THE STEFAN AND DEBORAH NUMBERS IN POLYMER CRYSTALLIZATION

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Abstract
A model of the phenomenon of gradual crystallization of a polymer melt subjected to an unsteady temperature distribution is presented. The model allows for gradual changes of the degree of crystallization. It is shown that the values of two dimensionless parameters, the Stefan and Deborah numbers, simultaneously influence the behavior of the system. When the ratio of these two parameters, which we propose to call the Janeschitz-Kriegl number, becomes very large as compared to unity, the model degenerates into the classical abrupt crystallization model known in the literature as the Stefan problem. This asymptotic behavior is shown to hold through a modified boundary layer analysis, where the boundary layer stays attached to a moving, rather than a fixed boundary.