Approximate engineering calculation of chill molds for milk sugar in isohydric conditions

Abstract

Earlier, an attempt was made to create a mathematical model for the continuous crystallization of lactose in aqueous solutions at various supersaturations. The calculation method was based on a new criterion for the metastability of supersaturated solutions. The metastability criterion of the solution in this case is a dimensionless quantity from 0 to 1 and reflects the role of nucleation at any time. In other words, this dimensionless quantity, showing the ratio of the rates of nucleation and growth of crystals. We determined this value by mathematical modeling using the modified Gunther–Mat model. The practical significance of the criterion is the establishment of a crystallization region (mixed, nucleation and growth), taking into account the surface of the introduced crystalline phase. It is established that for a small surface, the crystallization process proceeds predominantly in the mixed region, in the absence of a seed (F = 0), when the metastability limit is exceeded, goes into the blast nucleation "*"(Pg = 0.1), with large surfaces of the crystals F. The process proceeds in the growth region even at high supersaturations (Pg = 0.9), i.e. it allows you to quickly determine the required amount of seed to intensify the crystallization process. It can be used for any crystallizable substance if kinetic parameters of the process are available (rate constants and kinetic orders of nucleation and growth, solubility, etc.). However, the presence of nonsugars and the corresponding instrument base cause great errors in finding the above parameters of the process of working solutions, therefore, we decided on a simplified engineering calculation method.