, Mario

doi:10.1103/physrevlett.64.2269

Cited by 165 publications

(147 citation statements)

References 6 publications

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“…Note that on a curved surface the rate of strain tensor is different from the normal derivative of the tangential component of the flow so all the terms in Eq. (2) need to be considered [49]. A century of agreement between experimental results in liquids and theories derived assuming the no-slip boundary condition (i.e., λ = 0) had the consequence that today many textbooks of fluid dynamics fail to mention that the no-slip boundary condition remains an assumption.…”

Section: The Previous Centuriesmentioning

confidence: 99%

Microfluidics: The No-Slip Boundary Condition

Lauga

Brenner

Stone

2007

Springer Handbook of Experimental Fluid Mechanics

591

674

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The no-slip boundary condition at a solid-liquid interface is at the center of our understanding of fluid mechanics. However, this condition is an assumption that cannot be derived from first principles and could, in theory, be violated. In this chapter, we present a review of recent experimental, numerical and theoretical investigations on the subject. The physical picture that emerges is that of a complex behavior at a liquid/solid interface, involving an interplay of many physico-chemical parameters, including wetting, shear rate, pressure, surface charge, surface roughness, impurities and dissolved gas.

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Section: The Previous Centuriesmentioning

confidence: 99%

Microfluidics: The No-Slip Boundary Condition

Lauga

Brenner

Stone

2007

Springer Handbook of Experimental Fluid Mechanics

591

674

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“…Recent analytical and molecular dynamics studies [4,5] suggest that the velocity profile in a rarefied cylindrical Couette flow can become inverted. In the case of a stationary outer cylinder and rotating inner cylinder, 'inverted' means that the radial velocity of the gas becomes greater further away from the moving centre.…”

Section: A Cylindrical Couette Flowmentioning

confidence: 99%

“…2), Maxwell's original slip condition (Eq. 1), DSMC (direct simulation Monte Carlo) molecular dynamics [5], and the analytical method of Einzel, Panzer and Liu [4].…”

Section: A Cylindrical Couette Flowmentioning

confidence: 99%

Velocity boundary condition at solid walls in rarefied gas calculations

et al. 2004

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Maxwell's original slip boundary condition is widely misapplied in current rarefied gas flow calculations (e.g. in hypersonics, microfluidics). If its commonly-accepted form is applied in simulations of gas flows over curved or moving surfaces, crucial physics can be lost. We give examples of such cases. We also propose a new higher-order boundary condition which is based on Maxwell's original equation and the constitutive relations derived by Burnett. Unlike other higher-order models this is generally applicable to three-dimensional moving surfaces. It is shown that these 'MaxwellBurnett' boundary conditions give much closer agreement with experimental data for Poiseuille flow than existing higher-order models and can also predict Sone's thermal-stress slip flow -a phenomenon which cannot be captured by conventional slip boundary conditions.

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“…We directly deduce that v e = (ε d ζ/η)E ∞ . Nevertheless, the partial slip BC has to be modified to take into account the sphere curvature [35]: indeed, this condition accounts for the equality of friction λv θ and viscous σ rθ tangential stresses, but in spherical coordinates the expression of the stress tensor at a radius a includes a curvature term: σ rθ = η(∂ r v θ − v θ /a). We obtain a generalized slip condition at a surface with curvature a:…”

Section: Curvature Effectsmentioning

confidence: 99%

Liquid friction on charged surfaces: From hydrodynamic slippage to electrokinetics

Joly

Ybert

Trizac

et al. 2006

The Journal of Chemical Physics

209

229

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Hydrodynamic behavior at the vicinity of a confining wall is closely related to the friction properties of the liquid/solid interface. Here we consider, using Molecular Dynamics simulations, the electric contribution to friction for charged surfaces, and the induced modification of the hydrodynamic boundary condition at the confining boundary. The consequences of liquid slippage for electrokinetic phenomena, through the coupling between hydrodynamics and electrostatics within the electric double layer, are explored. Strong amplification of electro-osmotic effects is revealed, and the non-trivial effect of surface charge is discussed. This work allows to reconsider existing experimental data, concerning ζ potentials of hydrophobic surfaces and suggest the possibility to generate "giant" electro-osmotic and electrophoretic effects, with direct applications in microfluidics.

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Boundary condition for fluid flow: Curved or rough surfaces

Cited by 165 publications

References 6 publications

Microfluidics: The No-Slip Boundary Condition

Microfluidics: The No-Slip Boundary Condition

Velocity boundary condition at solid walls in rarefied gas calculations

Liquid friction on charged surfaces: From hydrodynamic slippage to electrokinetics

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