✍ Scribed by André Bénard; Suresh G. Advani; Jerold M. Schultz
No coin nor oath required. For personal study only.
Solidification of semicrystalline materials often occurs in significantly undercooled melts. The crystal growth process in such melts is convoluted due to the fact that the interface between the solid and liquid domains of the microscopic crystals is a t an unknown temperature. However, it is possible to let the temperature of this interface be unspecified and solve the problem with a semianalytical method if the growth velocity is prescribed. Solutions for the temperature profiles in both solid and liquid phases are presented in this work, along with the interface temperature, for phase change processes controlled by the kinetics of crystallization rather than diffusion processes, which is typical for polymers. The method is used for one-dimensional problems in Cartesian, cylindrical, and spherical geometries that correspond to commonly found microstructures. It is found'that the temperature of the interface is significantly below the equilibrium melting point and a quasi steady-state regime is reached rapidly. Comparison with the classical Neumann's solution shows that the temperature profiles are similar but the position of the interface differs considerably.
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