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On hydrodynamic permeability of a membrane built up by porous deformed spheroidal particles

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Abstract

This paper concerns the slow viscous flow of an incompressible fluid past a swarm of identically oriented porous deformed spheroidal particles, using particle-in-cell method. The Brinkman’s equation in the porous region and the Stokes equation for clear fluid region in their stream function formulations are used. Explicit expressions are investigated for both the inside and outside flow fields to the first order in a small parameter characterizing the deformation. The flow through the porous oblate spheroid is considered as the particular case of the porous deformed spheroid. The hydrodynamic drag force experienced by a porous oblate spheroid and permeability of a membrane built up by porous oblate spheroids having parallel axis are evaluated. The dependence of the hydrodynamic drag force and the hydrodynamic permeability on particle volume fraction, deformation parameter and viscosity of porous fluid are also discussed. 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 hydrodynamic permeability have been verified. The model suggested can be used for evaluation of changing hydrodynamic permeability of a membrane under applying unidirectional loading in pressure-driven processes (reverse osmosis, nano-, ultra- and microfiltration).

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Authors and Affiliations

  1. Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Allahabad, 211004, India

    Pramod Kumar Yadav

  2. Department of Mathematics, University of Allahabad, Patna-80000, Allahabad, 211002, India

    Satya Deo

  3. Department of Mathematics, National Institute of Technology Patna, Patna, 800005, India

    Manoj Kumar Yadav

  4. Department of Higher Mathematics, Gubkin Russian State University of Oil and Gas, 119991, Leninsky Prosp., 65-1, Moscow, Russia

    Anatoly Filippov

Authors
  1. Pramod Kumar Yadav
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  2. Satya Deo
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  3. Manoj Kumar Yadav
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  4. Anatoly Filippov
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Correspondence to Pramod Kumar Yadav.

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Yadav, P.K., Deo, S., Yadav, M.K. et al. On hydrodynamic permeability of a membrane built up by porous deformed spheroidal particles. Colloid J 75, 611–622 (2013). https://doi.org/10.1134/S1061933X13050165

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  • DOI: https://doi.org/10.1134/S1061933X13050165

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