Mathematical model of non-isothermal viscoelastic polymer film molding

Abstract

The steady-state non-isothermal process of forming a viscoelastic flat polymer film is considered. The polymer melt is extruded through a flat die subjected to uniaxial stretching and simultaneous air cooling, and then finally cooled down on a chill roll. It is assumed that the film is wide enough and the distance between the extruder head and the chill roll is small to such an extent that the change in the film width during the longitudinal stretching can be neglected. It is also assumed that the forces of gravity, inertia and surface tension can be neglected. Rheologically, the polymer melt is a viscoelastic liquid. The Upper Convected Maxwell model is used. Thermophysical properties, viscosity and relaxation time are considered to be dependent on temperature and degree of crystallinity. The mathematical model is supplemented by equations of heat balance and kinetics of non-isothermal crystallization. The problem is solved numerically using the finite difference method.