Classical one-phase Stefan problems for describing polymer crystallization processes

Abstract

A free boundary problem framework is proposed to approximate the solution of a deterministic nonisothermal polymer crystallization model in which crystallization fronts appear as the result of the combination of two heat transfer processes: the heat conduction due to the application of a cooling temperature below the polymer melting temperature threshold, and the latent heat production due to the phase change. When the latent heat is larger than the sensible heat of the crystallization process, a classical one-phase Stefan problem can be formulated which allows one to derive analytical approximations describing, for arbitrary applied cooling temperature profiles, the main features of the crystallization process: the relation between the latent heat and the specific heat capacity, the evolution of the temperature distribution, and the advance of the crystallization front. Analytical expressions of magnitudes of industrial interest such as the crystallization time are also derived, allowing the design of optimal cooling strategies for the applied temperature. The limits of the suitability of this framework are discussed, pointing out its applicability to other polymer crystallization models.