An objective model for slow orientation kinetics in concentrated fiber suspensions: Theory and rheological evidence

Charles L. Tucker, Jin Wang, John F. O'Gara

Research output: Contribution to journalArticle


Recent experiments suggest that short fibers in concentrated suspensions align more slowly as a function of strain than models based on Jeffery's equation predict. We develop an objective model that captures the slow orientation kinetics exhibited by short-fiber suspensions. The standard moment-tensor equation of fiber orientation is used to find equations for the change rates of the eigenvalues and eigenvectors of the orientation tensor. As a phenomenological assumption, the growth rates of the eigenvalues are reduced by a constant scalar factor, while the rotation rate expressions for the eigenvectors are unchanged. The eigenvalue/eigenvector equations are then reassembled as a tensor equation. An equivalent kinetic theory is also developed. The new model is tested in a variety of flows, and found to exhibit slower kinetics than the standard model but similar steady-state orientations. The model provides an excellent fit to the shear stress transient in a shear reversal experiment with a 30% glass fiber filled polybutylene terephthalate resin melt, and we show how this experiment can be used to determine the parameters of the model.

Original languageEnglish (US)
Pages (from-to)1179-1200
Number of pages22
JournalJournal of Rheology
Issue number5
StatePublished - Aug 28 2008



  • Fiber orientation
  • Fiber suspensions
  • Injection molding
  • Orientation kinetics
  • Suspension rheology

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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