Principles Of Comminution, I-Size Distribution And Surface Calculations (870a450d-7044-4cfe-8106-d1029f5a91cb)

PROBLEMS in expressing, interpreting, and using size-distribution data recur in many phases of mineral dressing; therefore it is desirable that size analyses be expressed in such a form, either numerically or graphically, that comparisons can be made readily. The size distribution of comminuted material is a result of a specific physical operation on the material and therefore should be governed by some definite physical principle, or cause-effect relation. Although this principle has not been discovered, it has been found that the size distribution of comminuted, homogeneous solids may be expressed by relatively simple mathematical equations. Two equations in particular, proposed by Gaudin1 and by Rosin and Rammler,2 respectively, have stood out, both having wide demonstrated ranges of application. The form and the method of application of the two appear almost irreconcilably different on the surface, but, as will be shown, they are asymptotic in the fine sizes when expressed in the same units. This paper gives the results of a further study of the Gaudin and Rosin-Rammler relations, made with the object of developing a form of size-distribution equation that will be more usable and more significant-particularly in comminution studies, both for interpreting the nature of size distribution and for evaluating surface. The work is summarized in the following: I. An equation relating cumulative per cent finer to particle size in the fine sizes is derived from Gaudin's original equation. That equation relates weight per cent retained on one size and through the next larger size in a geometric series of sizes to size (of the retaining screen, for example). 2. Comparisons with Gaudin's equation and with the Rosin-Rammler equation show that the cumulative equation applies to the fine sizes of all size distributions that fit either of these earlier relations, and, furthermore, has some advantages over each. 3. A simple graphical method of surface calculation based on the cumulative-equation plot is evolved and illustrated. 4. Additional confirmation of the cumulative equation was obtained in the more severe test of sizing down to the limit of a sedimentation balance a sample of jaw-crushed quartz. The equation was closely followed over a 20o-fold range in size, from approximately 0.4 mm. (35 mesh) down to 0.0023 mm. (2.3 microns), the lower limit of the size analysis made. There is no indication that the equation will not hold further to well below 2.3 microns. 5. Calculations of the surface produced in the jaw-crushing test mentioned above showed that at least 8o per cent of the total new surface was on particles finer than 35 mesh (about ½ 5 of the crusher setting). The minus 35-mesh portion was only