 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| A.I. Prostomolotov and N.A. Verezub, "Mathematical Simulation of Crystal Growing in Water-Salt Solutions," Mech. Solids. 57 (4), 883-892 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
4 |
Pages |
883-892 |
| DOI |
10.3103/S002565442204015X |
| Title |
Mathematical Simulation of Crystal Growing in Water-Salt Solutions |
| Author(s) |
A.I. Prostomolotov (Ishlinsky Institute for Problems in Mechanics of Russian Academy of Sciences, Moscow 119526, Russia, aprosto@inbox.ru)
N.A. Verezub (Ishlinsky Institute for Problems in Mechanics of Russian Academy of Sciences, Moscow 119526, Russia, verezub@ipmnet.ru) |
| Abstract |
A detection of the conditions of high-rate single crystal growth with an appropriate quality is a priority for an industrial production of crystalline materials. The crystals of potassium dihydrogen phosphate (KDP) are the important optical materials. They are growing from water-salt solutions. The flow and mass transfer are modeled within the framework of continuous medium, which is considered as a water solution of a special salt-potassium dihydrogen phosphate. This salt dissolves in water to a saturation level at a high temperature. Then, such supersaturated solution is used to grow crystals at lower temperatures in static crystallizers (without inflow and outflow) and in continuous-flow crystallizers. The mathematical model is considered in a conjugate formulation with taking into an account of mass transfer in "solution-crystal" system. The local features of hydrodynamics and mass transfer in a solution near a surface of growing crystal are established, which may affect to a local (for a particular place and direction) crystal growth rates and a defect formation. The requirements to the crystallizers for providing a “necessary” solution hydrodynamics are discussed. The validation of this model is shown for the task of flow around a long horizontal plate, which simulating the growing crystal facet. The rate of salt precipitation is estimated by means of proposed mathematical model, in which a solution flow and salt concentration are calculated by solving Navier-Stokes and mass transfer equations for an incompressible fluid. Then the calculated salt flux on crystal surface is applied in a thermodynamic relationship for a normal growth of facets under conditions of two-dimensional nucleation. The action of continuous-flow crystallizers was analyzed for various solution inflows (axial and ring) and its outflow through the bottom hole. |
| Keywords |
computer simulation, mass transfer, impurities, interfaces, saturation |
| Received |
07 February 2022 | Revised |
18 February 2022 | Accepted |
21 February 2022 |
| Link to Fulltext |
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