Physics of Gravitational Separation as a Mass Process

"At present, theoretical concepts of gravitational separation processes are mainly limited by the study of the interaction between a flow and a solitary particle. Then the main conclusions of this analysis are applied to a mass process. However, this analysis is absolutely insufficient, because some elementary phenomena such as the ingress of coarse particles into the fine product output and vice versa cannot be interpreted from its standpoint. It is also impossible to predict the results of the classification of a material with a specific granulometric composition on a specific apparatus on its basis.In the present paper, an extended model of the process is suggested. The model is based on the behavior of all the particles of a specific narrow size class, and not on that of an individual particle. Similarity criteria of the process, which were empirically derived previously, are obtained from the analysis of this model.INTRODUCTIONIn case of gravitational separation, a part of solid phase moves, as a rule, vertically upwards with the flow, while another part settles against the flow. This flow is extremely complicated and chaotic due to various random factors. Among these factors are mass interactions of particles with each other and with the apparatus walls, non-uniform character of concentration and velocity fields, turbulent vortices and local fluctuations, real particles shape difference from spherical one, etc.Particles rotation results in a transverse force (Magnus' effect). At the motion of a non-rotating particle in a non-uniform velocity field, a transverse force also arises (Saffman's effect).A great number of publications have been devoted to the account for all these factors in two-phase flows in recent decades. Very complicated models have been developed, but the problem has not been completely solved as yet [1, 3].At the same time, simplified models of the behavior of a solitary particle in a flow are being developed. Despite their schematic nature, such models often prove to be useful for establishing general laws of the process and its similarity criteria [1]."