Sharpness of cut

The sharpness of cut can be expressed in terms of the differences in size distribution F(d) of the solids in the underflow Fu(d), in comparison with that of the overflow F0(d). These are well resolved when the cut is sharp. The values of dso and da converge as the... 

Three parameters define the performance of a classifier. These are cut size, sharpness of cut, and capacity. Cut size, X50, is the size at which 50 percent of the material goes into the coarse product and 50 percent into the fine. (This should not be confused with the cutoff size, a name sometimes given to the top size of the fine product.)... 

These ratios are not always adequate to define the sharpness of cut [5]. In many cases it is important to keep the amount of fines in the coarse or the amount of coarse in the fines as small as possible. For these cases a measure of the effectiveness of a separation process is given by the following For the coarse yield ... 

The conventional hydrocyclone has been subjected to considerable development to improve its characteristics. Sharpness of cut, for example, can be improved by injection of clean liquid into the flow near the apex of the cone. Another way is to operate the cyclone upside down so that the solids are separated into a container above the cyclone and subsequently fall back into the cyclone to be washed again. There is also some evidence that a flat bottom hydrocyclone can give better sharpness of cut. 

In the pulp and paper industry, water is often added in the underflow rejects chamber to reduce losses of fibre with the rejected granular dirt. Similarly, the sharpness of cut in the classification of granular solids can be improved by injecting clean liquid into the flow near the apex of the cone. The liquid displaces the slime fraction that would normally end up in the underflow commercial systems exist for this (e.g. Krebs Engineer s Cyclowash). The quantity of liquid added is usually equal to or greater than the underflow rate without liquid injection. The benefits of this depend on the cost of clean liquid needed for the injection reclassification may be a cheaper alternative. 

In classification, the system cut size is purposely set within the size distribution of the solids, depending where the cut needs to be made. The arrangement in Figure 15.1 is capable of a significant improvement in the sharpness of cut compared with that of a single-stage separator and this is further discussed and documented in chapter 16. 

The last point needs explaining a little further. There are two reasons for deriving the sharpness index from the reduced grade efficiency curve rather than from the actual one. Firstly, the sharpness of cut is always to some degree affected by Rf and this way the effect is removed. Secondly, as can be seen later, the sharpness index for the actual grade efficiency curve sometimes cannot have a value because the whole of the curve may be greater than 25% and X25 cannot be determined. 

Table 16.2 Sharpness of cut improvement with number of stages, in a series arrangement on overflow...

As to the sharpness of cut, the multiple pass system does improve it a little (see Table 16.4) but nowhere near as well as a simple overflow system— compare with Table 16.2. 

As to the sharpness of cut, both of the recycling arrangements A and B sharpen the cut in comparison with a simple overflow series but there is very little difference between them. Thus, for example, for a three-stage system, the sharpness index 1/75/25 varies as follows ... 

Figure 16.13 Comparison of sharpness of cut for the overflow and underflow series (both plotted against dimensionless particle size)...

The separator in stage 1 is not efficient enough for classification, i.e. it misplaces too much of the fine particles into the coarse product and of the coarse particles into the fine product. This performance in classification is characterized by the so-called sharpness of cut derived from the shape of the grade efficiency curve. In this section we measure the sharpness of cut by the sharpness of index 1/75/25 defined as the ratio of the particle sizes at 75% and 25% on the grade efficiency curve. 

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