Clean-size-fraction characterization

Recovery of a certain fraction is the ratio between the masses of any fraction in the suitable product and in the original material. The recovery shows which part of useful particles contained in the feed gets into a suitable product. The coarse and fine fraction recoveries are expressed by yc = mcCc/m0C0, yf = mfFf/m0F0, respectively. Cleanness and dirtiness characterize quality of the separated products. In contrast, fraction recovery characterizes the separation efficiency. In particular if the original product is composed only of particles having cut size, its fraction recovery is 50%. 

Most theoretical studies of heat or mass transfer in dispersions have been limited to studies of a single spherical bubble moving steadily under the influence of gravity in a clean system. It is clear, however, that swarms of suspended bubbles, usually entrained by turbulent eddies, have local relative velocities with respect to the continuous phase different from that derived for the case of a steady rise of a single bubble. This is mainly due to the fact that in an ensemble of bubbles the distributions of velocities, temperatures, and concentrations in the vicinity of one bubble are influenced by its neighbors. It is therefore logical to assume that in the case of dispersions the relative velocities and transfer rates depend on quantities characterizing an ensemble of bubbles. For the case of uniformly distributed bubbles, the dispersed-phase volume fraction O, particle-size distribution, and residence-time distribution are such quantities. 

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