LINEAR-STABILITY ANALYSIS OF CONE AND PLATE FLOW OF AN OLDROYD-B FLUID

A linear stability analysis of the cone and plate flow of an Oldroyd-B fluid is carried out. We show that the base flow is stable to a class of axisymmetric perturbations provided that the Deborah number is les s than a critical value and that at the critical value there is exchan ge of stability. The value of the critical Deborah number for both cre eping and non-creeping flow is obtained. The critical value of the Deb orah number at which instability is predicted for non-creeping flows i s shown to be less than the value for creeping flows, indicating that inertia is destabilizing.