https://doi.org/10.1140/epjs/s11734-025-02069-x
Regular Article
Continuous mode of bulk crystallization with mass/heat exchange with the environment: an analytical solution
Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, 620000, Ekaterinburg, Russian Federation
Received:
24
August
2025
Accepted:
13
November
2025
Published online:
19
November
2025
In this paper, we consider a nonlinear model of continuous crystallization taking mass/heat source/sink and withdrawal of product crystals into account. In addition, particle growth rates dependent on supersaturation/supercooling as power functions and particle growth fluctuations leading to diffusion of the crystal-radius distribution are considered. The mathematical model is analytically solved using the method of variables separation, and saddle-point technique to evaluate the Laplace-type integral. Our analytical solutions show that the metastability degree and the particle-radius distribution can be oscillating functions of time when controlling the mass/heat source/sink functions and withdrawal of product crystals. The analytical solution obtained enables us to control the operation mode of bulk continuous crystallization.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
