PROBABILITY OF PARTICLE-BUBBLE COLLISION IN PNEUMO-MECHANICAL FLOTATION CELL

摘要

The particle – air bubble collision is one of three elementary processes which determine the rate of bubble mineralizationin flotation. It is the result of bubble –,particle hydrodynamic interactions and depends mainly on the ratio of the particle sizeto the bubble size. The efficiency of the process is measured by the probability of particle-bubble collision.In the practice of upgrading in the cell with mechanical agitation of the pulp both the diameter of a particle and ofair bubbles has a certain distribution. Assuming that the diameter of particle d_paadhnrd eth er daiamnedtero ofm bublevariables, the probability of collision is the function of the quotient of independent random variables D_pAaDb.pnplydingthe theorems of probability calculus concerning the function of random variables, a general formula of probability densityfunction of the quotient of two random variables DpIDb was presented. The family of gamma distributions is the most oftenapplied and giving the best agreement with the experiment fo distribution of the D_p random variable. In this paper it was assumed that it is Rayleigh's distribution which characterizes well the distribution of particle size in the narrow size fraction. Simirlarly, for the distribution of the Db random variable, the three-parameter log-normal distribution is applied, apart from the distribution applied in granulometry. These are, however phenomenological approaches. In this paper the distribution obtained as a result of heuristic considerations has been used for the air bubble distribution. The air getting into the flotation cell is subject to dispersion in the turbulent vortexes of the liquid. Assuming that the newly formed surface of bubbles possesses energies corresponding to Boltzmann's distribution, the author obtained Rayleigh's distribution for the air-bubble diameter. The parameter of this distribution depends upon the surface tension of the flotation solution, gas flow-rate and power transmitted into the flotation cell. Calculating the most probable value of the quotient of Dd.D_b random variable, the expression for the probability of bubble-particle collision in the cell with mechanical pulp agitation was obtained. This probability depends on surface tension of the solution, gas flow-rate, gas hold-up, turbulent energy dissipation, volume concentration of the solid state in the cell and the average particle size.