Emergence of singular structures in Oldroyd-B fluids

Becca Thomases, Michael Shelley

Research output: Contribution to journalArticle

Abstract

Numerical simulations reveal the formation of singular structures in the polymer stress field of a viscoelastic fluid modeled by the Oldroyd-B equations driven by a simple body force. These singularities emerge exponentially in time at hyperbolic stagnation points in the flow and their algebraic structure depends critically on the Weissenberg number. Beyond a first critical Weissenberg number the stress field approaches a cusp singularity, and beyond a second critical Weissenberg number the stress becomes unbounded exponentially in time. A local approximation to the solution at the hyperbolic point is derived from a simple ansatz, and there is excellent agreement between the local solution and the simulations. Although the stress field becomes unbounded for a sufficiently large Weissenberg number, the resultant forces of stress grow subexponentially. Enforcing finite polymer chain lengths via a FENE-P penalization appears to keep the stress bounded, but a cusp singularity is still approached exponentially in time.

Original languageEnglish (US)
Article number103103
JournalPhysics of Fluids
Volume19
Issue number10
DOIs
StatePublished - Oct 2007

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stress distribution
cusps
Fluids
fluids
stagnation point
polymers
Polymers
simulation
approximation
Chain length
Computer simulation

ASJC Scopus subject areas

  • Fluid Flow and Transfer Processes
  • Computational Mechanics
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Emergence of singular structures in Oldroyd-B fluids. / Thomases, Becca; Shelley, Michael.

In: Physics of Fluids, Vol. 19, No. 10, 103103, 10.2007.

Research output: Contribution to journalArticle

Thomases, Becca ; Shelley, Michael. / Emergence of singular structures in Oldroyd-B fluids. In: Physics of Fluids. 2007 ; Vol. 19, No. 10.
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