Undersize/underflow

The products are an oversize (underflow, heavies, sands) and an undersize (overflow, lights, slimes). An intermediate size can also be produced by varying the effective separating force. Separation size maybe defined either as a specific size in the overflow screen analysis, eg, 5% retained on 65 mesh screen or 45% passing 200 mesh screen, or as a d Q, defined as a cut-off or separation size at which 50% of the particles report to the oversize or undersize. The efficiency of a classifier is represented by a performance or partition curve (2,6), similar to that used for screens, which relates the particle size to the percentage of each size in the feed that reports to the underflow. 

Actual screens do not or provide an incisive separation. Rather, the screen analyses of the overflow and the underflow are like those shown in Figure 2.13 (C). The overflow contains a good amount of particles smaller than the desired cut diameter, and the underflow contains particles bigger than the cut diameter. The two curves overlap, as shown in Figure 2.13 (C). It may also be added that the mass of the two outgoing streams will not equal the individual masses of A and B unless it occurs that the undersize material in the overflow is equal to the oversize material in the underflow. 

Classification or size separation is the unit operation that separates the particles according to their size. In general, it can be carried out dry or wet. The fraction of the feed having size less than the size of the screen aperture is the undersize, while that of greater size is the oversize. The fraction of the undersize that flows through the apertures is called underflow (or passing), while the particles that do not pass are called overflow (or remaining). In solid-waste treatment, classification is carried out almost always on screens and in dry, because the particles to be classified are relatively coarse and wet processes are undesirable. 

Disc screens are composed of a series of parallel, horizontal, and equally spaced bars or shafts, which are installed perpendicular to the flow of the material. Each shaft is equipped with interlocking serrated or star-shaped discs, installed at equal distances across the width of each bar. Undersized material falls in the space between the discs, while oversized material overflows the discs. The adjustment of the distance between the discs determines the materials size to be separated as underflow. After suitable adjustment, the same screen can be used to separate materials into different size. 

If Xq and represent the mass fractions of oversize material, i.e. particles larger than a, in the feed, overflow and underflow, respectively, and Xp, x and x j represent the corresponding undersize mass fractions, then a balance on the oversize material gives... 

Equation 9.138 gives a measure of the success of recovering oversize particles in the overflow stream, equation 9.139 of undersize material in the underflow stream. For perfect screening both Eq and Eq will be unity. Equations 9.138 and 9.139 require values of the mass flow rates F, O and U, but substitution from equations 9.132 and 9.133 can eliminate these quantities ... 

A simpler form of equation 9.140 is often used to express the recovery of true undersize material in the overflow fraction, on the assumption that all the underflow stream consists of undersize material, i.e. = 1 ... 

For classification of particles above size r and below size r respectively, into the underflow and the overflow of a solid-liquid classifier, define component 1 to be the undersize particles and component 2 to be the oversize particles. Show that the extent of separation based on mass fractions in such a case is given by... 

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