Applied Scientific Research, Section A

, Volume 12, Issue 3, pp 213–222 | Cite as

Creeping flow past a sphere of a Reiner-Rivlin fluid

  • Robert D. Foster
  • John C. Slattery


A variational principle for incompressible Reiner-Rivlin fluids proposed by Bird has been applied to creeping flow past a sphere of a fluid with constant coefficients of viscosity η and normal-stressη c . The drag coefficientf is found to be given byf = C/Re, whereC =C(η c v /ηR). Available data in the literature for (apparently) Newtonian fluids show no indication of a non-zero normal-stress coefficient.


Drag Coefficient Stream Function Newtonian Fluid Trial Function Creeping Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


A, B, D, Ks,Gp

constants in general trial function for stream function (23)


function ofRn defined by (28)


rate-of-deformation tensor defined by (2)

E, F, G

constants in trial function for stream function (26)


friction factor defined by (13)


drag force which fluid exerts on sphere in the positive z direction


variational functional defined by (8)




spherical coordinate


radius of sphere


dimensionless Reynolds number defined as (2Rv ∞ρ/η).


dimensionless group defined as (η c v /ηR)


stress tensor


velocity vector


physical components of the velocity vector in ther and0 directions


hysical component of the velocity vector in the positivez direction


magnitude of vz at a large distance from the sphere


used to indicate integration over the volume of the system as in (8)


dimensionless radiusr/R


rectangular coordinate


spherical coordinate defined as π/2 — θ


Kronecker delta = 0(ij) = 1(i =j)


functions of II, III defined by (3)


constants defined by (6)

θ, ϕ

spherical coordinates




viscous portion of the stress tensor


stream function defined by (16)


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Copyright information

© Martinus Nijhoff, The Hague/Kluwer Academic Publishers 1963

Authors and Affiliations

  • Robert D. Foster
    • 1
  • John C. Slattery
    • 1
  1. 1.Department of Chemical EngineeringNorthwestern UniversityEvanstonU.S.A.

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