In this paper, we propose a mathematical model of the process of changing the productivity of a membrane, both through the formation of a continuous gel layer, and by blocking individual pores. Also, the results of modeling the process of dia- ultrafiltration (DUF) purification of pectin solutions and their concentration by ultrafiltration (UF) using hollow fiber membranes are presented. The effect of periodic washing of the membrane and the process of gelation along the membrane on the productivity of the plant was studied. Thus, the process is characterized by two parameters, and A is the main parameter of the problem, which is the same for all stages, and the second parameter, the ratio (k =F0/F'), characterizes the degree of pore purification with a general cleaning of the membrane surface and is thus one from the characteristics of a single cycle. The valuesof a number of parameters are determined experimentally. It is shown that when the system of differential equations, represented in the normal Cauchy form describing the given technological process, is jointly solved, the productivity of the DUF system can be increased by the frequency of flushing. The conducted experiments demonstrated the advantage of the use of the DUF process in the production of pectin and the features of purification and concentration of apple and sunflower pectins in this process. It is established that the use of DUF causes the introduction of an energy-saving technological process in the production of pectin to produce the target product that meets the required quality and environmental safety of production. The introduction of the proposed methods of DUF and UF into the production of pectin leads to an improvement in the quality and cost of the product.
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