Slow Motion of a Porous Sphere Translating Along the Axis of a Circular Cylindrical Pore Subject to a Stress Jump Condition

Saad, E. I.; Faltas, M. S.

doi:10.1007/s11242-013-0263-6

Cited by 13 publications

(5 citation statements)

References 43 publications

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“…The review of the known analytical solutions and basic applications of the micropolar liquids are given in Khanukaeva and Filippov. 6 Using the numerical techniques, Saad and Faltas 7 solved the coupled flow problem of an incompressible viscous fluid flow over a porous sphere located in a circular cylindrical pore and calculated the normalized hydrodynamic drag of the porous particle. Using linear slip and Basset-type boundary conditions, the motion of a solid spherical particle in an incompressible axisymmetric micropolar Stokes flow was investigated by Faltas and Saad 8,9 for two cases: perpendicular translation to the free surface and rotation about a diameter which is also perpendicular to the free surface and parallel translation to the free surface and rotation about a diameter which is lying in the free surface.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Stokes flow of micropolar fluid through a porous cylinder

Maurya

Deo

Khanukaeva

2021

Math Methods in App Sciences

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The present study concerns the Stokes flow of a micropolar fluid through a porous cylinder whose axis is perpendicular to the plane of the flow. Stream functions, velocities, fluid pressures, and stresses are evaluated for the corresponding fluid flow regions. Streamlines for various values of different parameters are plotted and discussed. Also, the fluid velocity vector and microrotation vector for inside and outside the cylinder are plotted for the different values of the viscosity coefficients and discussed for boundary conditions with continuity of couple stress/continuity of tangential stress. A comparative study of the streamlines, velocity components, and microrotation components is presented for two types of the boundary value problems. In case of boundary value problem with continuity of tangential stress, streamlines have circulatory behavior inside the porous cylinder whereas, streamlines have non-circulatory nature in case of boundary value problem with continuity of couple stress.

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Section: Introductionmentioning

confidence: 99%

Analysis of Stokes flow of micropolar fluid through a porous cylinder

Maurya

Deo

Khanukaeva

2021

Math Methods in App Sciences

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“…The solution of the external and internal flow of the porous particle in spherical coordinates can be expressed using the stream functions (Saad & Faltas 2014):…”

Section: Solution Based On Stream Functionmentioning

confidence: 99%

“…By substituting the stream function given by (2.19) into (2.56), we can obtain the simple relation (Saad & Faltas 2014):…”

Section: Drag Force and Velocities Of Particlesmentioning

confidence: 99%

“…Studies on porous particles translating in a cylindrical channel have been more limited. Saad & Faltas (2014) solved the flow of a single porous particle in a cylindrical channel using an analytical-numerical method, constructing a general solution from the superposition of the fundamental solutions in both cylindrical and spherical coordinate systems and solving the boundary conditions using a collocation technique. To the best of our knowledge, there is no literature on the solution to the problem of creeping flow passing and within two or more porous spherical particles translating in a cylinder.…”

Section: Introductionmentioning

confidence: 99%

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Slow viscous flow of two porous spherical particles translating along the axis of a cylinder

Yao¹,

Ng²,

Teo³

et al. 2018

J. Fluid Mech.

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We describe the motion of two freely moving porous spherical particles located along the axis of a cylindrical tube with background Poiseuille flow at low Reynolds number. The stream function and a framework based on cylindrical harmonics are adopted to solve the flow field around the particles and the flow within the tube, respectively. The two solutions are employed in an iterated framework using the method of reflections. We first consider the case of two identical particles, followed by two particles with different dimensions. In both cases, the drag force coefficients of the particles are solved as functions of the separation distance between the particles and the permeability of the particles. The detailed flow field in the vicinity of the two particles is investigated by plotting the streamlines and velocity contours. We find that the particle–particle interaction is dependent on the separation distance, particle sizes and permeability of the particles. Our analysis reveals that when the permeability of the particles is large, the streamlines are more parallel and the particle–particle interaction has less effect on the particle motion. We further show that a smaller permeability and bigger particle size generally tend to squeeze the streamlines and velocity contour towards the wall.

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“…Using the ratio of pore size to the macroscopic length scale as a small parameter, the dominant jump conditions are found at the first order, and the generality of such asymptotic analysis allows them to make direct comparison with several pre-existing models such as the pioneering slip model by Beavers and Joseph 21 . It is worth mentioning that the approach adopted by Angot et al [22][23][24] was suggested by Worster et al 25,26 , where the empirical formula for the jump boundary conditions is similar to those used and/or derived in many other works [27][28][29][30][31][32][33][34][35][36][37] .…”

Section: Introductionmentioning

confidence: 99%

Slightly deformable Darcy drop in linear flows

2019

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The small-deformation of a poroelastic drop due to an external linear flow field in the suspending medium is investigated. A two-phase flow model is developed to study the small-deformation of such a poroelastic drop under linear flows. Inside the drop a deformable porous network with a bending rigidity and a viscosity is fully immersed in a viscous fluid. When the viscous dissipation of the interior fluid phase is negligible (compared to the friction between the fluid and the skeleton), the two-phase flow is reduced to a poroelastic Darcy fluid with a deformable porous network. At the interface between the poroelastic drop and the exterior Stokesian fluid, a novel set of boundary conditions are derived by the free energy dissipation principle. Both slip and permeability are taken into account and the permeating flow induces dissipation that depends on the elastic stress of the interior solid. Assuming that the porous network is slightly deformed from its original spherical shape due to its large bending rigidity, a small-deformation analysis is conducted. A steady equilibrium is computed for two different linear flows: a uniaxial extensional flow and a planar shear flow. By exploring the interfacial slip, permeability and network elasticity various flow patterns are found at equilibrium of these slightly deformed poroelastic drops. Linear dynamics of the small-amplitude deviation of the poroelastic drop from the spherical shape is governed by a nonlinear eigenvalue problem, and the eigenvalues are determined numerically, and asymptotically in certain limits. These results lay the foundation for studying the rheology of a suspension of poroelastic spherical particles, and give insight to possible flow patterns of a system of selfpropelling swimmers with porous flow (such as intracellular cytosol) inside.

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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

Cited by 13 publications

References 43 publications

Analysis of Stokes flow of micropolar fluid through a porous cylinder

Analysis of Stokes flow of micropolar fluid through a porous cylinder

Slow viscous flow of two porous spherical particles translating along the axis of a cylinder

Slightly deformable Darcy drop in linear flows

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