Mathematical model of movement of a single spherical lupine particle in the extractor using low-frequency mechanical vibrations

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...