The process of drying food is extremely complex. Therefore, the mathematical modeling of the process needs high requirements. The combination of approaches in modeling is of practical interest. On the one hand, analytical solutions based on the application of physical laws or phenomenological equations are used. On the other hand, experimental identification of the relationship between temperature and body moisture, which is considered as a peculiar characteristic of heat and mass transfer for each material. It is proposed to consider vacuum microwave drying from the standpoint of physical chemistry as a quasitopochemical heterogeneous reaction and perform mathematical modeling of this process based on the laws of chemical kinetics.
At present, there are no reliable criteria for acceptable drying temperatures; so, a new approach is proposed to determine the range of acceptable drying conditions based on a joint solution of the equations that determine the drying kinetics and the kinetics of changes in the process characteristics of the product. For a given product quality, the logarithm of the maximum allowable drying time linearly depends on the reciprocal of the absolute temperature of the drying agent. The method for calculating the drying time is simplified based on a new product characteristic - equivalent moisture content. The criterion of acceptable conditions, which is the maximum temperature of the drying agent, is a function of the magnitude of the thermal effect, the parameters of the drying kinetics, and the kinetics of the process properties of the product.
It is shown that the existing approaches to drying process modeling, based on a system of interconnected differential equations of heat and mass transfer or on statistical processing of drying process experimental data, have significant drawbacks. It greatly complicates the development of computer means for controlling production processes. During modeling it is proposed to consider drying process from the standpoint of physical chemistry as a quasi-topochemical heterogeneous reaction and perform mathematical modeling of this process based on the laws of chemical kinetics. The basic issues of methodology of drying process modeling based on the laws of chemical kinetics are reviewed: the study of the equation of drying rate during the removal of free and bound moisture; methods for determining composition of the aqueous fractions with different forms and energy of moisture in materials; methods of determination of an activation energy of moisture; the influence of the concentration of moisture and other process factors on the drying speed. The methodological approach considered in the article allows developing reliable mathematical models of drying kinetics for the purposes of computer technologies for managing production processes and avoiding the errors that the authors note in previously published works.
The article considers various approaches to modeling the drying of finely dispersed products: based on the classical theory of diffusion, from the standpoint of the thermodynamics of an irreversible process. An analysis of the scientific and technical literature on the problem revealed not high accuracy of the convective drying models of finely dispersed products developed on the existing theoretical basis. It is shown that the improvement of drying modeling can be based on the kinetics theory of chemical reactions. In this case, drying is considered as a quasi-topochemical heterogeneous reaction. At the same time, a combined approach to drying modeling is proposed: the phenomenological equation of chemical kinetics, which describes the speed of the process, is supplemented by the experimentally established relationship between the temperature and moisture content of the material. Based on the proposed approach, mathematical models of the kinetics of convective drying of finely dispersed products for periods of constant and decreasing speed have been developed, which allow to establish a clear type of the influence of the temperature regime on the kinetics of the process and reduce the amount of experimental research. A mathematical model of the temperature curve of drying for a period of decreasing speed is developed. The relationship between the speed of the first and second drying periods is established. The reliability of the obtained mathematical models is confirmed by experimental verification of the kinetic equation obtained for a period of constant velocity.
In many chemical, food, biochemical and other industries, drying is the prime process that is characterized by high energy consumption and determines the quality of the finished product. In this regard, the development of mathematical models that allow of optimization and reliable control of the drying process is relevant. A large set of physical and physicochemical phenomena accompanying drying, as well as their mutual influence on each other, gives rise to numerous uncertainties in the mathematical description of this process. The modeling process becomes more complicated under conditions of combined energy supply, for example, convective and microwave energy supply. In this article, based on the laws of chemical kinetics, the authors propose the original approach to modeling the drying process, which, together with experimental studies, allows obtaining a reliable mathematical model that can be used as the basis for optimizing and controlling this process. During the mathematical modeling of drying, it was proposed to apply new process parameters: the degree of drying (the share of removed moisture) and the degree of absorbed energy (the ratio of the amount of energy absorbed by the product at a given moment to the amount of energy absorbed by the product during the entire process). The expediency of characterizing the kinetics of drying by the dependence of the degree of drying on the degree of absorbed energy is demonstrated. The scientific hypothesis was substantiated and confirmed: the generalized characteristic, the kinetics of drying - the dependence of the degree of drying on the degree of energy absorbed by the product, does not depend on the parameters characterizing the drying mode. The proposed model makes it possible to determine the ratio of the components of convective and microwave energy flows when moisture is removed from the material, which can be used as the basis for optimization and reliable control of the process.
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