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

作者：Moore Matthew N J^*; Shelley Michael J

来源：Journal of Non-Newtonian Fluid Mechanics, 2012, 183: 25-36.

DOI：10.1016/j.jnnfm.2012.07.001

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

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.

• 出版日期2012-9