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Linear shear flow past a porous particle

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Abstract

Linear shear flow past a porous spherical particle is studied using a generalized boundary condition proposed by Jones. The torque on a porous sphere rotating in a quiescent fluid is calculated. Streamlines patterns are illustrated for the case of a particle freely suspended in a simple shear flow. These patterns are shown to differ significantly from those associated with an impermeable rigid sphere. Finally, an expression for the effective viscosity of a dilute suspension of porous spherical particles is obtained.

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Abbreviations

A, B :

dimensionless flow parameter

a :

radius of the porous sphere

C, E, F:

constants of integration

d :

shear strength

d :

constant rate of deformation of ambient field

e :

rate of strain tensor

f, g :

functions of distance

k :

permeability of the porous medium

n :

unit normal vector

p :

pressure

p :

unit vector

Q :

coefficient of spherical harmonic

q :

filter velocity within the porous medium

r :

polar spherical coordinate

S p :

surface of porous particle

S, T, T*:

coefficients of spherical harmonics

T :

torque exerted on the particle

u :

fluid velocity vector

x :

cartesian coordinates

α :

dimensionless constant

θ, φ :

polar spherical coordinates

λ :

dimensionless flow parameter

μ :

viscosity of the fluid

σ :

stress tensor

Ω :

rotational velocity of the particle

ω :

rotational velocity of the ambient field.

References

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Authors and Affiliations

  1. Dept. of Chem. Eng., Technion-Israel Inst. of Techn., Haifa, Israel

    A. Nir

Authors
  1. A. Nir
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Nir, A. Linear shear flow past a porous particle. Appl. Sci. Res. 32, 313–325 (1976). https://doi.org/10.1007/BF00411782

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  • DOI: https://doi.org/10.1007/BF00411782

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