Steady Viscous Flow Around a Permeable Spheroidal Particle

Madasu, Krishna Prasad; Bucha, Tina

doi:10.1007/s40819-019-0692-1

Cited by 7 publications

(3 citation statements)

References 25 publications

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“…However, we have to specify the conditions which are found appropriate from the physical as well as mathematical view. For the low permeability problem, the interface condition at the spheroidal interface r = a[1 + α m ϑ m (ζ )] are the continuity of normal components of velocity, proportionality of the shear stress with the tangential velocity components, i.e., Beavers-Joseph-Saffman-Jones slip condition [7,10,11,49,51] and the normal stress acting on fluid to be identical to the pressure in the permeable area, i.e., a jump condition for pressures [49,54].…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…On account of the viscous flow, a resisting force is exerted on the spheroidal particle inside a cell. To evaluate the drag, we adopt the following formula [14,44,51]…”

Section: Hydrodynamic Drag Acting On the Particlementioning

confidence: 99%

“…In an article by Yadav et al [50], the steady flow over a porous membrane consisting of impervious spheroid wrapped with a porous layer is discussed, and thereafter, they evaluated the hydrodynamic permeability acting on the membrane. Employing the condition of Beavers-Joseph-Saffman-Jones, the viscous flow past a Darcy's governed permeable spheroid was demonstrated by Prasad and Bucha [51]. They employed the condition of balancing the normal stress in the fluid area with the pressure in the permeable area of flow.…”

Section: Introductionmentioning

confidence: 99%

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Archive of Mechanical Engineering

Bucha,

Prasad

2021

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The perspective of the current analysis is to represent the incompressible viscous flow past a low permeable spheroid contained in a fictitious spheroidal cell. Stokes approximation and Darcy's equation are adopted to govern the flow in the fluid and permeable zone, respectively. Happel's and Kuwabara's cell models are employed as the boundary conditions at the cell surface. At the fluid porous interface, we suppose the conditions of conservation of mass, balancing of pressure component at the permeable area with the normal stresses in the liquid area, and the slip condition, known as Beavers-Joseph-Saffman-Jones condition to be well suitable. A closed-form analytical expression for hydrodynamic drag on the bounded spheroidal particle is determined and therefore, mobility of the particle is also calculated, for both the case of a prolate as well as an oblate spheroid. Several graphs and tables are plotted to observe the dependence of normalized mobility on pertinent parameters including permeability, deformation, the volume fraction of the particle, slip parameter, and the aspect ratio. Significant results that influence the impact of the above parameters in the problem have been pointed out. Our work is validated by referring to previous results available in literature as reduction cases.

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Section: Boundary Conditionsmentioning

confidence: 99%

“…On account of the viscous flow, a resisting force is exerted on the spheroidal particle inside a cell. To evaluate the drag, we adopt the following formula [14,44,51]…”

Section: Hydrodynamic Drag Acting On the Particlementioning

confidence: 99%