In our case, the solid body is the raw material of plant origin-lupine, crushed into grits, and the extractant is the cheese whey. The turbulent situation in the apparatus was created by the imposition of low-frequency mechanical vibrations, which have a significant impact on the characteristics of hydro-mechanical, mass transfer and thermal processes. This feature must be taken into account in the calculation of the extraction apparatus. The basic assumptions for the solution of the problem are formulated. The equation of motion of a single particle, which is contained in a number of works (Sow, an introduction, Chen, Protodyakonov, etc.). It is true in the instant values of the parameters. A simpler equation describing the motion of the dispersed particle and time correlation tensors with their subsequent decomposition into the Fourier integral are written. Further, taking into account the definition of tensors, the dependences for the calculation of the intensity of the chaotic motion of continuous and dispersed phases are shown, and the final expression is obtained, showing the ratio of the intensities of the phases. The coefficient of turbulent diffusion of each phase is proportional to the intensity of the chaotic motion of the corresponding phase. Therefore, the written finite equation for the phase ratio allows to estimate the ratio of the turbulent diffusion coefficients of the liquid and dispersed phases in the extraction apparatus. In our case, the ratio of the density of Hg / Hg is 1.1. Since the density of lupine and cheese whey differ quantitatively, we should expect some increase in the relative velocity of the phases, which will increase the rate of mass transfer. The intensities of the phases chaotic motion will not be the same, as well as the coefficients of turbulent diffusion. Thus, the case of motion of a single particle in a turbulent flow is complex and can be solved only under sufficiently serious assumptions formulated below.

It is noted that the model is designed to create the largest possible pressure change in the cheese whey in the extractor, since the rate of transfer of the target components is proportional to the pressure difference at the ends of the capillaries. The mathematical description of impregnation as the main or important auxiliary operation is given in detail. The equations for the impregnated part of the capillary, the ratio of impregnation rates at different times are given. From the above dependencies, the equation Washburne regarding the time of impregnation. The formulas for calculating the volume of extractant passed through the capillary, serum and forced out of the capillary air taking into account the viscous resistance of the latter. After integration of the equation of the speed of capillary impregnation of the obtained expression allows to estimate the final value of the impregnation in the initial stage. For different cases of capillary impregnation expressions are written at atmospheric pressure, vacuuming and overpressure. The introduction of dimensionless values allowed to simplify the solution and to obtain an expression for calculating the time of pore impregnation. The analysis of the equation of dimensionless impregnation time taking into account the application of low-frequency mechanical vibrations is made. It is noted that the processes of impregnation and extraction occur simultaneously, so the impregnation time is often neglected, which impoverishes the understanding of the physics of the process, reduces the accuracy of the calculation. Taking into account the diffusion unsteadiness of the process of substance transfer due to hydrodynamic unsteadiness, the equation containing the effective diffusion coefficient is written. The equation of unsteady diffusion for a spherical lupine particle in a batch extractor is supplemented with initial and boundary conditions. Taking into account the balance equation, the kinetic equation of the process is obtained. We studied the distribution of pores in the particle lupine along the radii and squares, the calculated value of the porosity of the particle. The values of De and Bi are determined by the method of graphical solution of the balance equation, the equation of kinetics and the parameters included in these equations. Conclusions on the work.

Despite the observed trend of a ubiquitous transition to continuously operating apparatuses, the specificity of the production technology of many microbiological products retains the advisability of using batch apparatuses. As an example, we mention the cooled bioreactors and yeast concentrate collectors used in the production of baker’s yeast. The work considers the problem of the mathematical description of unsteady recuperative heat transfer in a batch capacitive apparatus (bioreactor) with a product distributor on a heat transfer surface during countercurrent movement of coolants with a filling level of the apparatus changing during the process. The problem is formulated by partial differential equations (in coordinate and time) with a moving boundary between sections with different heat transfer conditions. When formulating the problem, simplifying assumptions and boundary conditions were adopted. The mathematical problem posed is solved using the Laplace transforms. The mathematical description of recuperative heat transfer in bioreactors during the filling of the apparatus showed that with countercurrent movement of heat transfer liquids and coolants, the apparatus has an advantage in terms of the main indicator - heat transfer capacity and has a higher energy efficiency. The performed calculations make it possible to choose the apparatus design correctly and determine the rational thermal regime of its operation regarding related technological operations.

In many cases, extraction is accompanied by thermal phenomena. We have established the possibility of intensifying the process through the use of heated cheese whey. Lupine has a geometric shape (sphere, cylinder, plate) loaded into an extractor filled with cheese whey. Due to the temperature difference between the solid and the liquid, temperature gradients are observed. As the body warms up, the temperature gradient decreases and then disappears. For example, an organized step temperature mode. However, such a regime should be technologically and energetically justified. Thus, during extraction there is a periodic non-stationarity. The emergence of this period is noted in the main works. The expression for the increase in entropy per unit time is written. Given the changes in entropy, the Gibbs equation is written. The basics of equations are the second laws of thermodynamics. As a result, the results obtained as a result of thermodynamic driving forces were obtained. The equations of energy (heat) and mass transfer of substances are written. Thermodynamic forces contribute to the formation of heat flux and mass flow of substances. The consumption of a substance depends not only on the gradient (diffusion), but also on the temperature gradient (thermal diffusion). Air temperature is defined as a temperature gradient. The differential equations of heat and mass transfer of Lykov were rewritten taking into account the extraction process. The numerical values of the coefficients Dт and aс they relate to the assessment of the effect of superposition effects (thermal diffusion and diffusion thermal conductivity). The overlay effect can be neglected, since the relatively small gradients of temperatures and concentrations arising in the lupine. It is noted that the possibility of simplified differential equations is associated with small values of the Lykov criterion. Because of this, there should be little.

Optimal design and management of baker’s yeast production should be based on an in-depth analysis of individual technological processes. Filtration of suspensions using excipients refers to complex technological processes and depends on a large number of factors. In this paper, the kinetic and technological regularities of the process of filtration of suspensions using excipients are considered. The main kinetic regularities of the filtration process are revealed depending on the thickness of the sediment, the pressure drop, concentration, temperature and microbiological purity of the suspension. The effect of the suspension temperature on the main qualitative indicators of yeast: lifting force, acidity and persistence has been established. The performed experimental studies of the filtration process on an industrial continuous vacuum filter and the analysis of the obtained patterns allowed us to formulate a number of recommendations aimed at effective management of the process, reducing losses during the processing of baker’s yeast. Recommendations have also been developed to reduce starch consumption and increase the cycle of operation of the vacuum filter.