In a previous paper the author and Demay advanced a model to explain the melt fracture
instability observed when molten linear polymer melts are extruded in a capillary rheometer
operating under the controlled condition that the inlet flow rate was held constant. The model
postulated that the melts were a slightly compressible viscous fluid and allowed for slipping
of the melt at the wall. The novel feature of that model was the use of an empirical switch law
which governed the amount of wall slip. The model successfully accounted for the oscillatory
behavior of the exit flow rate, typically referred to as the melt fracture instability, but did not
simultaneously yield the fine scale spatial oscillations in the melt typically referred to as shark
skin. In this note, a new model is advanced which simultaneously explains the melt fracture
instability and shark skin phenomena. The model postulates that the polymer is a slightly
compressible linearly viscous fluid but assumes no-slip boundary conditions at the capillary
wall. In simple shear the shear stress τ and strain rate d are assumed to be related by
d = Fτ, where F ranges between
F2 and F1 > F2.
A strain-rate dependent yield function is introduced and this function governs whether F evolves
towards F2 or F1. This model accounts for the
empirical observation that at high shears polymers align and slide more easily than at low
shears, and explains both the melt fracture and shark skin phenomena.
