The paper presents the results of experimental data on the kinetic characteristics of ultrafiltration tubular elements, such as the output specific flow, retention coefficient, diffusion permeability coefficient, distribution coefficient. To study the purification of milk whey, we used tubular ultrafilters BTU 05/2 with membrane material fluoroplast (F), polyethersulfone (PESF), polysulfone (PS). For theoretical calculation of the retention coefficient, output specific flux, diffusion permeability coefficient, distribution coefficient, mathematical expressions were developed and empirical coefficients were obtained. The developed mathematical expression describes the experimental data with good reliability. The obtained experimental and calculated data can be used with high reliability in calculating mass-transfer fluxes of substances through a semi-permeable membrane, as well as in engineering methods for calculating and predicting efficiency, and using membrane processes for concentrating serum. The protein concentration in real milk whey was determined by formol titration. On the basis of the studies carried out, the dependence of the growth of the output specific flow on pressure was established, that the optimal pressure for concentrating milk whey on the ultrafiltration membranes we have chosen is 0.25 MPa. For three types of ultrafilters, the experimental value of the coefficient was within 99% for protein. For the theoretical calculation of the retention coefficient, a program in the MAXIMA language was developed and registered. Due to the method of applying the membrane to the reinforcing element, the membrane material polyethersulfone (PESF) and polysulfone (PS) have a substrate, due to which they sorb more substances on themselves, because of this, the diffusion permeability coefficient and the distribution coefficient are much higher than that of a filter element with membrane made of fluoroplastic (F), which does not have a substrate.

membrane, concentration, whey, retention coefficient, specific flux, distribution coefficient, mathematical model

1. Mikhailenko I.G., Fedorenko B.N. Concentration of milk whey on flat ceramic membranes. Food ingredients and biologically active additives in food technologies and perfumery and cosmetics. 2019. pp. 142-147. (in Russian).

2. Anisimov G.S. et al. Changes in the thermophilic microflora of secondary milk raw materials in the process of electrodialysis processing. State and prospects for the development of the best available technologies for specialized food. 2019. pp. 97-101. (in Russian).

3. Kostyukov D.M. et al. Regularities of concentration of curd whey by nanofiltration. Dairy Bulletin. 2012. no. 1. (in Russian).

4. Leshchenko E.G., Kostenko K.V. Investigation of the process of recovery of dry milk whey by the method of ultrasonic cavitation and electrochemical treatment of water. Rational nutrition, food additives and biostimulants. 2016. no. 4. pp. 34–40. (in Russian).

5. Merkel A., Ashrafi A. M., E?er J. Bipolar membrane electrodialysis assisted pH correction of milk whey. Journal of Membrane Science. 2018. vol. 555. pp. 185-196.

6. Chen G. Q. et al. A pilot scale study on the concentration of milk and whey by forward osmosis. Separation and Purification Technology. 2019. vol. 215. pp. 652-659.

7. Torkamanzadeh M. et al. Comparative experimental study on fouling mechanisms in nano-porous membrane: cheese whey ultrafiltration as a case study. Water Science and Technology. 2016. vol. 74. no. 12. pp. 2737-2750.

8. Corbat?n-B?guena M.J., ?lvarez-Blanco S., Vincent-Vela M.C. Evaluation of fouling resistances during the ultrafiltration of whey model solutions. Journal of Cleaner Production. 2018. vol. 172. pp. 358-367.

9. Pavel N. et al. Hydrodynamics and mass transfer with gel formation in a roll type ultrafiltration membrane. Foods and Raw materials. 2018. vol. 6. no. 2.

10. VLADIPOR. Available at: http://www.vladipor.ru/catalog/show/&cid=010&id=1 (in Russian).

11. Rodionov D.A. et al. Ultrafiltration plant for concentrating milk whey. Cheese making and butter making. 2020. no. 1. pp. 40–41. (in Russian).

12. GOST 25179–2014. Milk and dairy products. Methods for determining the mass fraction of protein. Moscow, Standartinform, 2015. 16 p. (in Russian).

13. Lazarev S.I. et al. Research of diffusion permeability of proteins through ultrafiltration membranes. Proceedings of VSUET. 2019. vol. 81. no. 1. (in Russian).

14. Bogomolov V.Y. et al. Sorption capacity of ultrafiltration membranes and the potential of the field of surface forces in solutions of milk proteins. Sorption and chromatographic processes. 2018. vol. 18. no. 1. pp. 104–110. (in Russian).

15. Rodionov D.А., Pchelintsev A.N., Lazarev S.I., Mishchenko S.V. Calculation of empirical parameters for the retention coefficient of the baromembrane concentration of cheese whey. Certificate RF, no. 2019663815, 2019.