Dynamics of the spurt instability in polymer extrusion

A study of a phenomenological model describing the spurt instability in polymer extrusion is presented. Following Georgiou and Crochet [J. Rheol. 38 (1994) 639], we assume a nonmonotonic wall shear stress versus wall slip velocity relation. In this way we obtain a two-dimensional dynamical system for the wall slip velocity and the pressure in the barrel, which is similar to the van der Pol equations. The well-known fact that compressibility and a nonmonotonic slip law lead to spurt is incorporated by assuming the flow in the barrel to be compressible. The obtained dynamical system allows analytical evaluation, and, most importantly, gives a clear exposition of the dynamics underlying the spurt phenomenon. We give explicit expressions for the oscillation frequency and the size of the spurt window. Shear thinning is shown to give rise to quantitative differences only. It reduces the size of the spurt window and slightly enhances the period of the spurt oscillations. The linear scaling relation between the period of the spurt oscillations and the length of the die and the barrel height, is demonstrated to be independent of shear thinning or the precise form of the slip relation