On the converging flow of viscoelastic fluids through cones and wedges

Abstract

A novel approximation method for obtaining solutions to the slow flow of viscoelastic fluids through converging cones and wedges is presented. The method involves considering two distinct regions in the flow field divided by a streamline: an inner irrotational sink flow occupying most of the flow field and an outer highly sheared self-lubricating layer adjacent to the walls. This procedure greatly simplifies the governing equations and allows analytic expressions to be obtained. Since the two regions are seperated by a streamline, different constitutive equations can be used for the inner and outer flow fields. This enables constitutive models to be used which model polymer melt rheology reasonably accurately and still retain analytic solutions. The method is applied to both wedges and cones; extensions to converging annuli are straightforward. Finally, an example flow field is considered in relation to a typical die-entry flow in polymer proccessing.