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A numerical study of the accelerating motion of a dense rigid sphere in non‐newtonian power law fluids
Author(s) -
Chhabra Rajendra P.,
Soares Armando A.,
Ferreira Jose M.
Publication year - 1998
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450760611
Subject(s) - power law , mechanics , non newtonian fluid , drag , reynolds number , shear thinning , power law fluid , newtonian fluid , physics , dimensionless quantity , classical mechanics , spheres , law , rheology , mathematics , thermodynamics , turbulence , statistics , astronomy , political science
Abstract The equations of motion of an accelerating sphere falling through non‐Newtonian fluids with power law index n in the range 0.2 ≤ n ≤ 1.8 were integrated numerically using the assumption that the drag on the sphere was a function of both power law index and terminal Reynolds number, Re t For 10 −2 ≤ Re t ≤ 10 3 both dimensionless time and distance travelled by the sphere under transient conditions showed a much stronger dependence on the flow behaviour index, n , for shear‐thinning than for shear‐thickening fluids. The form of this dependence is investigated here. Furthermore, results in four typical shear‐thinning fluids suggested a strong correlation between the distance and time travelled by the sphere under transient conditions and the value of the fluid consistency index. The analysis reported herein is, however, restricted to dense spheres falling in less dense fluids, when additional effects arising from the Basset forces can be neelected.