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E I Saad - One of the best experts on this subject based on the ideXlab platform.
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axisymmetric motion of a porous sphere through a spherical envelope subject to a Stress Jump condition
Meccanica, 2016Co-Authors: E I SaadAbstract:The flow problem of an incompressible axisymmetrical quasisteady translation and steady rotation of a porous sphere in an eccentric spherical container is discussed using a combined analytical–numerical technique. A continuity of velocity components and normal Stress together with the Stress Jump condition for the tangential Stress are used at the interface between porous and clear-fluid regions. The fluid flow outside the particle is governed by the classical Stokes equations while the fluid flow inside the porous region is treated by Brinkman model. In order to solve the Stokes equations for the flow field, a general solution is constructed from the superposition of the basic solutions in the two spherical coordinate systems based on both the porous sphere and spherical envelope. Solutions for translational and rotational motion of porous eccentric spherical particle in a spherical envelope are obtained using the boundary collocation technique. The hydrodynamic drag force and couple exerted by the surrounding fluid on the porous particle which is proportional to the translational and angular velocities, respectively, are calculated with good convergence for various values of the ratio of porous-to-container radii, the relative distance between the centers of the porous and container, the Stress Jump coefficient, and a coefficient that is proportional to the permeability. In the limits of the motions of a porous sphere in a concentric container and near a container surface with a small curvature, the numerical values of the normalized drag force and the normalized coupling coefficient are in good agreement with the available values in the literature.
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slow motion of a porous sphere translating along the axis of a circular cylindrical pore subject to a Stress Jump condition
Transport in Porous Media, 2014Co-Authors: E I Saad, M S FaltasAbstract:The coupled flow problem of an incompressible axisymmetrical quasisteady motion of a porous sphere translating in a viscous fluid along the axis of a circular cylindrical pore is discussed using a combined analytical–numerical technique. At the fluid–porous interface, the Stress Jump boundary condition for the tangential Stress along with continuity of normal Stress and velocity components are employed. The flow through the porous particle is governed by the Brinkman model and the flow in the outside porous region is governed by Stokes equations. A general solution for the field equations in the clear region is constructed from the superposition of the fundamental solutions in both cylindrical and spherical coordinate systems. The boundary conditions are satisfied first at the cylindrical pore wall by the Fourier transforms and then on the surface of the porous particle by a collocation method. The collocation solutions for the normalized hydrodynamic drag force exerted by the clear fluid on the porous particle is calculated with good convergence for various values of the ratio of radii of the porous sphere and pore, the Stress Jump coefficient, and a coefficient that is proportional to the permeability. The shape effect of the cylindrical pore on the axial translation of the porous sphere is compared with that of the particle in a spherical cavity; it found that the porous particle in a circular cylindrical pore in general attains a lower hydrodynamic drag than in a spherical envelope.
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stokes flow past an assemblage of axisymmetric porous spherical shell in cell models effect of Stress Jump condition
Meccanica, 2013Co-Authors: E I SaadAbstract:The quasisteady axisymmetrical flow of an incompressible viscous fluid past an assemblage of porous concentric spherical shell-in-cell model is studied. Boundary conditions on the cell surface that correspond to the Happel, Kuwabara, Kvashnin and Cunningham/Mehta-Morse models are considered. At the fluid-porous interfaces, the Stress Jump boundary condition for the tangential Stresses along with continuity of normal Stress and velocity components are employed. The Brinkman’s equation in the porous region and the Stokes equation for clear fluid are used. The hydrodynamic drag force acting on the porous shell by the external fluid in each of the four boundary conditions on the cell surface is evaluated. It is found that the normalized mobility of the particles (the hydrodynamic interaction among the porous shell particles) depends not only on the permeability of the porous shells and volume fraction of the porous shell particles, but also on the Stress Jump coefficient. As a limiting case, the drag force or mobility for a suspension of porous spherical shells reduces to those for suspensions of impermeable solid spheres and of porous spheres with Jump.
G Raja P Sekhar - One of the best experts on this subject based on the ideXlab platform.
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stokes flow of an assemblage of porous particles Stress Jump condition
Zeitschrift für Angewandte Mathematik und Physik, 2011Co-Authors: Jai Prakash, G Raja P Sekhar, Mirela KohrAbstract:The present article investigates the overall bed permeability of an assemblage of porous particles. For the bed of porous particles, the fluid-particle system is represented as an assemblage of uniform porous spheres fixed in space. Each sphere, with a surrounding envelope of fluid, is uncoupled from the system and considered separately. This model is popularly known as cell model. Stokes equations are employed inside the fluid envelope and Brinkman equations are used inside the porous region. The Stress Jump boundary condition is used at the porous-liquid interface together with the continuity of normal Stress and continuity of velocity components. On the surface of the fluid envelope, three different possible boundary conditions are tested. The obtained expression for the drag force is used to estimate the overall bed permeability of the assemblage of porous particles and the behavior of overall bed permeability is analyzed with various parameters like modified Darcy number (Da*), Stress Jump coefficient (β), volume fraction (e), and effective viscosity.
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overall bed permeability for flow through beds of permeable porous particles using the effective medium model Stress Jump condition
Chemical Engineering Communications, 2010Co-Authors: Jai Prakash, G Raja P SekharAbstract:An effective medium model is used for predicting the overall bed permeability (OBP) for the flow through beds of permeable porous spherical particles. The effective medium model used here assumes that a single permeable porous spherical particle is surrounded by a hypothetical fluid envelope and an effective medium beyond the envelope. Stokes equations are used in the fluid region and Brinkman equations are used inside the porous regions. At the porous-liquid interfaces, the Stress-Jump condition is used together with the continuity of velocity components and the continuity of normal Stress. Fa[xacute]en's law for drag and torque acting on the surface of permeable porous sphere is determined and hence the overall bed permeability is calculated as an implicit relation. This model converges to the existing models in various limiting cases.
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viscous flow past a porous spherical shell effect of Stress Jump boundary condition
Journal of Engineering Mechanics-asce, 2005Co-Authors: M K Partha, P V S N Murthy, G Raja P SekharAbstract:Using the Stress Jump boundary condition for the tangential Stresses at the porous liquid interface along with the continuity of the velocity components and normal Stress, the uniform viscous flow past a porous spherical shell with external radius r1 , internal radius r2 is studied. The flow inside the porous region is governed by Brinkman equation. The flow in the liquid region is governed by the Stokes equation. The flow field is computed by matching the boundary conditions at the porous-fluid interface. The effect of Stress Jump coefficient β on the flow field is very much felt. An increase in the drag with permeability is found for different R , different ratio of r1 ∕ r2 , and also a change in magnitude of the drag for different values of Stress Jump coefficient β is observed. Also, the variation of torque and shear Stress with permeability and the Stress Jump coefficient is discussed.
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stokes flow inside a porous spherical shell Stress Jump boundary condition
Zeitschrift für Angewandte Mathematik und Physik, 2005Co-Authors: Anindita Bhattacharyya, G Raja P SekharAbstract:An arbitrary Stokes flow of a viscous, incompressible fluid inside a sphere with internal singularities, enclosed by a porous spherical shell, using Brinkman’s equation for the flow in the porous region is discussed. At the interface of the clear fluid and porous region Stress Jump boundary condition for tangential Stresses is used. The drag and torque are found by deriving the corresponding Faxen’s laws. It is found that drag and torque not only change with the varying permeability, but also change for different values of Stress Jump coefficient. Critical permeability is found for which drag and torque change their behavior. As a limiting case the corresponding Faxen’s laws for the rigid spherical shell with internal singularities has been obtained.
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viscous flow past a porous sphere with an impermeable core effect of Stress Jump condition
Chemical Engineering Science, 2004Co-Authors: Anindita Bhattacharyya, G Raja P SekharAbstract:Abstract An arbitrary flow of a viscous, incompressible fluid past a porous sphere of radius ` a ' with an impermeable core of radius ` b ', using Brinkman's equation in the porous region is discussed. At the interface of the clear fluid and porous region, Stress Jump boundary condition for the tangential Stresses along with the continuity of normal Stresses and the velocity components are used. On the surface of the impermeable core no slip condition is used. The corresponding Faxen's laws are derived to compute the drag and torque acting on the surface r = a . It is found that the drag and torque not only change with the change of the permeability, but also a significant effect of the Stress Jump co-efficient is observed. The variation of drag and torque with permeability for different thickness ( a - b ) of the porous region as well as for different values of Stress Jump coefficient is discussed when the basic flow is due to uniform flow, two dimensional irrotational flow, doublet in a uniform flow, stokeslet, rotlet. In case of uniform flow the flow field has been plotted. In all the cases, a significant effect of the Stress Jump coefficient has been realized.
A V Kuznetsov - One of the best experts on this subject based on the ideXlab platform.
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influence of the Stress Jump condition at the porous medium clear fluid interface on a flow at a porous wall
International Communications in Heat and Mass Transfer, 1997Co-Authors: A V KuznetsovAbstract:Abstract This paper presents an analytical solution for the steady fully developed fluid flow in a composite region, which is partly filled with a porous medium and partly with a clear fluid. The Brinkman-Forchheimer equation is utilized to model the flow in a porous region. Different from the previous investigations, the Stress Jump boundary condition suggested by Ochoa-Tapia and Whitaker is used at the porous medium/clear fluid interface.
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analytical investigation of the fluid flow in the interface region between a porous medium and a clear fluid in channels partially filled with a porous medium
Flow Turbulence and Combustion, 1996Co-Authors: A V KuznetsovAbstract:In this paper analytical solutions for the steady fully developed laminar fluid flow in the parallel-plate and cylindrical channels partially filled with a porous medium and partially with a clear fluid are presented. The Brinkman-extended Darcy equation is utilized to model the flow in a porous region. The solutions account for the boundary effects and for the Stress Jump boundary condition at the interface recently suggested by Ochoa-Tapia and Whitaker. The dependence of the velocity on the Darcy number and on the adjustable coefficient in the Stress Jump boundary condition is investigated. It is shown that accounting for a Jump in the shear Stress at the interface essentially influences velocity profiles.
Mario Minale - One of the best experts on this subject based on the ideXlab platform.
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modelling the flow of a second order fluid through and over a porous medium using the volume averages ii the Stress boundary condition
Physics of Fluids, 2016Co-Authors: Mario MinaleAbstract:In this paper, a Stress boundary condition at the interface between a porous medium saturated by a viscoelastic fluid and the free viscoelastic fluid is derived. The volume averages are used to upscale the problem. The boundary condition is obtained on the assumption that the free fluid Stress is transferred partially to the fluid within the porous medium and partially to the solid skeleton. To this end the momentum balance on the solid skeleton saturated by the viscoelastic fluid is derived and a generalised Biot’s equation is obtained, which is coupled with the generalised Brinkman’s equation derived in Part I of the paper. They together state that the whole Stress carried by the porous medium, sum of that of the fluid and that of the solid skeleton, is not dissipated. The boundary condition here derived does not show any Stress Jump and as in Part I, to emphasize the effect of elasticity, a second order fluid of Coleman and Noll is considered as viscoelastic fluid. Also the Stress boundary condition at the interface between a homogeneous solid and the porous medium saturated by the viscoelastic fluid is obtained.
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momentum transfer within a porous medium ii Stress boundary condition
Physics of Fluids, 2014Co-Authors: Mario MinaleAbstract:In this paper, we derive a boundary condition at the interface between a free fluid and a porous medium stating that the Stress is transferred both to the fluid within the porous medium and to the solid skeleton. A zero Stress Jump is obtained so that the total Stress is preserved at the interface. The boundary condition is obtained with the volume averaging method following the approach of Ochoa-Tapia and Whitaker [“Momentum transfer at the boundary between a porous medium and a homogeneous fluid—I. Theoretical development,” Int. J. Heat Mass Transfer 38(14), 2635–2646 (1995)], but starting from the momentum balances written on the fluid and on the solid of the porous region, the latter was derived in part I of this paper. In the same way, also the boundary condition at the interface between a porous medium and a homogeneous solid is obtained. Both boundary conditions describe the equilibrium of forces at the interface, where part of the Stress is carried by the solid skeleton and part by the fluid within the porous medium. With the derived boundary conditions, together with the Stress transfer equation within the solid skeleton, it is now possible to satisfy the overall force equilibrium on a shear cell partially filled with a porous medium.
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Shear flow over a porous layer: Velocity in the real proximity of the interface via rheological tests
Physics of Fluids, 2011Co-Authors: Claudia Carotenuto, Mario MinaleAbstract:In this paper, we have experimentally investigated the velocity profile of a fluid undergoing simple shear above a porous medium. To this end, we used for the first time rheological tests performed with a constant Stress rheometer equipped with parallel plate geometry with a real porous medium glued on the lower plate. The velocity at the interface between the porous layer and the free fluid was inferred by extrapolating the linear velocity profile in the free fluid to the interface. These data were nicely compared with predictions obtained integrating the Brinkman extension of Darcy law in the porous medium together with Stokes equations in the free fluid coupled at the interface by the continuity of velocity and by the momentum balance suggested by Ochoa-Tapia and Whitaker [Int. J. Heat Mass Transfer 38(14), 2635 (1995)]. In the literature, the physical origin of the Stress Jump imposed by Ochoa-Tapia and Whitaker at the interface has been attributed to a perturbation of the velocity profile in the vici...
Alberto J Ochoatapia - One of the best experts on this subject based on the ideXlab platform.
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velocity and Stress Jump conditions between a porous medium and a fluid
Advances in Water Resources, 2013Co-Authors: Francisco J Valdesparada, Alberto J Ochoatapia, C G Aguilarmadera, Benoit GoyeauAbstract:Abstract Modeling transport phenomena in hierarchical systems can be carried out by either a one domain approach or a two domain approach. The first one involves assuming the system as a pseudo-continuum and is expressed in terms of position-dependent effective medium coefficients. In the two domain approach, the differential equations have position-independent coefficients but require accounting for the corresponding boundary conditions that couple the equations between each homogeneous region. For momentum transport between a porous medium and a fluid, Stress boundary conditions have been derived in terms of a Jump coefficient that needs to be predicted within a two-domain approach formulation. However, continuity of the velocity is postulated at the dividing surface. In this work, we propose a methodology for the derivation of boundary conditions for both the velocity and the Stress. These conditions are expressed in terms of Jump coefficients that are computed from the solution of an ancillary macroscopic closure problem. This problem accounts for the deviations from the one and two domain approaches. From the closure problem solution we were also able to determine the position at which the Jump conditions should be applied, i . e . , the dividing surface position. In addition, we used this methodology adopting the assumptions proposed by Ochoa-Tapia and Whitaker as well as those by Beavers and Joseph. We found that any version of the two domain approach was in agreement with the one domain approach in the bulk of the porous medium and the fluid. However, the same is not true for the process of capturing the essential information of the inter-region.
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Jump momentum boundary condition at a fluid porous dividing surface derivation of the closure problem
Chemical Engineering Science, 2007Co-Authors: Francisco J Valdesparada, Benoit Goyeau, Alberto J OchoatapiaAbstract:The method of volume averaging is used to derive a Stress Jump boundary condition that takes the form eβω-1∂〈vβ〉ω∂y-∂〈vβ〉η∂y=-K-1avs〈vβ〉ω. Here K-1K-1 is the tangential component of a mixed Stress tensor which combines the global and Brinkman Stresses at the dividing surface. The computation of the Brinkman Stress at the boundary is carried out by using polynomial functions describing the spatial changes of the porosity. Local closure problems are derived for the determination of the global Stress contribution at the inter-region. At this stage, an alternative methodology is proposed in order to estimate the mixed Stress tensor, which has been related to the Stress Jump coefficient proposed in the literature. Results for the Jump coefficient are found to be in good agreement with previous calculations.
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momentum transfer at the boundary between a porous medium and a homogeneous fluid ii comparison with experiment
International Journal of Heat and Mass Transfer, 1995Co-Authors: Alberto J Ochoatapia, Stephen WhitakerAbstract:Abstract In Part I of this paper a Stress Jump condition was developed based on the non-local form of the volume averaged Stokes' equations. The excess Stress terms that appeared in the Jump condition were represented in a manner that led to a tangential Stress boundary condition containing a single adjustable coefficient of order one. In this paper we compare the theory with the experimental studies of Beavers and Joseph [J. Fluid Mech. 30, 197–207 (1967)], and we explore the use of a variable porosity model as a substitute for the Jump condition. The latter approach does not lead to a successful representation of all the experimental data, but it does provide some insight into the complexities of the boundary region between a porous medium and a homogenous fluid.