Model for Melt Fracture Instabilities in the Capillary Flow of Polymer Melts

Self-consistent dynamics of wall slip

A simple molecular model is studied to explain wall slip in a polymer melt. We consider a tube model for tethered chains in which the most important relaxation mechanisms: convective constraint release and chain stretching (retraction), are incorporated. Furthermore, we take the interactions between tethered chains and bulk flow self-consistently into account. Numerical simulations show that our model exhibits an entanglement-disentanglement transition, leading to a jump in the slip velocity which increases with the number of entanglements and the grafting density. The wall shear stress is found to be a nonmonotonic function of the slip and plate velocity, yielding the possibility of hysteresis and spurt instabilities. In a simplified version of the model we show via an analytical approach that the stick-slip transition is asymmetrical: the transition from stick to slip is much faster than the slip to stick transition. Our analysis reveals the existence of a dimensionless parameter that determines the time scale of the dynamics for the slowing down of the bulk flow. The relative rate at which relaxation of the tethered chains and slowing down of the bulk take place, seems to be quintessential for the slip behavior of the melt.

Boundary layer variational principles: a case study

Considering the model heat conduction problem in the setting of Grad's moment equations, we demonstrate a crossover in the structure of minima of the entropy production within the boundary layer. Based on this observation, we formulate and compare variation principles for solving the problem of boundary conditions in nonequilibrium thermodynamics.

The sharkskin instability of polymer melt flows

Flows of polymeric liquids undergo instabilities whose origins are quite different from those of Newtonian flows, due to their elastic character and the complexity of the fluid/solid boundary condition. This article reviews recent studies of one such instability, the sharkskin phenomenon observed during extrusion of many linear polymers. Key experimental observations are summarized; one important fact that has become clear is the importance of the interaction between the molten polymer and the solid walls of the flow channel, especially near the contact line at the exit of the channel. Recent developments in understanding the relationship between wall slip and disentanglement of wall-adsorbed polymers from the bulk flow are briefly described, and putative heuristic mechanisms relating the instability to slip and contact line motion are presented. Finally, we review mathematical analyses of the stability of viscoelastic shear flows with slip boundary conditions. Some recent analyses yield instability predictions that are consistent with experiments, but further work is required to discriminate between the various mechanisms that have been proposed. (c) 1999 American Institute of Physics.