期刊
JOURNAL OF NON-NEWTONIAN FLUID MECHANICS
卷 183, 期 -, 页码 25-36出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.jnnfm.2012.07.001
关键词
Oldroyd-B; Boger fluid; Transient velocity overshoot; Weak-coupling; Lagrangian method; Birefringent strand
类别
资金
- NFS [DMS-0652775]
- DOE [DE-FG02-88ER2505]
- MRSEC Program of NSF [DMR-0820341]
- Air Force [FA9550-10-1-018]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [920930] Funding Source: National Science Foundation
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. (C) 2012 Elsevier B.V. All rights reserved.
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