Mathematical modeling of mixing atcultivation of biological agents sensitive to transverse strain

Abstract

The development of modern production of various goods is determined largely by the introduction of new technologies, including the biotechnology, which is based on the use of biological agents for the synthesis of new goods. The use of biological agents in industrial processes is possible when creating favorable conditions (temperature level, substrate transportation, removal of metabolic products) for their activity in industrial equipment, namely, in fermenters. To ensure favorable conditions various methods of mixing are used. The article studies the process of mixing in the fermenter for cultivation of the biological agents, sensitive to the action of transverse strains. A mathematical model of movement of culture fluid in the boundary layer near the moving elements of a mixing device was developed. The solution of the mathematical model helps to determine the distribution of velocities along the thickness of the boundary layer, velocity gradients, distribution of transverse strains, of the friction force on the surface of a switching device and power consumption for overcoming of the friction force when the mixer’s blade is moving in the culture fluid. The graphic dependences of velocity and transverse strain, obtained by calculation, were presented. The mathematical model permits to determine the dependence of the transverse strain on the number of mixers’ rotations and the angle of inclination of mixers’ plane to the direction of movement.