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Flow of a simple non-newtonian fluid past a sphere

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Summary

Creeping flow past a sphere is solved for a limiting case of fluid behaviour: an abrupt change in viscosity.

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Abbreviations

d ij :

Component of rate-of-deformation tensor

F d :

Drag force exerted on sphere by fluid

G τ(d) :

Coefficients in expression for τ ij in terms of d ij

G τ(d) YOJK :

Coefficients in power series representing G τ(d)

R :

Radius of sphere

r :

Spherical coordinate

V :

Velocity of fluid very far from sphere

v i :

Component of the velocity vector

x :

Dimensionless radial distance, r/R

x i :

Rectangular Cartesian coordinate

β :

Dimensionless quantity defined by (26)

Г τ(d) :

Potential defined by (7)

γ :

Value of x denoting border between Regions 1 and 2 as a function of θ

η 1, η 2 :

Lower and upper limiting viscosities defined by (10)

θ :

Spherical coordinate

θ*:

Value of θ for which γ=1

\(\tilde \theta \) :

Value of θ denoting border between regions 1 and 2 as a function of x

μ :

Newtonian viscosity

τ ij :

Component of the stress tensor

ϕ :

Spherical coordinate

ψ 1, ψ 2 :

Stream functions defined by (12) and (14)

\(\begin{gathered}\bar I\bar I_{d,} \bar I\bar I_\tau , \hfill \\\bar I\bar I\bar I_{d,} \bar I\bar I\bar I_\tau \hfill \\\end{gathered} \) :

Second and third invariants of the stress tensor and of the rate-of-deformation tensor, defined by (3)

References

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Authors and Affiliations

  1. Department of Chemical Engineering, Northwestern University, Evanston, Illinois, U.S.A

    John Slattery

Authors
  1. John Slattery
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Slattery, J. Flow of a simple non-newtonian fluid past a sphere. Appl. sci. Res. 10, 286 (1961). https://doi.org/10.1007/BF00411921

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  • DOI: https://doi.org/10.1007/BF00411921

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