Unsteady, steady, and self-oscillatory modes of the bulk continuous crystallization with mass influx and withdrawal of product crystals
Laboratory of Multi-Scale Mathematical Modeling, Laboratory of Stochastic Transport of Nanoparticles in Living Systems, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin ave., 51, 620000, Ekaterinburg, Russian Federation
Accepted: 25 April 2023
Published online: 24 May 2023
This paper is devoted to the study of operating modes of the crystallizer with allowance for the processes of nucleation and evolution of particles, removal of product crystals, and fines dissolution. The stationary and non-stationary analytical solutions describing various crystallization scenarios are derived. We show that the unsteady-state distributions of crystals approach their stationary distribution over time. In addition, the linear analysis of dynamic instability shows that the regions of oscillatory instability and absolute stability exist. These regions are divided by the neutral stability curve dependent of the physical parameters of crystallization process. We show that the oscillatory instability domain becomes wider when increasing the nucleation and growth rate constants. As a result, the process of volumetric crystallization under consideration can operate in a mode of self-oscillations sustained by a feedback between the nucleation rate and the process driving force (supersaturation).
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