Slow viscous flow through a membrane built up from porous cylindrical particles with an impermeable core

Deo, Satya; Yadav, Pramod Kumar; Tiwari, Ashish

doi:10.1016/j.apm.2009.08.014

Cited by 34 publications

(25 citation statements)

References 16 publications

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“…The stream function for a slow viscous flow through an array of porous cylindrical particles with Happel's boundary condition was considered in [51]. The drag force exerted to each porous cylindrical particle in a cell was evaluated.…”

Section: Cell Models: Cylindrical Particlesmentioning

confidence: 99%

Hydrodynamic permeability of aggregates of porous particles with an impermeable core

Deo

Филиппов

Tiwari

et al. 2011

Advances in Colloid and Interface Science

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Section: Cell Models: Cylindrical Particlesmentioning

confidence: 99%

Hydrodynamic permeability of aggregates of porous particles with an impermeable core

Deo

Филиппов

Tiwari

et al. 2011

Advances in Colloid and Interface Science

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“…Some of them have been solved in the literature for a reduced description of the problem, e.g. Case IV in Stechkina (1979), Deo (2004), Deo and Yadav (2008), Vasin and Filipov (2009), Deo et al (2010), Deo et al (2011), Case V (setting σ 1 → ∞ for solid obstacle) in Kuwabara (1959), Deo and Yadav (2008), Vasin and Filipov (2009) …”

Section: Effect Of σ 1 and σmentioning

confidence: 99%

“…Other outer-boundary conditions were later proposed, such as the prescribed tangential velocity (Mehta and Morse 1975) or its zero radial derivative (Kvashnin 1979). At the same time, cell model conditions were also extended over more complex physical systems, for example, describing Stokes flow across an array of permeable cylinders (Stechkina 1979;Deo 2004) and permeable spheres (Yamamoto 1971;Neale et al 1973;Davis and Stone 1993), with further extensions considering permeable shells around inclusions of spherical (Filipov et al 2006;Vasin et al 2008;Deo et al 2011;Yadav and Deo 2012) and cylindrical (Deo et al 2011;Deo and Yadav 2008;Vasin and Filipov 2009;Deo et al 2010) shapes. In parallel, lubrication theory experienced a similar evolution trend.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stokes–Brinkman–Darcy Solutions of Bimodal Porous Flow Across Periodic Array of Permeable Cylindrical Inclusions: Cell Model, Lubrication Theory and LBM/FEM Numerical Simulations

Silva

Ginzburg

2016

Transp Porous Med

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An analytical study is devised for the problem of bimodal porous flow across a periodic array of permeable cylindrical inclusions. Such a configuration is particularly relevant for porous media systems of dual granulometry, an idealization often taken, e.g. in the modelling of membranes and fibrous applications. The double-porosity system is governed by the Stokes-Brinkman-Darcy equations, the most general description in this class of flow problems characterized by the permeabilities of the surrounding matrix and inclusions, their porosities and the relative volume fraction. We solve this problem with the Kuwabara cell model and lubrication approach, providing analytical solutions for the system effective permeability in closed analytical form. The ensemble of results demonstrates the self-consistency of the bimodal solutions in eight possible limit configurations and supports the validity of the Beavers-Joseph interface stress jump condition for transmission from the open Stokes flow to low-permeable Darcy region. At the same time, these solutions bring further insight on the relative significance of the governing parameters on the effective permeability, with a focus on the role of the effective viscosity (porosity) distribution. Furthermore, although the cell model is restricted to relatively small volume fractions in open flow, its validity extends in lesspermeable background flow inside Brinkman/Brinkman description. In turn, the lubrication approximation remains more adequate in the opposite limit of the dense impermeable inclusions. These conclusions are drawn from comparisons with the numerical solutions obtained with the developed lattice Boltzmann model and the standard finite element method. The two methods principally differ in the treatment of the interface conditions: implicit and explicit, respectively. The purpose of this task is therefore twofold. While the numerical schemes help quantifying the validity limits of the theoretical approach, the analytical solutions offer a non-trivial benchmark for numerical schemes in highly heterogeneous soil.

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“…They investigated the influence of the porous shell on the total permeability by applying the Mehta-Morse boundary condition on the cell boundary. Deo et al (2010) This work is concerns with the axisymmetric Stokes flow of an incompressible viscous fluid past a swarm of porous cylindrical shells with four known boundary conditions as Happel's, Kuwabara's, Kvashnin's and Cunningham/Mehta-Morse's. Drag force experienced by the porous cylindrical shell within a cell is evaluated.…”

Section: Introductionmentioning

confidence: 99%

Axisymmetric Stokes Flow past a Swarm of Porous Cylindrical Shells

Ansari

Deo

2016

JAFM

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The problem of an axisymmetric Stokes flow for an incompressible viscous fluid past a swarm of porous cylindrical shells with four known boundary conditions as Happel's, Kuwabara's, Kvashnin's and Cunningham/Mehta-Morse's is tackled. The Brinkman equation is taken for fluid flow through the porous region and the Stokes equation for fluid region in their stream function formulation are used. Drag force experienced by the porous cylindrical shell within a cell is evaluated. The hydrodynamic permeability of the membrane built by the porous particles is also investigated. For different values of parameters, the variation of drag force and the hydrodynamic permeability are presented graphically and discussed.

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Slow viscous flow through a membrane built up from porous cylindrical particles with an impermeable core

Cited by 34 publications

References 16 publications

Hydrodynamic permeability of aggregates of porous particles with an impermeable core

Hydrodynamic permeability of aggregates of porous particles with an impermeable core

Stokes–Brinkman–Darcy Solutions of Bimodal Porous Flow Across Periodic Array of Permeable Cylindrical Inclusions: Cell Model, Lubrication Theory and LBM/FEM Numerical Simulations

Axisymmetric Stokes Flow past a Swarm of Porous Cylindrical Shells

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