A Mixing Transition in a Viscoelastic Fluid

Dynamical behavior in low Reynolds number viscoelastic flows is investigated numerically in the Oldroyd-B model. For low Weissenberg number, flows are ``slaved" to the four-roll mill geometry of the body forcing. For sufficiently large Weissenberg number, such slaved solutions are unstable and under perturbation transit in time to a structurally dissimilar flow state dominated by a single large vortex, rather than four vortices of the four-roll mill state. The transition to this new steady-state also leads to regions of well-mixed fluid, and may be related to a recently discovered transition in cross-channel flows of a viscoelastic fluid.