Die-swell, splashing drop and a numerical technique for solving the Oldroyd B model for axisymmetric free surface flows

M.F. Tomé, L. Grossi, A. Castelo, J.A. Cuminato, S. McKee, K. Walters

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This work deals with the development of a numerical method for simulating viscoelastic axisymmetric free surface flow of an Oldroyd B fluid. A novel formulation is developed for the computation of the non-Newtonian extra-stress components on rigid boundaries and on the symmetry axis. The full free surface stress conditions are employed. The resulting governing equations are solved by finite differences on a Marker-and-cell (MAC) type grid. Validation is provided by simulating a pipe flow problem. The classical die-swell problem is solved and swelling ratios are provided. The height of the splash caused by a falling liquid drop for various Reynolds and Weissenberg numbers is then studied, and the height of the splash is shown to diminish with increasing viscoelasticity.

Original languageEnglish
Pages (from-to)148-166
Number of pages19
JournalJournal of Non-Newtonian Fluid Mechanics
Issue number2-3
Early online date15 Oct 2006
Publication statusPublished - 15 Feb 2007



  • axisymmetric flow
  • constitutive equations
  • die-swell
  • finite difference
  • Oldroyd B
  • splashing drop
  • viscoelastic flow

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