A Combined Analytic and Numerical Method for Predicting the Solid-Layer Growth From Melt Crystallization

Abstract

The kinetics of crystallization limit the rate in which crystal growth can occur without incorporation of undesired impurity. If the rate of heat transfer exceeds the mass transfer rate of the impurity, the impurity can solidify, contaminating the product. One would like to specify a rate of crystallization and determine the temperature profile of the crystallizer wall that would achieve this result. This is an inverse problem that has not been solved in the previous crystallizer models. A combined analytic and numerical method for solving the inverse problem is given in this article. The method is illustrated by an example.

Prediction of the Layer Growth Rate in Static Melt Crystallization

“…The difference between T m,exp and T sl is positively correlated with the layer growth rate. The maximum difference was about 1 °C, which verifies that the assumption of Dai et al 16 is reasonable at high growth rates. The minimum difference at the low growth rate is only about 0.3 °C, in which T sl can be replaced by the temperature of the melt.…”

“…But for static layer melt crystallization in a tube crystallizer, such an assumption is not applicable. Dai et al proposed that the S-L interface temperature is equal to the melt phase temperature minus 1 °C by stirring the melt . Feng et al considered that the S-L interface temperature is equal to the equilibrium temperature corresponding to the melt concentration .…”

“…Dai et al proposed that the S-L interface temperature is equal to the melt phase temperature minus 1 °C by stirring the melt. 16 Feng et al considered that the S-L interface temperature is equal to the equilibrium temperature corresponding to the melt concentration. 17 temperature can be calculated, the melt temperature distribution can be ignored.…”

“…Layer melt crystallization is controlled by heat transfer . To solve the differential heat transfer equation, three calculation methods have been proposed including the approximate analytical solution, − semirigorous second-degree polynomial approximation method, − and numerical solution. − The boundary conditions are extremely important to all the above three calculation methods. The boundary conditions at the cooling wall can be determined by the operating temperature.…”

Mathematical modeling and design of layer crystallization in a concentric annulus with and without recirculation

“…Layer crystallization from melts has been widely applied for the purification of organics and inorganics such as sucrose and milk fat, and in seawater desalination . Modeling of solid layer melt crystallization has focused on the temperature and composition profiles inside the crystal layer, and multiple stages of crystallizers can be designed to meet the required product purity . For layer crystallization, the liquid phase is always at a higher temperature than the solid phase, so that in melts, the temperature is required to be higher than the melting point, but layer crystallization from solutions can be operated at much lower temperatures…”