Minerals Beneficiation - Energy-Size Reduction Relationship for the Grinding of Quartz

It has been demonstrated that for fine grinding operations, the energy input (E) and the product size modulus (k) are related by an equation of the form E = Ak1-n (1) where "A " and "n" are constants.(1) Also, it was suggested that "A" is determined by the comminuting device and that "n" depends primarily on the rock. It was the purpose of this investigation to study these constants by determining the form of an energy-size reduction relationship over an extreme range of energy inputs, and at the same time, to evaluate the minimum particle size produced during grinding. The comminution system consisted of a stainless steel laboratory ball mill in which quartz was ground at 60% solids for times ranging from 1 minute to 700 hours. The mill which measured 10" diameter by 12" long was loaded with about 60 pounds of balls ranging in diameter from 3/8" to 1-1/8" and was driven at 55 r.p.m. Quartz was selected for the tests because it is a brittle material for which size distribution data were expected to show a constant distribution coefficient regardless of product size.(1) This permitted specification of product size by a size modulus alone. The quantities measured were the time of grind (measure of energy input) and the specific surfaces of the products. Since no accurate method is available yet for determining particle size directly in the very fine size ranges specific surface data were used for this purpose. The relationship between these two quantities may be expressed as where Cis a constant which includes a shape factor, p is the specific gravity of the solid,_S is the specific surface and D is an equivalent particle diameter. For a material in which the distribution coefficient does not change with size the term (l/S) may be substituted for k in equation L if the proportionality constant "A" is changed correspondingly. This substitution was made in this work but in addition, screen analyses were made on several products to verify the equivalence of the two methods of size specification. EXPERIMENTAL DETAIL QUARTZ Quartz from two sources was tested. One series of tests was made on a clear, high purity crystalline quartz from Brazil and Arkansas, and another series was run on massive quartz fromNewHampshire. Grinding charges of the high purity material consisted of 2000 gram samples of -3-8 mesh particles, while the charges of the New Hampshire quartz were 500 gram samples of a -35+48 mesh screen fraction. The difference in the sizes of these two series of charges was not significant in view of the extreme size reduction accomplished, and the New Hampshire samples were smaller to permit ginding to finer sizes in shorter times than required for 2000 gram lots. SAMPLING AND ANALYSIS Separate charges were ground for all tests in which the grinding times were less than one hour and for all tests on New Hampshire quartz since these products were difficult to sample accurately without affecting the entire charge. During the long time grinding tests the mill was