Creeping Flow Past a Porous Spherical Shell

Yu, Qin; Kaloni, P. N.

doi:10.1002/zamm.19930730207

Cited by 41 publications

(20 citation statements)

References 16 publications

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“…this result agrees with a well-known result earlier reported by Brinkman (1947), Ooms et al (1970), Neale et al (1973), Masliyah et al (1987), Qin and Kaloni (1988), Qin and Kaloni (1993), Vasin and Kharitonova (2011a), Vasin and Kharitonova (2011b) and later Yadav and Deo (2012) for the drag force experienced by a permeable sphere in an unbounded clear fluid.…”

Section: Resultssupporting

confidence: 93%

Stokes Flow over Composite Sphere: Liquid Core with Permeable Shell

Jaiswal

Gupta

2015

JAFM

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This paper presents an analytical study of an infinite expanse of uniform flow of steady axisymmetric Stokes flow of an incompressible Newtonian fluid around the spherical drop of Reiner-Rivlin liquid coated with the permeable layer with the assumption that the liquid located outside the capsule penetrates into the permeable layer, but it is not mingled with the liquid located in the internal concave of capsule. The flow inside the permeable layer is described by the Brinkman equation. The viscosity of the permeable medium is assumed to be same as pure liquid. The stream function solution for the outer flow field is obtained in terms of modified Bessel functions and Gegenbauer functions, and for the inner flow field, the stream function solution is obtained by expanding the stream function in terms of S. The flow fields are determined explicitly by matching the boundary conditions at the pure liquid-porous interface, porous-Reiner-Rivlin liquid interface, and uniform velocity at infinity. The drag force experienced by the capsule is evaluated, and its variation with regard to permeability parameter α, dimensionless parameter S, ratio of viscosities λ 2 , and thickness of permeable layer δ is studied and graphs plotted against these parameters. Several cases of interest are deduced from the present analysis. It is observed that the cross-viscosity increases the drag force, whereas the thickness δ decreases the drag on capsule. It is also observed that the drag force is increasing or decreasing function of permeability parameter for λ 2 < 1.

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Section: Resultssupporting

confidence: 93%

Stokes Flow over Composite Sphere: Liquid Core with Permeable Shell

Jaiswal

Gupta

2015

JAFM

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“…Payne and Straughan [17] have shown that the solution to thermal flow problems depends continuously on the parameter α when Darcy's law is adopted in the porous medium and Stokes's flow holds in the fluid layer. Indeed, the Beavers-Joseph condition has proved successful in other slow-flow situations, such as flow past a porous sphere (see Qin and Kaloni [18]). However, the analysis of [17] casts serious doubt on whether (1.2) would be realistic for larger fluid velocities for which Navier-Stokes flow is valid.…”

Section: Introductionmentioning

confidence: 98%

Surface-Tension-Driven Convection in a Fluid Overlying a Porous Layer

Straughan¹

2001

Journal of Computational Physics

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“…The problem of creeping flow past a porous particle in terms of Brinkman's equation has been firstly treated by Higdon and Kojima [13], by using a direct boundary integral approach. Qin and Kaloni [33] used the Stokes and Brinkman equations for the Stokes flow past a porous spherical shell, and derived an explicit solution. Davis and Stone [5] studied the flow within and around a porous particle which is contained in a bed of many similar particles, and used two approximate models based on the Brinkman equations in order to describe the principal features of the flow.…”

Section: Introductionmentioning

confidence: 99%

Boundary integral equations for a three‐dimensional Brinkman flow problem

Kohr

Wendland

2009

Mathematische Nachrichten

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The purpose of this paper is to prove existence and uniqueness in Sobolev or Hölder spaces for a transmission problem which describes the flow of a viscous incompressible fluid past a porous particle embedded in a second porous medium, by using the Brinkman model and potential theory. Some particular cases, which refer to Stokes flow past a porous particle, or to Brinkman's flow past a void, are also presented together with corresponding asymptotic results for the flow velocity field and the hydrodynamic force exerted on the particle.

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Creeping Flow Past a Porous Spherical Shell

Cited by 41 publications

References 16 publications

Stokes Flow over Composite Sphere: Liquid Core with Permeable Shell

Stokes Flow over Composite Sphere: Liquid Core with Permeable Shell

Surface-Tension-Driven Convection in a Fluid Overlying a Porous Layer

Boundary integral equations for a three‐dimensional Brinkman flow problem

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