A test particle approach to flow classification for viscoelastic fluids

The formulation of the Deborah and Weissenberg dimensionless numbers for viscoelastic fluids by means of a scheme based on the response of hypothetical tracer test particles having the form of elastic dumbbells is presented. By considering the dynamics of these test particles, we can classify flows as being either strong or weak. Consideration of the amount of stretching of a swarm of dumbbells in one relaxation time also provides a definition of the Weissenberg number. A simple workable definition of the Deborah number is given, and, finally, the ideas are applied to a viscoelastic lubrication case, to an inlet flow, and to the flow through porous media.