Theoretical Approach to Crystallization Kinetics

For the design and optimization of melt crystallization processes it is vital to have a complete understanding of the process. To this, a detailed knowledge about the crystallization kinetics is essential. Nevertheless, there is only little theory available to describe melt crystallization processes mathematically or to predict their separation efficiency. This is mainly a consequence of the complex heat and mass transfer processes prevailing in the crystallizers which lead to a non-linerar system of differential equations for the transfer processes. These equations can only be solved numerically and even then require a considerable number of simplifying assumptions and boundary conditions. 

The first important part of every crystallization operation, namely the nucleation step, reveals the same mechanisms underlying the kinetics in the fields of melt and solution crystallization. Therefore, it is here referred to Section 2.2 of this book which gives a detailed introduction into the corresponding theoretical background. 

The crystal growth kinetics on the other hand differ in that the heat transfer is the dominant mechanism controlling the process in case of melt crystallization whereas in solution crystallization it is the mass transfer. This, of course is also reflected in the equations describing the process. 

In both, layer and suspension crystallization solid material forms from the melt starting with a nucleus through which a solid/liquid interface is created. As crystallization proceeds the mass of solidified substance steadily increases which causes the interface to move. The impurity components remaining in the melt thereby enrich in front of the solid/liquid interface, forming a concentration boundary layer. The concentration profile in this boundary layer changes as the interface advances which is in literature referred to as moving boundary problem.  

Among the first ones to present a complete theoretical approach are Burton, Prim, and Slitcher (1953). The authors developed a mathematical formulation of the problem for metallic systems with partial solid solubility crystallized from the melt in a suspension process. Their theory is based on a boundary layer model and does not account for the mutual dependence of heat and mass transfer but regards the influence of heat transfer as negligible. 

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