Technical Notes - Relationship Between Recovery and Rate of Flotation in Continuous Flotation Systems

In a study of the kinetics of flotation of coal, employing a single-cell continuous flotation system, Jowett and Safvi1 pointed out that it was experimentally impossible to float all of the coal which could be floated in a batch tests. On the other hand, deBruyn and Modi, in a discussion of their paper, suggested that under certain conditions the recovery of floatable material from a similar one-cell continuous system would have been 100%.2 Both of these pairs of authors make the assumption that a state of perfect mixing exist in the flotation cell. This assumption, usually made by investigators studying flotation kinetics in a continuous system, has been confirmed experimentally on several occasions. The work is summarized by Arbiter and Harris.3 It is the purpose of this note to demonstrate that, for conditions of perfect mixing, one of two conditions exist: 1) the recovery of floatable material is 100%, and the flotation is infinitely fast, or 2) the recovery of floatable material must be less than 100%. This theorem can be proved simply in the following manner: 1) If recovery, R, of the floatable material is 100%, the concentration in the tailing must be zero. This follows from the definition of recovery as