A generalised Phan–Thien—Tanner model

L. L. Ferrás, M. L. Morgado, M. Rebelo, Gareth H. McKinley, A. M. Afonso

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


In this work we propose a novel generalised form of the Phan–Thien and Tanner (PTT) model by considering a new functional form of the nonlinear expression characterizing the destruction of physical network junctions and entanglements. This new function of the trace of the stress tensor is given by the generalized Mittag–Leffler function, and contains the familiar exponential form of the original Phan–Thien and Tanner model as a limiting case, but affords additional fitting flexibility through the inclusion of one or two additional fitting constants. We perform fits to experimental data in shear and extension and show that this generalized expression allows a better description of the rheological responses for a range of complex materials such as polymer melts and semidilute polymer solutions. By using an appropriate information criterion, we also demonstrate that the resulting generelized model remains parsimonious but provides improved fits of real world data.

Original languageEnglish
Pages (from-to)88-99
Number of pages12
JournalJournal of Non-Newtonian Fluid Mechanics
Publication statusPublished - 1 Jul 2019


  • Fitting rheological data
  • Mittag–Leffler
  • PTT Model
  • Viscoelastic fluids


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