A weak-coupling expansion for viscoelastic fluids applied to dynamic settling of a body

Matthew N J Moore, Michael Shelley

Research output: Contribution to journalArticle

Abstract

The flow of viscoelastic fluids is an area in which analytical results are difficult to attain, yet can provide invaluable information. We develop a weak-coupling expansion that allows for semi-analytical computations of viscoelastic fluid flows coupled to immersed structures. In our method, a leading-order polymeric stress evolves according to a Newtonian velocity field, and this stress is used to correct the motion of bodies. We apply the method to the transient problem of a sphere settling through a viscoelastic fluid using the Oldroyd-B model, and recover previous results and observed behavior. The theory presented here is in contrast to the retarded-motion, or low-Weissenberg-number, expansions that have seen much application. One advantage of the weak-coupling method is that it offers information for Weissenberg numbers larger than one. The expansion's limit of validity is closely related to the diluteness criterion of a Boger fluid. We extend the classical settling problem to include an oscillatory body-force, and show how the introduction of a second time-scale modifies the body-dynamics.

Original languageEnglish (US)
Pages (from-to)25-36
Number of pages12
JournalJournal of Non-Newtonian Fluid Mechanics
Volume183-184
DOIs
StatePublished - Sep 2012

Fingerprint

Viscoelastic Fluid
Weak Coupling
settling
expansion
Fluids
Flow of fluids
fluids
Viscoelastic Flow
Coupling Method
Motion
Velocity Field
fluid flow
Fluid Flow
Time Scales
velocity distribution
Fluid
Model

Keywords

  • Birefringent strand
  • Boger fluid
  • Lagrangian method
  • Oldroyd-B
  • Transient velocity overshoot
  • Weak-coupling

ASJC Scopus subject areas

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

Cite this

A weak-coupling expansion for viscoelastic fluids applied to dynamic settling of a body. / Moore, Matthew N J; Shelley, Michael.

In: Journal of Non-Newtonian Fluid Mechanics, Vol. 183-184, 09.2012, p. 25-36.

Research output: Contribution to journalArticle

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