Stokes flow through a rectangular array of circular cylinders

Wang, C Y

doi:10.1016/s0169-5983(01)00013-2

Cited by 39 publications

(30 citation statements)

References 9 publications

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“…. The fluid is forced through a tortuous path, unlike the straight paths of Wang [5]. Fig 3 shows the streamlines parallel to the stagger for the same geometry.…”

Section: Results For Square Cylindersmentioning

confidence: 99%

“…The permeability is Several other approximate formulas are useful. The empirical formula for sparsely (but more or less evenly) distributed square cylinders [5] is…”

Section: Results For Square Cylindersmentioning

confidence: 99%

“…Recently Wang [5] studied the Stokes flow across a rectangular array of rectangular cylinders. This model is particularly important for seepage in rock fissures and resin impregnation of rectangular fiber bundles in the production of composites.…”

Section: Introductionmentioning

confidence: 99%

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Stokes flow through a staggered array of rectangular cylinders and the junction resistance

Wang

1999

Z. angew. Math. Phys.

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The micro-fluid mechanical problem of viscous flow across an array of staggered rectangular cylinders is studied by eigenfunction expansions and matching. Streamlines and permeabilities are determined for (mean) flows normal and parallel to the stagger. A variety of approximate formulas are deduced. The resistance of a T junction is determined.Mathematics Subject Classification (1991). 76D07, 31A30, 76S05.

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“…. The fluid is forced through a tortuous path, unlike the straight paths of Wang [5]. Fig 3 shows the streamlines parallel to the stagger for the same geometry.…”

Section: Results For Square Cylindersmentioning

confidence: 99%

“…The permeability is Several other approximate formulas are useful. The empirical formula for sparsely (but more or less evenly) distributed square cylinders [5] is…”

Section: Results For Square Cylindersmentioning

confidence: 99%

See 1 more Smart Citation

Stokes flow through a staggered array of rectangular cylinders and the junction resistance

Wang

1999

Z. angew. Math. Phys.

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“…3. From analytical investigations in Happel and Brenner (1973), Wang (2001) introduces the following estimation for the permeability (with our notations)…”

Section: Fibrous Mediamentioning

confidence: 99%

“…Estimation (17) for K I I I remains valid (Wang 2001). Therefore the different ranges of validity of the flow laws are as above.…”

Section: Fibrous Mediamentioning

confidence: 99%

On the Domain of Validity of Brinkman’s Equation

2008

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An increasing number of articles are adopting Brinkman's equation in place of Darcy's law for describing flow in porous media. That poses the question of the respective domains of validity of both laws, as well as the question of the value of the effective viscosity µ e which is present in Brinkman's equation. These two topics are addressed in this article, mainly by a priori estimates and by recalling existing analyses. Three main classes of porous media can be distinguished: "classical" porous media with a connected solid structure where the pore surface S p is a function of the characteristic pore size l p (such as for cylindrical pores), swarms of low concentration fixed particles where the pore surface is a function of the characteristic particle size l s , and fiber-made porous media at low solid concentration where the pore surface is a function of the fiber diameter. If Brinkman's 3D flow equation is valid to describe the flow of a Newtonian fluid through a swarm of fixed particles or fibrous media at low concentration under very precise conditions (Lévy 1983), then we show that it cannot apply to the flow of such a fluid through classical porous media.

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Boundary conditions at the interface between fluid layer and fibrous medium

Bai

Winoto

Low

2008

Numerical Methods in Fluids

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SUMMARYThe flow through a channel partially filled with fibrous porous medium was analyzed to investigate the interfacial boundary conditions. The fibrous medium was modeled as a periodic array of circular cylinders, in a hexagonal arrangement, using the boundary element method. The area and volume average methods were applied to relate the pore scale to the representative elementary volume scale. The permeability of the modeled fibrous medium was calculated from the Darcy's law with the volume-averaged Darcy velocity. The slip coefficient, interfacial velocity, effective viscosity and shear jump coefficients at the interface were obtained with the averaged velocities at various permeabilities or Darcy numbers.

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Stokes flow through a rectangular array of circular cylinders

Abstract: The slow viscous ow past a rectangular array of parallel circular cylinders is studied. The method of eigenfunction expansions and matching between two domains is used to obtain the ow. Permeabilities in the three principal directions are determined. Approximate formulas are derived.

Cited by 39 publications

References 9 publications

Stokes flow through a staggered array of rectangular cylinders and the junction resistance

Stokes flow through a staggered array of rectangular cylinders and the junction resistance

On the Domain of Validity of Brinkman’s Equation

Boundary conditions at the interface between fluid layer and fibrous medium

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