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Numerical modelling of multilayer polymer flows
The increased industrial use of coextrusion in polymer processing, particularly for packaging, has created a corresponding research interest in understanding the basic phenomena of coextrusion flows. This work was concerned with the numerical simulation of multilayer flows inside coextrusion dies, either planar or annular. An iterative streamline finite difference method was developed to model multilayer flows. Two key advantages of the method are its use of an arbitrary constitutive equation for viscosity (particularly a realistic model incorporating viscoelasticity) and its solution for unknown fluid/fluid interfaces. Velocity, viscosity, and normal stress difference profiles were calculated, including interface jumps in the latter two, which contribute to instabilities in the interface. From rules of thumb instability may be predicted by modelling a system. Different flow conditions were modelled and compared for their relative stability.^ Two dimensional flows (converging flows in particular) were modelled through use of the Lubrication Approximation. For viscoelastic, memory-integral fluids this requires evaluation of the strain history for a particle as it flows along a streamline. This was done both approximately through the assumption of locally straight converging streamlines and (more satisfactorily) numerically through material vector tracking. Both approaches were expedited by the use of streamline coordinates and the streamline finite difference grid. Results show that viscoelasticity can significantly affect the stress field even for slight convergence angles. For multilayer flows normal stress difference jumps along curved interfaces may be calculated and compared.^ Heat transfer effects were added to fully developed flow calculations, either by simply assuming adiabatic layers or by allowing a period of conduction, neglecting convection effects. Results show that simple zero-shear viscosity matching with temperature control (common in practice) is naive. Even matching of interface viscosities through the modelling may be insufficient once conduction is allowed. For developing flows the full energy equation has been solved to combine the effects of conduction and convection. Since the constitutive equation is coupled with temperature, calculated stress fields depend on the temperature history as well as the deformation history. ^
Nordberg, Martin Emery, "Numerical modelling of multilayer polymer flows" (1989). Doctoral Dissertations Available from Proquest. AAI9001547.