Undersize particle

Screening (continuous, commercial) and sieving (batch, laboratory test generally confined for size determination) are essentially mechanical separations of particles based on size, accomplished by using a perforated surface that serves as a go-no-go gauge. Both processes, like all other separation processes, have the drawback that a complete separation is seldom obtained, and some potential oversize/undersize particles are always left in the undersize/oversize fraction. 

The cumulative mass fraction undersize (particles that pass through the sieve) can be calculated by subtracting the cumulative mass fraction oversize from 1. For example, the cumulative mass fraction undersize for sieve 3 would be 0.51 ... 

The super-centrifuge is used for clarification of oils and fruit juices and for the removal of oversize and undersize particles from pigmented liquids. The liquid is continuously discharged, but the solids are retained in the bowl and must be removed periodically. 

Crystallization from an overall viewpoint represents transfer of a material from solution (or even a gas) to a solid phase by cooling, evaporation, or a combination of both. But there is more to it. Of considerable importance are economics, crystal size distribution, purity, and the shape of the crystals. Impurities or mother solution are carried along only in the surface or occlusions in the crystals. The partical size distribution depends on the distribution of seed crystals, which are injected into the crystallizer prior to initiation of crystallization (batch) or continuously from recycled undersized particles, the mixing in the system, the crystal growth rate, and the degree of supersaturation of the mother liquor. As in shown in the figures, both batch and continuous crystallization are used in industry. 

One problem associated with this technique is that the sediment consists both of oversize (greater than Stokes diameter) and undersize particles so that the sedimentation curve of amount settled P) against time (r) has to be differentiated to yield the weight (W) larger than Stokes diameter. Several balance systems, based on this equation, have been deseribed. 

The third, (c), is clear liquid overflow recycling to an elutriating leg which prevents undersized particles from escaping prematurely. Draft tube baffle (DTB) crystallizers contain elutriation legs, but DTB units are more commonly evaporative rather than cooling crystallizers. 

Fig. 6.6-34 is the flow diagram of a manufacturing process that was designed for this purpose. Approximately 10% of a bentonite clay (swelling agent) is added to the molten sulfur. The slurry together with make-up water is sprayed into the FDG (for startup, stored recycle from earlier production runs is introduced first) which, for this purpose is slightly modified as shown in Fig. 6.6-35. The discharge is screened and the undersized particles are returned to the granulator for fattening.

Fig. 6.1-3 Diagrams of a crusher with oversize recycling and various two- or three-stage crushing circuits [6.1.4]. Circles represent crushers or mills horizontal lines flanked by -h and - represent classifiers (screens) that split the crushed material into over- and undersized particles.

While for general applications the presence of some over and under sized particulates is often not objectionable, as an option the discharge from post-treatment may be separated into two or three size fractions. Fines (undersized particles) are discarded, used elsewhere, or recirculated to the agglomerator and coarse pieces (oversized particles and lumps) may be crushed in a closed loop whereby the fragments, which typically include again all three fractions, are recirculated to the sizing operation. Selection criteria for the crusher have been discussed in Section 6.1. 

By measuring absorbance changes as a function of time, the cumulative undersize particle distribution can be obtained by mathematical manipulation. However, in converting Equation 34-18 to the size distribution, it is necessary to know how the absorption coefficient K varies with d,. Alternatively, an external standard can be used for calibration. If correction is not made for variations in K. results are valid only for comparison purposes. 

The cumulative percentages of oversize and undersize particles may also be plotted against aperture size on a log-log basis Figure 2.17b). In this type of plot the cumulative undersize data tend to lie on a straight line over a wide range of particle size, about 100 to 1200 pm in this case. The undersize and oversize curves are clearly not mirror images, and oversize data are rarely correlated on this basis. 

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