Analysis and Suppression of Instabilities in Viscoelastic Flows

The viscoelastic character of polymer solutions and melts gives rise to instabilities that are not seen in the flows of Newtonian liquids. In industrial applications such as coating and extrusion, these so-called “elastic” instabilities can impose a limitation on the throughput. Hence, it is important to understand, and if possible, to suppress them. The first instability we study is the phenomenon of melt fracture, which occurs in the extrusion of polymer melts and takes the form of gross distortions of the surface of the extrudate. This instability is linked to the phenomenon of wall-slip, i.e., the velocity of the polymer at the wall relative to the velocity of the wall itself (also called the slip velocity) is non-zero. Several slip relations based on microscopic theories for polymers predict regions in which the slip velocity is multivalued. The expectation is that a multivalued slip relation will result in a multivalued flow curve, which in turn causes melt fracture. Using a simple slip relation, we show that when the dependence of the slip velocity on the pressure is taken into account, this is not necessarily true: a multivalued slip law does not necessarily imply a multivalued flow curve. The second instability we study is the “filament stretching instability,” which occurs in the extension of a polymeric liquid bridge between two parallel plates. This instability takes the form of a bifurcation to a non-axisymmetric shape near the endplates at