A Boundary Layer Model for Steady Directional Solidification of Polymer Melts

We analyze a one-directional model for steady-state directional solidification of a polymer melt due to a heat sink moving at constant speed V . The non-linear model, couples a local heat balance to Avrami crystallization kinetics, for instantaneous nucleation with one directional spherulite growth, and weak under cooling. It properly accounts for the self-generated thermal field due to the release of latent heat behind the solidification front. Two dimensionless parameters control the predictions. The first, e , a scaled characteristic crystallization time, typically small in prior experimental work, controls the width of a boundary layer adjacent to the liquid melt, wherein crystallinity develops almost completely. The second, v,  a scaled sink speed, also typically small, together with e , control the thickness of the solidified layer between the melt and the thermal sink. The global features predicted by a perturbation analysis (e.g. width of the solid layer versus sink speed) are consistent with the simple Stefan model. Comparison with numerical solutions confirm the key analytical predictions. Importantly, the analytical model directly verifies the Gryte-Lovindger ansatz, that the system "selects" a crystal growth rate that matches the sink speed.