The research work offers a new evaluation technique of longitudinal mixing intensity of biotechnological suspension in fixed reactors by counting the proportion of microorganisms that differ by the stay period in any certain reactor volume. To estimate the mixture level of microorganisms of different ages in a vessel volume of interest is important to both biotechnologist and equipment engineers to form the structural-functional model of two-phase suspension flow (including microorganisms), to control the flow and to define the main fluid dynamics and technological parameters of the implementing process. It has been known that when the microorganisms of too different age coexist in a unit volume of the production substrate, the biochemical process of directed mass transfer goes ineffective. Since the metabolic processes of microorganisms run with great speed, the change of their functional age character can be correlated with the residence time of the cells in the system. To make the principal decisions while constructing new equipment (or improving the existing one) with the aim of realizing the flow model which is close to piston flow, it is necessary to have the correct method of calculating the proportion of coexisting microorganisms with different stay periods in the bioreagents flow volume of interest. This research work offers a probability-theoretical approach to making the mathematical model of the two-phase fluid diffusion flux, that allows to calculate the proportion of coexisting microorganisms with different stay periods in the in the arbitrarily given vessel volume. The method is based on the mathematical apparatus of the Markovian diffusion process, which is characterized by mathematical simplicity and physical clearness. Thus the obtained results allow us to assume the fluid-flow state of the ‘production substrate–microorganisms’ system, and, building upon it, to predict the efficiency of biochemical processes realized in flow-through apparatus.

microorganisms, age, apparatus, residence time, flow pattern, mixing, diffusion model, Markov process, distribution function

1. Carrascosa A.V., Munoz R., Gonzalez R. Molecular Wine Microbiology. Academic Press. 2012. 360 p.

2. Varfolomeev S.D., Lukovenko A.V., Semenova N.A. Fizicheskaya khimiya bioprotsessov [Physical chemistry of biological processes] Moscow, KRASAND, 2014. 800 p. (in Russian)

3. Kelly W.J. Using computational fluid dynamics to characterize and improve bioreactor performance. Biotechnol. Appl. Biochem. 2008. vol. 49. pp. 225–238.

4. Singh H., Hutmacher D.W. Bioreactor studies and computational fluid dynamics. Adv. Biochem. Eng. Biotechnol. 2009. vol. 112. pp. 231–249.

5. Sarishvili N.G. Mikrobiologicheskie osnovy tekhnologii [Microbiological fundamentals of technology of champagne wines] Moscow, Pishchepromizdat, 2000. 364 p. (in Russian)

6. Almagambetov K.H. Biotekhnologiya mikroorganizmov [Biotechnology microorganisms] Astana, 2008. 244 p. (in Russian)

7. Pishchikov G.B. Activation of champagne in the organization of the wine using a bifunctional devel-ties of the surfaces of the fermentation biogeneration devices. Vinograd I vino v Rossii [Grapes and wine of Russia] 2009, no. 5. pp. 14–15. (in Russian)

8. Sharma C., Malhotra D., Rathore A.S. Review of Computational Fluid Dynamics Applications in Biotechnology Processes.  Biotechnol. Prog. 2011. vol. 27. no. 6. pp. 1497–1510.

9. Hutmacher D.W., Singh H. Computational fluid dynamics for improved bioreactor design and 3D culture. Trends in Biotechn. 2008. vol. 26. no. 4. pp. 166–172.

10. Kaiser S.C., Loffelholz C., Werner S., Eibl D. CFD for Characterizing Standard and Single-use Stirred Cell Culture Bioreactors. Minin I. (Eds.). Intech. 2011. pp. 97–122.

11. Johnson С., Natarajan М., Antoniou С. Verification of energy dissipation rate scalability in pilot and production scale bioreactors using computational fluid dynamics.  Biotechnol. Progr. 2014, vol. 30. no. 6, pp. 760–764.

12. Tikhonov V.I., Mironov M.A. Markovskii protsessy[Markov processes] Moscow, Sovetskoe radio, 1977. (in Russian)

13. Sveshnikov A.A. Prikladnye metody teorii [Applied methods of the theory of random functions] 464 p. (in Russian)

14. Pugachev V.S. Teoriya sluchainykh funktsii [Theory of random functions] Moscow, Fizmatgiz, 1960. pp. 79–83. (in Russian)

15. Feller V. Vvedenie v teoriyu veroyatnosti [Introduction to probability theory and its applications] Moscow, Mir, 1984. 528 p. (in Russian)

16. Madelung, E. Matematicheski apparat fiziki [Mathematical apparatus in physics] Moscow, Book on Demand, 2012. 618 p. (in Russian)

17. Beckenbach, E.F., Vekua I.N. Sovremennaya matematika [Modern mathematics for engineers] 1958. 618 p. (in Russian)

18. Davydov A.P., Zlydneva T.P. Metody matematicheskoi fiziki [Methods of mathematical physics. Classification of equations and formulation of problems. Method d'Alember] Moscow, INFRA-M, 2017. 100 p. (in Russian)