A mathematical model for the analysis of polymers P-V-T diagrams

In this paper we discuss a model for the solidification of a molten polymer sample in a cylindrical cooling chamber in which a prescribed pressure is imposed by a movable piston, The system shrinks during cooling because of thermal contraction and of the increase of the crystalline component. The corresponding flow enters the model only through the divergence of the velocity field, which numerical simulations show to be the only non-negligible term. The resulting problem is a system of p.d.e.'s with a free boundary described by a nonlocal condition. The boundary conditions for the thermal field are also nonlocal, due to the presence of the metallic body of the piston and of a rod supporting a thermocouple along the axis of the cylinder, which behave as concentrated capacities.