https://doi.org/10.1140/epjs/s11734-024-01354-5
Regular Article
Two-step nucleation and growth of crystals in a metastable solution with mass exchange with the environment
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
Received:
8
August
2024
Accepted:
1
October
2024
Published online:
16
October
2024
This study is concerned with the influence of mass exchange with the environment on the two-step nucleation and growth of crystals in a metastable solution. The mass exchange processes include two mechanisms of product crystals withdrawal from a saturated solution and impurity inflow to the liquid to maintain its saturation. The integro-differential model of kinetic and balance equations includes the growth velocity of spherical crystals for the two-step nucleation mechanism as well as initial and boundary conditions. We derived the exact analytical solutions in the case of steady-state crystallization mode. In the case of unsteady crystallization, this non-linear model is solved by means of a combined use of the Laplace transform and saddle-point methods. Namely, the liquid supersaturation, crystallization time and particle-size distribution are obtained in a parametric form with the maximum size of spherical particles being the decision variable. The analytical theory under consideration is in agreement with the experimental data.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.