Modeling of metastable zone width behavior with dynamic equation

Identification of the metastable zone width (MZW) is crucial for product quality control in industrial crystallization. Traditionally, the MZW in batch cooling crystallization has been defined as a kind of static property of a solution that primarily depends on cooling rate. In industrial batch crystallization operations, however, the cooling rate does not remain constant but changes with time based on the operation recipe. The existing models with static relationship between MZW and cooling rate have a limit to predict the behavior of the MZW under such a dynamic situation. In this study, the MZW is newly elucidated as a dynamic state that predominantly depends on the cooling rate among other operating variables. For this, a first-order dynamic model with input nonlinearity has been proposed between the cooling rate and the MZW. To verify the proposition, a series of experiments have been conducted for crystallization of ammonium sulfate, potassium aluminum sulfate, and potassium chloride under various cooling scenarios. From our experiments, it is observed that (1) holding temperature after cooling affects the nucleation time, (2) undersaturated starting temperature of cooling, affects the nucleation temperature, and (3) solution thermal history before saturation temperature also affects the nucleation temperature.