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Slow Motion of a Porous Cylindrical Shell in a concentric cylindrical cavity

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Abstract

This paper concerns the Slow Motion of a Porous Cylindrical Shell in a concentric cylindrical cavity using particle-in-cell method. The Brinkman’s equation in the porous region and the Stokes equation for clear fluid in their stream function formulations are used. The hydrodynamic drag force acting on each porous cylindrical particle in a cell and permeability of membrane built up by cylindrical particles with a porous shell are evaluated. Four known boundary conditions on the hypothetical surface are considered and compared: Happel’s, Kuwabara’s, Kvashnin’s and Cunningham’s (Mehta-Morse’s condition). Some previous results for hydrodynamic drag force and dimensionless hydrodynamic permeability have been verified. Variation of the drag coefficient and dimensionless hydrodynamic permeability with permeability parameter σ, particle volume fraction γ has been studied and some new results are reported. The flow patterns through the regions have been analyzed by stream lines. Effect of particle volume fraction γ and permeability parameter σ on flow pattern is also discussed. In our opinion, these results will have significant contributions in studying, Stokes flow through cylindrical swarms.

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Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Patna, Patna, 800005, Bihar, India

    Pramod Kumar Yadav

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  1. Pramod Kumar Yadav
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Correspondence to Pramod Kumar Yadav.

Appendix

Appendix

Happel’s cell model

Kuwabara’s cell model

Kvashnin’s cell model

Cunningham/Mehta-Morse’s cell

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Yadav, P.K. Slow Motion of a Porous Cylindrical Shell in a concentric cylindrical cavity. Meccanica 48, 1607–1622 (2013). https://doi.org/10.1007/s11012-012-9689-0

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  • DOI: https://doi.org/10.1007/s11012-012-9689-0

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