An explicit equation for the terminal velocity of solid spheres falling in pseudoplastic liquids

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An explicit equation is proposed which predicts directly the terminal velocity of solid spheres falling through stagnant pseudoplastic liquids from the knowledge of the physical properties of the spheres and of the surrounding liquid. The equation is a generalization of the equation proposed for Newtonian liquids. By properly defining the dimensionless diameter, d*, a function of the Archimedes number, Ar, and the dimensionless velocity, U*, a function of the generalized Reynolds number, Re, to account for the non-Newtonian characteristics of the liquid, the final equation relating these two variables has similar form to the Newtonian equation. The predictions are very good when they are compared to 55 pairs of Re - CD for non-Newtonian data and 37 pairs for Newtonian data published previously. The root mean square error on the dimensionless velocity is 0.081 and much better than the only other equation previously proposed.

Original languageEnglish
Pages (from-to)4437-4447
Number of pages11
JournalChemical Engineering Science
Issue number21
Publication statusPublished - 1 Nov 2004



  • Explicit terminal velocity
  • Non-Newtonian fluids
  • Particle
  • Sedimentation
  • Slurries
  • Suspension

ASJC Scopus subject areas

  • Chemistry(all)
  • Chemical Engineering(all)
  • Industrial and Manufacturing Engineering

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