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.