A model for the boundary condition of a porous material. Part 2

Richardson, S. M.

doi:10.1017/s002211207100209x

Cited by 262 publications

(100 citation statements)

References 2 publications

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“…Calculations have been made for periodic and random surfaces [111,127,140,164] and are related to earlier work on the boundary conditions for porous materials [133,155] and the Laplace equation [139].…”

Section: Surface Roughnessmentioning

confidence: 99%

Microfluidics: The No-Slip Boundary Condition

Lauga

Brenner

Stone

2007

Springer Handbook of Experimental Fluid Mechanics

583

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: Surface Roughnessmentioning

confidence: 99%

Microfluidics: The No-Slip Boundary Condition

Lauga

Brenner

Stone

2007

Springer Handbook of Experimental Fluid Mechanics

583

674

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“…Analytical work is limited to somewhat artificial situations (see e.g. Richardson 1971;Taylor 1971) or relatively high porosities (see e.g. James & Davis 2001).…”

Section: Introductionmentioning

confidence: 99%

Pressure-driven flow in a channel with porous walls

Liu

Prosperetti

2011

J. Fluid Mech.

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The finite-Reynolds-number three-dimensional flow in a channel bounded by one and two parallel porous walls is studied numerically. The porous medium is modelled by spheres in a simple cubic arrangement. Detailed results on the flow structure and the hydrodynamic forces and couple acting on the sphere layer bounding the porous medium are reported and their dependence on the Reynolds number illustrated. It is shown that, at finite Reynolds numbers, a lift force acts on the spheres, which may be expected to contribute to the mobilization of bottom sediments. The results for the slip velocity at the surface of the porous layers are compared with the phenomenological Beavers-Joseph model. It is found that the values of the slip coefficient for pressure-driven and shear-driven flow are somewhat different, and also depend on the Reynolds number. A modification of the relation is suggested to deal with these features. The Appendix provides an alternative derivation of this modified relation.

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“…As described before, the formation of this secondary ring is due to the development of the boundary layer. Beavers and Joseph, 25 Taylor, 26 and Richardson 27 suggest that the boundary layer penetrates into the porous media. Hence, the weak formation of the secondary vortex ring is clearly explained by increment in the extension onto the foam material with porosity, affecting the boundary layer.…”

Section: Resultsmentioning

confidence: 99%

Vortex rings impinging on permeable boundaries

Mujal-Colilles

Dalziel

Bateman³

2015

Physics of Fluids

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Experiments with vortex rings impinging permeable and solid boundaries are presented in order to investigate the influence of permeability. Utilizing Particle Image Velocimetry, we compared the behaviour of a vortex ring impinging four different reticulated foams (with permeability k ~ 26 - 85 × 10-8 m2) and a solid boundary. Results show how permeability affects the stretching phenomena of the vortex ring and the formation and evolution of the secondary vortex ring with opposite sign. Moreover, permeability also affects the macroscopic no-slip boundary condition found on the solid boundary, turning it into an apparent slip boundary condition for the most permeable boundary. The apparent slip-boundary condition and the flux exchange between the ambient fluid and the foam are jointly responsible for both the modified formation of the secondary vortex and changes on the vortex ring diameter increase.Peer ReviewedPostprint (published version

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A model for the boundary condition of a porous material. Part 2

Cited by 262 publications

References 2 publications

Microfluidics: The No-Slip Boundary Condition

Microfluidics: The No-Slip Boundary Condition

Pressure-driven flow in a channel with porous walls

Vortex rings impinging on permeable boundaries

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