Study on the Kinetic Parameters of Crystallization Process Modelled by Partial Differential Equations

Abstract

Abstract The physical properties of the crystal are affected by the crystal morphology, and the morphology will be affected by the crystallization environment. To obtain the expected physical properties, it is necessary to study the relationship between crystal growth conditions and crystal morphology. As snowflake is rich in crystal morphology, it is very suitable for studying this relationship. Crystal growth kinetics can be used to explore the mechanism of how the crystal growth conditions influence on crystal morphology. However, due to the impact of growth conditions in both time and space coordinates, it is difficult to identify the kinetic parameters of the crystallization process. In this work, the dynamic equation of snowflake growth was established through data regression, and the relationship between snowflake morphology and snowflake growth conditions was studied. In general, cellular automata (CA) is used to simulate the growth process of snowflakes, and the data of whether different positions are in crystallization state and the change of water vapor density with time are extracted, so as to avoid the interference of complex growth conditions on the growth data. Then, data are regressed from the perspective of the reaction-diffusion system, and the crystallization kinetics in the form of partial differential equation (PDE) related to time and space is obtained. This equation is solved by finite difference method to simulate the complex snowflake morphology under different conditions, to analyse the influence of different reaction rate and diffusion rate on the crystal morphology. This work provides a new way to study how crystal morphology is impacted by process parameters, which could be a reference for the planning of crystallization experiments to obtain the specified crystal morphology.