Differential size distribution

E Work index of mill feed W Vector of differential size distribution ... 

The process to be analyzed is represented by Figure 16.4. What will be found are equations for the cumulative and differential size distributions in terms of residence time and growth rate. The principal notation is summarized here. 

With a polydisperse size distribution, the total fraction remaining, F, can be determined by summing over the differential size distribution 0 where 0 is the fraction of total particle volume with initial diameters from dj... 

Figure 6. Differential size distribution—less than optimum dose of low molecular weight PEI produces small aggregates and increased suspension turbidity (mol wt—1200 polymer dose—0.50 mgjL mixing intensity— 201 sec initial particle count—2.915E 071 ML reaction time H) 0 min ...

Figure 8. Differential size distribution—optimum dose of medium molecular weight (1800) PEI produces larger aggregates but no change in suspension turbidity (mol wt—1800 polymer dose—5.00 mgjL mixing intensity—201 sec initial panicle count—2.350E 07/ML reaction time— ( j 0 min (0) 60 min)...

Figure 10. Differential size distribution—growth of large aggregates reduces suspension turbidity by 50%, following flocculation with high molecular weight (60,000) PEI (mol wt—60000 polymer dose—0.50 mgjL mixing intensity—20 j sec initial particle count—2.813E 07/ML reaction time—(Dj 0 min (O) 60 min)...

Equations 15.1 and 15.2 can be used to compute the grade efficiency curves for each system in Figures 15.1 and 15.7. This calculation is best performed in a spreadsheet where each line in Table 15.1 is processed by the two equations, yielding two additional columns. These are given in Table 15.2 where the given values of particle size x and differential size distribution in the feedy(x) are repeated in the first two columns. 

Use the data from Appendix 5.A the feed solids properties, the overall efficiency, the grade-efficiency curve and Eq. (16.1.1) to calculate the differential size distribution of the overflow fraction from the first-stage cyclone. 

Convert this differential size distribution to a cumulative one... 

The second step is to convert this differential size distribution to a cumulative one. This is straightforward. We use Eq. (2.3.3) or its finite equivalent ... 

Differential size distribution functions (N2/S102, loop HI), 1-percolation method, 2- standard method (adsorption branch), 3- standard method (desorption branch). 

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