A note on transient stress calculation via numerical simulations

Vittorio Cristini, Christopher W. Macosko, Thomas Jansseune

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We revisit the experiments of start-up shear of an immiscible dilute polymer blend presented in [J. Non-Newtonian Fluid Mech. 99 (2001) 167] and calculate the transient stresses via numerical simulations. As part of this investigation, we validate a stress-relaxation experimental technique [J. Non-Newtonian Fluid Mech. 99 (2001) 167; J. Non-Newtonian Fluid Mech. 93 (2000) 153] for the measurement of the interfacial contribution. The simulations assume Newtonian behavior, thus, not including bulk viscoelastic effects, and are performed using an adaptive boundary-integral method [Phys. Fluids 10 (8) (1998) 1781; J. Comput. Phys. 168 (2001) 445] to describe highly deformed drops and the effect of breakup events on the stresses. When viscoelasticity is negligible, we find agreement between simulations and experiments for the total stress and interface contribution at both subcritical and supercritical capillary numbers, and demonstrate that no existing analytical models are capable of describing correctly the stress evolution. Interestingly, we find that the breakup time is independent of the capillary number at high capillary number, and depends on the viscosity ratio only. When viscoelasticity is important, the comparison between the simulation results and the experimental data allows us to quantify the effect of viscoelasticity on the stresses by isolating correctly the Newtonian contribution.

Original languageEnglish (US)
Pages (from-to)177-187
Number of pages11
JournalJournal of Non-Newtonian Fluid Mechanics
Issue number2-3
StatePublished - Aug 15 2002

Bibliographical note

Funding Information:
Vittorio Cristini and Christopher W. Macosko were supported by grant DAAD19-991-0337 from the Army research office. Vittorio Cristini also acknowledges the Institute for Mathematics and its Applications for their hospitality, and the Minnesota Supercomputing Institute for a Research Scholarship, and for computing time and support. Finally, the authors acknowledge a Referee for inspiring the development of a scaling argument to predict the breakup time in a blend. The experimental work was supported by a grant (GOA 98/06) from K.U. Leuven. Finally, the authors acknowledge Professor J. Mewis for useful discussions.


  • Boundary-integral simulations
  • Immiscible polymer blends
  • Rheology
  • Start-up flow
  • Stress transients

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