Abstract
The flow instability has been examined in a polymer liquid extruded from a die, especially periodic spurt observed under constant piston moving. A stick-slip model of a group of microscopic springs has been presented toexplain the macroscopic slip which is supposed to occur during theinstability. The constitutive relationship of the slip velocity and theapplied force has been derived and the coupling of the slip dynamics and thecompressibility of the melt in the reservoir has been considered. Thesteady state solution, the linear stability analysis, and the numericalcalculation suggested the followings. 1) The flow curve is basicallyN-shaped. 2) The range of the negative slope in the flow curve can beunstable. 3) In the unstable range, limit cycle appears around an unstablesteady state. 4) The controlling parameter of the stability is the meltdepth in the reservoir, which determines the compliance of the whole system.Experimental examination of the periodic spurt of polyethylene has confirmedthose theoretical predictions. The results clearly suggest that theinstability should be treated as a bifurcation of the dynamical system.
