Existence of solutions for all Deborah numbers for a non-Newtonian model modified to include diffusion

Ardith W. El-Kareh, L. Gary Leal

Research output: Contribution to journalArticlepeer-review

138 Scopus citations


We consider the existence of solutions for a non-Newtonian fluid that is based upon a nonlinear dumb-bell model. It is shown that a rigorous existence proof can be obtained for solutions on a bounded domain at arbitrary values of Deborah number provided the model includes a spatial diffusion term that is usually neglected in the derivation of the model by assuming that the structure is spatially homogeneous. Although this diffusion term is critical to the existence proof, it is expected to be numerically small compared to other terms in the constitutive model, except possibly in the vicinity of very large stress gradients, which it will tend to smooth out. The proof also requires that the stress always remain bounded. Although it is likely that this will be true for a model with a nonlinear (FENE) spring, it is difficult to prove rigorously. Hence, in the existence proof we resort to an ad hoc assumption that is equivalent to asserting that the polymer breaks (degrades) if the end-to-end distance exceeds some prescribed values that is less than the full cotour length but is otherwise arbitrary.

Original languageEnglish (US)
Pages (from-to)257-287
Number of pages31
JournalJournal of Non-Newtonian Fluid Mechanics
Issue number3
StatePublished - 1989

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanical Engineering
  • Applied Mathematics


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