Stokes flow past a porous sphere using Brinkman's model

Padmavathi, B.S.; Amaranath, T.; Nigam, S. D.

doi:10.1007/bf00942818

Cited by 49 publications

(29 citation statements)

References 11 publications

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“…Now, taking into account the fact that (Φ 0 , h 0 ) is a solution to the system of equations (5.13) and (5.14), and making use of the relations (4.31)-(4.35) and (4.50)-(4.52), we obtain the properties 25) in view of which we get the equality …”

Section: The Potential Theory For the System Of Equations (26) And (mentioning

confidence: 99%

Existence and uniqueness result for the problem of viscous flow in a granular material with a void

Kohr

Sekhar

2007

Quart. Appl. Math.

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Section: The Potential Theory For the System Of Equations (26) And (mentioning

confidence: 99%

Existence and uniqueness result for the problem of viscous flow in a granular material with a void

Kohr

Sekhar

2007

Quart. Appl. Math.

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“…Under our modeling assumptions, the settling velocity, U, of the sphere is given by the balance of Stokes' drag (neglecting permeability effects 14 ) and buoyancy, 2013) where ρ e (z) is the ambient fluid density, z = Z(t) is the sphere center depth, and V is the sphere volume. The mass of the sphere, M sph (t), is dependent on the porosity of the sphere P and solid density ρ s , M sph (t) = P Vρ s + P M fl (t) , where P = (1 − P).…”

mentioning

confidence: 99%

Retention and entrainment effects: Experiments and theory for porous spheres settling in sharply stratified fluids

Camassa¹,

Khatri²,

McLaughlin³

et al. 2013

Physics of Fluids

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We present an experimental study of single porous spheres settling in a near two-layer ambient density fluid. Data are compared with a first-principle model based on diffusive processes. The model correctly predicts accelerations of the sphere but does not capture the retention time at the density transition quantitatively. Entrainment of lighter fluid through a shell encapsulating the sphere is included in this model empirically. With this parametrization, which exhibits a power law dependence on Reynolds numbers, retention times are accurately captured. Extrapolating from our experimental data, model predictions are presented.

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“…, and for the flow inside the porous region the following representation is used which is a complete general solution of the Brinkman and continuity equations (3)(see Padmavathi [2])…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…In this case, we are interested in considering oscillatory flow in the liquid region and Darcy's law as given in (2) in the porous region, we set the velocity and pressure fields v f and p…”

Section: Oscillatory Analysismentioning

confidence: 99%

Steady and oscillatory analysis of porous catalysts in fluidized beds

Sekhar

Prakash

Kohr

2008

Proc Appl Math and Mech

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In this paper, we consider the steady /oscillatory flow field within a porous particle contained in a fixed or fluidized bed, in which the spherical porous particle is placed in a spherical envelope of fluid. Stokes equations are employed inside the fluid envelope and Brinkman/Darcy equations are used inside the porous region. We compute drag force acting on the particle and hence the overall bed permeability of the bed. Consider a porous sphere of radius a and permeability k centered in a spherical envelope of radius b, which contains a Newtonian fluid of viscosity µ f . We consider Stokes equation for the flow inside the fluid envelope given byand in the porous region Darcy's law asin case of oscillatory model and the Brinkman equationin case of steady model. In the above equations (V, P ) represents velocity and pressure respectively and superscripts p and f denote flow quantities in the porous region and fluid region respectively. The governing equations are non -dimensionalized usingX = X a ,Ṽ p =

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Stokes flow past a porous sphere using Brinkman's model

Cited by 49 publications

References 11 publications

Existence and uniqueness result for the problem of viscous flow in a granular material with a void

Existence and uniqueness result for the problem of viscous flow in a granular material with a void

Retention and entrainment effects: Experiments and theory for porous spheres settling in sharply stratified fluids

Steady and oscillatory analysis of porous catalysts in fluidized beds

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