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Motion through spherical droplet with non-homogenous porous layer in spherical container

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Abstract

The problem of the creeping flow through a spherical droplet with a non-homogenous porous layer in a spherical container has been studied analytically. Darcy’s model for the flow inside the porous annular region and the Stokes equation for the flow inside the spherical cavity and container are used to analyze the flow. The drag force is exerted on the porous spherical particles enclosing a cavity, and the hydrodynamic permeability of the spherical droplet with a non-homogeneous porous layer is calculated. Emphasis is placed on the spatially varying permeability of a porous medium, which is not covered in all the previous works related to spherical containers. The variation of hydrodynamic permeability and the wall effect with respect to various flow parameters are presented and discussed graphically. The streamlines are presented to discuss the kinematics of the flow. Some previous results for hydrodynamic permeability and drag forces have been verified as special limiting cases.

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Abbreviations

a, b, c, :

radii of spherical particles

(r, θ, φ):

spherical polar coordinates

vr,vθ :

velocity components of fluid

p, :

fluid pressure

σ̃rr :

normal stress

σ̃rθ :

tangential stress

U :

uniform velocity of fluid

k 0 :

permeability parameter

γ:

particle volume fraction

λ:

viscosity ratio

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Authors and Affiliations

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

    P. K. Yadav

  2. Department of Mathematics, Birla Institute of Technology Science, Pilani, 333031, Rajasthan, India

    A. Tiwari

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

    P. Singh

Authors
  1. P. K. Yadav
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  2. A. Tiwari
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  3. P. Singh
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Corresponding author

Correspondence to P. K. Yadav.

Additional information

Project supported by the Science and Engineering Research Board, New Delhi (No. SR/FTP/MS-47/2012)

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Yadav, P.K., Tiwari, A. & Singh, P. Motion through spherical droplet with non-homogenous porous layer in spherical container. Appl. Math. Mech.-Engl. Ed. 41, 1069–1082 (2020). https://doi.org/10.1007/s10483-020-2628-8

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  • DOI: https://doi.org/10.1007/s10483-020-2628-8

Keywords

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2010 Mathematics Subject Classification

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