ABSTRACT
In this paper we model the mesoscale crystallization of the crystals in the dilute solution concentration in the sense that the microscale model is a stochastic process and meanwhile the macroscale model is a deterministic heat diffusion process. The crystallization process includes the steps of nucleation, nucleus radial growth and nuclei aggregation. In the case of the dilute solution concentration we may neglect the effect of the nuclei aggregation, i.e. the crystallization neglects the impingement. The coupled model of crystallization and heat diffusion show the mesoscale characteristic between the micro- and macro- aspect. Furthermore we reformulate the simultaneous identification of nucleation rate and crystal growth speed in the stochastic birth-growth process by the inverse approaches. The regularization strategy is adopted to implement the numerical inversion of the inverse problem. Finally, numerical examples are provided to show the effectiveness of the proposed algorithm.
Acknowledgments
The first-named author are also appreciative for the discussion with Professor M. Yamamoto and Dr Y. K. Liu during the stay in the University of Tokyo in August 2017 and February 2018.
Disclosure statement
No potential conflict of interest was reported by the authors.