FRACTAL INTERPRETATION OF ULTRASONIC CRYSTALLIZATION OF SOLUTIONS

1 KATZ Valery
Co-authors:
1 MAZOR Gedalya
Institution:
1 SCE - Shamoon College of Engineering, Beer-Sheva, Israel, valery@sce.ac.il
Conference:
24th International Conference on Metallurgy and Materials, Hotel Voronez I, Brno, Czech Republic, EU, June 3rd - 5th 2015
Proceedings:
Proceedings 24th International Conference on Metallurgy and Materials
Pages:
1482-1487
ISBN:
978-80-87294-58-1
ISSN:
2694-9296
Published:
12th January 2015
Proceedings of the conference were published in Web of Science and Scopus.
Metrics:
286 views / 118 downloads
Abstract

Experiments were performed on the crystallization of a CuSO4 solution upon the action of the temperature gradient with the forming of mono crystals three wedges crystal system (prisms). We found that the fractal dimension of crystals equals 2.45, which is consistent with the literature data. Crystal growth is represented as the-rd translation of each side of the crystal lattice with its own speed and with relation to the formation of similar structures – fractals. A mathematical model of ultrasonic crystallization of a CuSO4 solution was proposed. The model is based on the combined use of differential transport equations of momentum, mass, energy and sound waves and a method of similarity and dimensional analysis. The calculated formulas for the concentration of - Ccr, the equivalent diameter of the formed crystals - dcr and the intensity of internal energy source – Φ* ,associated with the interaction of crystals with the hydro mechanical, heat and sound fields were obtained. Fractal interpretation of ultrasonic crystallization of the CuSO4 solution was made. It was found that on the growth of crystal size - dcr directly affects translation - N, i.e., an increase in the number of sets of crystals of infinitely small size ε, corresponds to the size of the crystal lattice. In turn translation of crystals depends on the geometry of the crystallizer and the physical parameters of external force fields, acting on the CuSO4 solution. A connection of results of the mathematical modeling with the results of fractal analysis of the ultrasonic crystallization of solutions was established.

Keywords: ultrasonic crystallization of solutions, physical and mathematical simulation, fractal interpretation

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