Partial Gravimetric Efficiency

The total efficiency defined by Equation 10.14 includes all particle sizes present in the feed solids. If only a narrow range of particle sizes is of interest. 

A typical example of partial efficiency is the so-called hygienic efficiency used as a criterion to verify ambient air quality, which includes particles in the range of 0.5-5 pm considered harmful for the human respiratory system. 

Two usual definitions of partial efficiency are the rejection efficiency and the acceptance efficiency or recovery index. The rejection efficiency, relevant in classification of powders, is considered as the mass of coarse product greater than the cut size (the limiting size dividing a particle size distribution into fines and coarse fractions) related to the mass of feed solids greater than the same cut size. According to this, in Equation 10.21 Xj would represent the cut size (X50) and X2 would be the maximum particle size in the feed. The rejection efficiency E, can be expressed as a function of cumulative oversize (coarse) percentage and the cumulative percentage of coarse fraction in the feed F, as 

With regard to the acceptance efficiency, it may be considered opposite to the rejection efficiency in the sense that the undersized particles are those considered as the reference for defining such efficiency. In this case, Xi in Equation 10.21 would represent zero, while X2 would be taken as the cut point. The acceptance efficiency can be expressed as a function of cumulative undersized (fines) percentage Ff and the cumulative percentage of fines fraction in the feed F, as 

A special case of acceptance efficiency is the one known as screen or sieve efficiency E, which assumes a perfectly formed screen so that the underflow is free from particles larger than the equivalent screen diameter x. According to this criterion. Equation 10.23 can be reexpressed as 

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