Origin of the Sharkskin Instability: Nonlinear Dynamics

The appearance of surface distortions on polymer melt extrudates, often referred to as sharkskin instability, is a long-standing problem. We report results of a simple physical model, which link the inception of surface defects with intense stretch of polymer chains and subsequent recoil at the region where the melt detaches from the solid wall of the die. The transition from smooth to wavy extrudate is attributed to a Hopf bifurcation, followed by a sequence of period doubling bifurcations, which eventually lead to elastic turbulence under creeping flow. The predicted flow profiles exhibit all the characteristics of the experimentally observed surface defects during polymer melt extrusion.

Figure 1

Schematic of the polymer melt extrusion process and an indicative domain tessellation. For a magnification of the mesh very close to the singularity see Fig. S1.

Figure 2

The route to elastic turbulence for $\epsilon =0.1$ and $\mathrm{Ec}=1000$. Flow profiles for various Wi close to the die exit, along with the free surface height ($F_s$) close to the die exit ($x=1.51$) versus time, and the limit cycle in the phase space defined by $F_s$, ${\tau }_{xx}$, and ${\tau }_{xy}$, calculated at $x=1.51$. (a) $\mathrm{Wi}=0.0774$ (single frequency), (b) $\mathrm{Wi}=0.07808$ (two frequencies), (c) $\mathrm{Wi}=0.07829$ (four frequencies), (d) $\mathrm{Wi}=0.07836$ (chaotic). For the spatial form of the wave see [33].

Figure 3

(a) Critical Weissenberg number (${\mathrm{Wi}}_c$) versus $\epsilon$. (b) Startup extensional viscosities versus time ($t$) of polymer melts 1 and 2 at extension rate $100{\mathrm{s}}^{-1}$, normalized by the steady value of the extensional viscosity at the same extension rate. (c) and (d) Flow profiles near the die exit for polymer melts 1 and 2, with a streamline superimposed on contours of the $xx$ component of the deformation rate tensor.