Oversize particle cumulative frequency

Figure 18. Example of the sedimentation of particles in a clay suspension, monitored using an Oden balance, showing (a) the measured cumulative mass of particles collected versus time (b) a graphical derivative of the first curve, with respect to time, showing the cumulative mass of oversize particles and (c) a graphical second derivative of the first curve, with respect to time, showing the frequency by mass of particles. (Reproduced with permission from reference 5. Copyright 1986 Marcel Dekker.)...

Diagram of cumulative frequency of oversized particles for (a) feed, (b) ideal separation, and... 

Particle sizes dso and da, corresponding to G(d) = 0.5 and G(d) = E, serve as useful parameters of the function. The former indicates the size of particle with an equal probability of reporting to either outlet. The latter is usually termed the analytical cut size and corresponds to a cumulative (oversize) frequency of the feed material which divides it exactly in the proportion of E, as though GW) were a step function. 

Most modem instrumental particle size analysers readily present data in a variety of forms, such as frequency, cumulative undersize or oversize, and interconvert between number, mass and other distributions. Acquisition of data in a suitable form is therefore not usually a problem. 

Figure 2.11 Sedimentation of clay particles in an Oden balance experiment, showing the cumulative weight (%) versus time (a), cumulative weight of oversize material (%) versus time (b), and frequency by weight versus time (c). From Hiemenz [87]. Copyright 1986, Dekker.

If the data are in a cumulative form, as cumulative percentage undersize or oversize (see section 2.5), conversions between the different particle size distributions can be made without having to differentiate the curves to obtain the size frequencies, as follows. 

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