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 language | English (US) |
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Pages (from-to) | 25-36 |
Number of pages | 12 |
Journal | Journal of Non-Newtonian Fluid Mechanics |
Volume | 183-184 |
DOIs | |
State | Published - Sep 2012 |
Keywords
- Birefringent strand
- Boger fluid
- Lagrangian method
- Oldroyd-B
- Transient velocity overshoot
- Weak-coupling
ASJC Scopus subject areas
- General Chemical Engineering
- General Materials Science
- Condensed Matter Physics
- Mechanical Engineering
- Applied Mathematics