Instabilities and bifurcations of von Kármán similarity solutions in swirling viscoelastic flow (Q1891376)

We derive an asymptotic model that describes the swirling flow of a viscoelastic fluid between a rotating cone and a stationary plate when the gap angle, \(\alpha\), is small and inertia is neglected. The model, which uses the Phan-Thien Tanner constitutive law, is valid in the limit \(\alpha\to 0\) and for Deborah number order unity. We show that the model admits similarity solutions of von Kármán type. A solution corresponding to a viscometric flow is obtained.