Torsional flow: elastic instability in a finite domain

Abstract

A rotational shear flow is examined in the parallel plate geometry for the Oldroyd-B fluid. The Stokes solution is found to have eigenfunctions in an unbounded radial domain while it is unique for general boundary conditions in a finite radial domain. Critical conditions for the onset of an axisymmetric secondary flow are determined for the viscoelastic fluid, and we show that there is an almost linear relationship between the aspect ratio of the plates and the critical Deborah number for this model, especially at small values of the aspect ratio. The form of the initial secondary flow is also in agreement with experimental results obtained for a Boger fluid.