(untitled) (Journal of Mathematics Mechanics and Computer Science, 2018)
This work is devoted to the study of centrifugation processes, which are one of the most complex processes of technology. The use of the action of the centrifugal force field for the separation of heterogeneous liquid systems in a rotor system (centrifuge) is very effective. Separability of centrifuged materials, multiphase dispersion, the relationship between phases cause ambiguous processes of centrifugation, and therefore it is not always possible to accurately predict and evaluate the main characteristics of the separation of heterogeneous systems in the centrifugal force field. For a qualitative assessment of the main separation characteristics, such as the angular velocity of rotation, the dependence of the angles of inclination of the glasses on the angular velocity, the settling time of particles, etc., is created a mathematical model of the vertical rotor system. The rotor represents a round disk on which cups (vial) with a multiphase liquid are symmetrically suspended. A particular case of a fixed rotor is considered. Nonlinear differential equations of motion of the suspension particle, which have no exact solution, are obtained. The research is conducted by analytical and numerical methods. The dependence of the slope angles of the tubes from the angular rotational speed of the rotor, sedimentation curves are obtained , which allow estimating the time of particle deposition and the effect of the particle size distribution on the separation process. The results of this research work allow us to determine with sufficient accuracy all the necessary characteristics of the sedimentation working process, and also, in certain cases, it is possible to exclude the conduct of experimental work. The results of the work confirm the physical meaning of the process, which can serve as a justification for the use and introduction of this mathematical model in industrial production.