Comparing the wall slip and the constitutive approach for modelling spurt instabilities in polymer melt flows

At high flow rates during polymer melt extrusion, pressure oscillations can be observed. The phenomenon is usually referred to as spurt, due to the irregular - in bursts - emergence of the melt out of the die. Spurt, or equivalently, the associated pressure oscillations have been modelled successfully through the mechanism of relaxation-oscillations by Molenaar and Koopmans. The presence of a non-monotone flow curve is at the heart of this modelling. In this paper the curve is deduced from conservation laws combined with a die wall boundary condition and specific constitutive equations. Subsequently, three `model curves' are compared. Model A, a Newtonian fluid with a `switch function' defining an alternating stick-slip boundary condition. Model B is a non-monotone constitutive equation i.e. a Johnson-Segalman-Oldroyd (JSO) fluid with a no-slip condition. Model C consists of two Newtonian fluids in concentric die regions and a no-slip condition. It is shown that Models A and C are able to describe spurt that is in qualitative agreement with experiments reported in literature. Model B, however, does not lead to spurt, in spite of the non-monotone nature of the steady stress-strain rate curve! These results tend to show that there are many options to describe experimental flow curves with equations based on geometrical, operational and polymer property parameters. Accordingly, from a mathematical point of view, and in view of the equivalence in results between model A and C, it can be concluded that the existing controversy between slip or no-slip (i.e. constitutive) supporters is not a fundamental one.