Analysis of the flow instabilities in the extrusion of polymeric melts (Q2785779)

In this book, written as the author's Ph.D. thesis, mathematical analyses and numerical computations have been used to investigate various types of instabilities during an extrusion process of polymeric melts. Particular attention is paid to the sharkskin-type of instability as well as to the spurt flows connected with persistent oscillations in the spin line. The following flows are discussed in greater detail:NEWLINENEWLINENEWLINE1) Pressure-driven shear flow of a Kaye-Berstein-Kearsley-Zapas (KBKZ) fluid, modelling the flow of a polymer melt through a cylindrical capillary under a constant pressure gradient. In particular, the mathematical formulation, the steady-state solutions, the stability analysis and the transient flow behaviour are considered. It is shown that the spurt phenomenon can be explained on the basis of constitutive instabilities, and the wall-slip boundary condition is not necessary.NEWLINENEWLINENEWLINE2) Piston-driven shear flow of Johnson-Segalman-Oldroyd (JSO) model, describing the flow of a polymeric melt through a cylindrical capillary with a constant volumetric flow rate. It is shown that persistent oscillations may occur as observed in experiments, and the corresponding critical conditions for the onset of oscillations are established.NEWLINENEWLINENEWLINE3) Extrusion of a JSO fluid, combined with compression, leading to a global relation between the pressure in the barrel and the volumetric flow rate in the capillary. The occurrence of persistent oscillations has been explained by means of linearized stability analysis.NEWLINENEWLINENEWLINEIn the last section an agreement of theoretical results with experimental observations is presented, and further perspectives connected with various forms of instabilities are discussed in detail.NEWLINENEWLINENEWLINEIn the paper, very spectacular from the mathematical point of view, certain physical assumptions may be questioned. These are isothermal and inertialess conditions of flow which may seriously influence the character of dynamic solutions. On the other hand, when dealing with stability of particular rheological models, one has to remember that the results can be quite different as compared with other reasonable models.