Document Type : Original Article
Authors
1
Department of Higher Mathematics and Information Technologies, Voronezh State University of Engineering Technologies, Voronezh, Russia
2
Department of Information Security, Voronezh State University of Engineering Technologies, Voronezh, Russian Federation
3
Department of Higher Mathematics and Information Technologies, Voronezh State University of Engineering Technologies, Voronezh, Russian Federation
4
Faculty of Management and Informatics in Technological Systems, Voronezh State University of Engineering Technologies, Voronezh, Russia
Abstract
In this article, an object of a research is the mechanism of incorporation of mother liquor components in the growing crystals of sucrose and establishment of the dependence allowing to estimate quantitatively inclusion of components of the mother liquor in industrial crystals of granulated sugar. Water and a complex of not sugars are considered as components of sugar solution. To date, experimental estimates of the inclusions of various non-sugars in sugar crystals have been accumulated, and a qualitative and quantitative analysis of impurities in crystals have been made, which showed that the number of inclusions depends on the purity of the crystallized solution, the rate of crystallization, the hydrodynamic situation in the apparatus, temperature and concentration fields, the viscosity of the solution, and other factors. These factors are mainly due to the technological regime of the crystallization process, and understanding the degree of their influence on the inclusion of impurities allows authors to minimize the capture of non-sugars by growing crystals. It is shown that the inclusion of non-sugars occurs mainly during the formation of crystals and their subsequent growth at a high supersaturation coefficient. However, the available data is not sufficient to identify and formalize all the laws of this rather complex phenomenon. At this stage, it is more appropriate to use the mathematical methods of probabilistic interpretation. The purpose of the study was a creation of a mathematical model that could be used to estimate the amount of components of the masterbatch solution (non-sugar and water) passing from solution to crystal, depending on the supersaturation of the solution, its temperature, viscosity, purity, and dry matter content. Based on the probability theory, a mathematical model of the deposition of the mother liquor in industrial crystals of granulated sugar has been developed. The mother liquor includes water in which sucrose and a complex of non-sugars are dissolved. Some of the non-sugars and water can be trapped by the growing crystal. The model allows you to calculate the amount of non-sugars and water that have passed into the sucrose crystal during its growth. The average relative error of the model is 8-10%.
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