Statistical Principles of Gravitational Separation in a Two-phase Vertical Flows

Physical principles of two-phase flows with a polyfractional solid phase have not received a sufficient theoretical interpretation as yet. Two-phase flows in the separation mode with a counter-flow of particles are even more complicated. Only statistical methods give an insight into general regularities of such processes. These processes can be interpreted best by analogy with the statistical model of an ideal gas developed by L. Boltzmann, although here a number of difficulties arise. The notion of a statistical system for such flows is substantiated. A mathematical estimation of a statistical system is presented. New notions are introduced, namely, potential extraction of a system and lifting factor. A relationship having the physical meaning of entropy is derived for a two-phase flow in the separation modes. The connection of this new entropy with flow parameters, such as the number of particles, separation factor and chaotizing factor, is established. Properties of this entropy are analyzed, as well as the analogy and difference between this entropy and Boltzmann?s entropy. The notion is formulated and the definition of the chaotizing factor of a process is suggested. In the framework of a statistical approach to two-phase flows in the separation mode, the notion of flow mobility has been formulated. Principal regularities of mass transfer in zone/apparatus sys-tem are analyzed. Principal ideas of a cellular model of the process are formulated, and main relationships for its description are derived. Proceeding from the cellular model, a dependence describing the degree of fractional separation of a narrow size grade is found. The analysis of this dependence makes it possible to reveal the crucial role of the Froude criterion for gravitational separation processes. It is found empirically that this parameter is a basis for the affinization of separation curves (Barsky E, Barsky M, 2006; Barsky, 1980).