Numerical simulations of interfacial and elastic instabilities

Abstract

<h2>Abstract</h2> The interplay of elasticity and capillarity in free-surface flows of viscoelastic fluids gives rise to intriguing flow instabilities. We present novel numerical simulations and analyse the physics related to the appearance of surface distortions on polymer melt extrudates, often referred to as "sharkskin" instability, and the abrupt increase in the rise velocity of a bubble in a viscoelastic solution. Regarding the extrusion process, the transition from smooth to wavy extrudate with increasing flow rate is attributed to a Hopf bifurcation, followed by a sequence of period-doubling bifurcations, which eventually lead to elastic turbulence under creeping flow. We suggest that the inception of these waves is related with intense stretch of polymer chains and subsequent recoil at the region where the melt detaches from the solid wall of the die. The ‘velocity discontinuity' of the rising bubble is attributed to a hysteresis loop, triggered by the change of shape of the rear pole into a tip that favors the formation of intense stress gradients, which reduce the fluid viscosity and facilitate the bubble translation. Finally, we discuss the numerical methodology that has allowed us to obtain stable numerical solutions in highly deformed meshes and for high values of the Weissenberg number.