Instantaneous dimensionless numbers for transient nonlinear rheology

Simon Rogers, Jun Dong Park, Ching Wei Johnny Lee

Research output: Contribution to journalArticle


Two instantaneous dimensionless numbers that act as Deborah and Weissenberg numbers are introduced to diagnose flow conditions for transient nonlinear rheology. The utility of the new numbers is demonstrated on the steady alternating large amplitude oscillatory shear response of a colloidal Ludox glass, the soft glassy rheology model, and a viscoelastic wormlike micelle solution. Complex nonlinear trajectories through Pipkin space are observed, from which it is concluded that large amplitude oscillatory shear represents a range of distinct flow types. These results indicate that the observation time may change significantly during a period of oscillation. The complex trajectories observed for all three systems go from close to one axis to close to the other and back in quick succession. Rather than existing in the dominant central area that Pipkin originally marked as “?”, LAOS may simply be the way by which the axes of Pipkin space are dynamically linked.

Original languageEnglish (US)
Pages (from-to)539-556
Number of pages18
JournalRheologica Acta
Issue number8
StatePublished - Aug 1 2019


  • Deborah number
  • Large amplitude oscillatory shear
  • Nonlinear viscoelasticity
  • Weissenberg number

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics

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