Dynamical stability in the capillary flow of polymer melt: A modeling with statistical stick-slip process

The now 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 to explain the macroscopic slip which is supposed to occur during the instability. The constitutive relationship of the slip velocity and the applied force has been derived and the coupling of the slip dynamics and the compressibility of the melt in the reservoir has been considered. The steady state solution, the linear stability analysis, and the numerical calculation suggested the followings. 1) The flow curve is basically N-shaped. 2) The range of the negative slope in the flow curve can he unstable. 3) In the unstable range, limit cycle appears around an unstable steady state. 4) The controlling parameter of the stability is the melt depth in the reservoir; which determines the compliance of the whole system. Experimental examination of the periodic spurt of polyethylene has confirmed those theoretical predictions. The results clearly suggest that the instability should be treated as a bifurcation of the dynamical system.