Mathematical modelling and simulation of non-isothermal crystallization of polymers

This paper is devoted to the study of mathematical problems arising in the modelling of nonisothermal polymer crystallization under industrial condition. A review of the hybrid stochastic-deterministic modelling procedure, which yields the BCE-model, is given and supplied by mathematical problems related to it. Furthermore, multiple scale effects in the crystallization process are studied using different scalings, focussing either on the heat conduction or on the crystallization part. It is shown that in the limit of fast nucleation and slow growth, the model is equivalent to a direct extension of the classical Avrami-Kolmogorov model equations. In addition, numerical simulations are presented to illustrate the behaviour during crystallization. Finally, open questions from mathematical and engineering view points are discussed.