The article is devoted to the analysis of pectin diffusion extraction in the extraction process from plant raw materials in a solid-liquid system. The molecular diffusion process from the inside of the extractable substance particles to their outer surface is considered as the limiting stage. The aim of this work is to study the possibility of creating an efficient production of pectin from agricultural products by carrying out a more complete extraction using a period of mass isolation in the extraction process. As it is generally recognized all over the world, the rational use of natural resources is the dominant trend in the development of the economy, which assumes the fullest use of vegetable raw materials consumed by humans in the processing. To implement such approaches, a mathematical model of the discrete diffusion process in porous diffusionally isotropic particles has been developed. A conclusion is made about the effect of mass isolation on the extraction rate for a regular mode, while the regularities of the process remain unchanged.

Optimization of extracting food products from plant raw materials using a mathematical model is suggested. The model has been derived for the analysis of extracting pectin from Jerusalem artichoke. Multistage anti-cyclic extraction, non-stationary diffusion for the initial element of the processed raw material in the form of plates is considered. The calculations take into account the effect of reverse solvent change, the time of the solvent drain from the solid phase, among other process parameters. The derived equation makes it possible to analyze the effect of the impregnation of a part of the miscella at an intermediate stage of a countercurrent multistage extraction on the efficiency of the process. The correctness of the mass conductivity coefficient calculations was confirmed using the performance indicators of the extractor. Based on the data obtained, a mathematical model was created that describes the extraction process with a variable coefficient of mass conductivity. Thus, it is possible to determine the optimal parameters of the process including the rate of fluid flow through the material, the crushed material particle size, the thickness of the particles, and the processing time.