The kinetics of batch wet grinding of quartz from a feed of 600×425 μm to a product of 80% less than 8 μm have been determined using sieving and laser diffractometer sizing for size analysis. A dispersing agent was added while proceeding to longer grinding times to prevent particle agglomeration in the mill. The specific rates of breakage (Si) values obtained were higher than those of dry grinding of quartz at the same experimental conditions, but the primary breakage distribution (Bi,j) values were the same. Non-first order grinding was observed with continued decrease of the specific rates of breakage for finer grinding. The simulations of the product size distributions were in good agreement with the experimental data, providing the decrease in rates was included.

The data of Dunn and Martin (1978) is reanalyzed using a rigorous application of Hertzian theory to the impact process. The Young’s modulus of steel required to fit their data to the theory is a factor of about 103, too low compared to the values quoted for steels. Thus, doubt is thrown on the validity of their experimental technique, and it is possible that their values for maximum impact force and stress are far too low.

It is shown that solutions of the integro-differential equation of batch grinding and the size discrete-time continuous Reid form for the equation of batch grinding give almost identical results for typical data. It is argued that the Reid form is as equally likely to be the `correct' form as the integro-differential form, and it is much easier to use and program. If the specific rates of breakage fit the form Si=Axiα, and the primary breakage functions fit the form Bi,j=Φ(xi−1/xj)γ+(1−Φ)(xi−1/xj)β for the Reid equation, then the corresponding forms for the integro-differential equation are S(x)=axα, B(x/y)=φ(x/y)γ+(1−φ)(x/y)β and equations are given for the relations between a and A and φ and Φ.

The grinding of quartz sand to produce high purity silica flour was studied using ceramic balls, ceramic cylinders or flint pebbles in a laboratory mill and three full-scale closed circuit mills of 2.2, 2.3 and 2.8 m internal diameter. The primary breakage distribution determined in laboratory tests was the same for the three media types but the characteristic slope (gamma) was changed from 1.05 to 0.95 to fit the full-scale results. An approximate correction was used for non-first order breakage kinetics. Simulation models were developed for the air separator and the mills. Simulations indicated that a mill lining of smooth ceramic gave media slip and was less efficient than flint linings. Higher circulating loads reduced specific grinding energy even though the recycle of fine mill product to mill feed increased. Ceramic balls gave the lowest grinding energy, wear rate and cost per ton of product.

Equations are derived to allow for different mean velocities of axial flow for different sizes of particles in fully mixed ball mills. The equations are modified to allow for the exit classification that occurs in grate-discharge autogenous and semiautogenous tumbling mills. An approximate treatment is given that applies for other forms of residence time distribution, provided that the mill contents are close to fully mixed.

In many industrial applications a major part of the data on size distributions uses screening to define size, whereas an important part of the size distribution information is determined using sub-sieve size analysis. It is necessary to have an accurate method of converting one type of data to the other. A technique is presented for conversion of Sedigraph size distribution data to equivalent screen size. The technique consists of first characterizing the material by determining the Sedigraph size distribution on a sample of the powder carefully wet-screened to lie between 270 and 400 mesh (53−38 μm) and fitting the data by a log-normal or log-logistic distribution function to give μ and σ or μ and λ values characteristic of the material. The Sedigraph size distribution of a sample of less than 400 mesh powder screened from the total sample can then be converted to an equivalent screen size distribution by a back-calculation technique, using the characteristic parameters of the material in a constrained search program. The technique is illustrated by application to data taken around an industrial grinding mill.

Using an instrumented laboratory high-pressure grinding rolls mill, the grinding force, gap dimension, mass flow rate and net mill power were measured for six coals and a crystalline quartz. A technique was developed to estimate the compressive stress-strain curves for compression of the materials in the mill plus the effects of elastic decompression. To reconcile the mill power and grinding pressure results, it was necessary to allow for the energy recovery on decompression. No clear correlation was obtained between the form of the stress-strain curves or the variation of specific mill power factor with the Hardgrove grindability index (HGI), although coals with the lowest and highest HGIs (i.e., 44 and 106) gave results significantly different from the other coals. Feeds below 140 mesh (105 μm) flowed more rapidly than coarser feeds and would not build up high grinding pressures. This indicated shearing and fluidlike properties rather than compression as a locked bed.

ABSTRACT The mill power of a laboratory scale tumbling media mill was determined for the different shapes of media which are used industrially for dry grinding of quartz to produce silica flow. The tested media were ceramic balls and cylinders of high density alumina, and natural flint pebbles; tests were performed over ranges of filling levels and rotational speeds, with and without lifters in the mill. The experiments showed that ceramic balls at low levels of ball charge slipped excessively against the mill wall when the mill interior was smooth and without lifters. The use of lifters gave a consistent tumbling action and, under otherwise comparable conditions, mill power was linearly proportional to media density. Equations were developed which enable the comparison of mill conditions which give the same mill power draw for the different shapes and densities. Combined with studies of grinding kinetics, this enables comparison of the grinding efficiencies for different media shapes.

The objective in many cases of industrial grinding is not simply to produce fine sizes but to liberate one component from another by breakage of particles which contain both components locked together. Thus, it is not sufficient to know only the product size distribution, but it is also necessary to know also the range of interlocking within each size, called the liberation function for that size. This paper describes a technique for calculating the function from data where float-sink analysis can be used to separate different compositions and shows how the results can be represented graphically. Various size fractions of a hammer-milled coal and the same coal ground in a ball mill were examined to determine the liberation function M(C) for each size. It was found to be necessary to fit a three parameter function to points on the Mayer curve of ash (mineral matter) units floating versus mass floating. The function was A(M) = k1M + k2Mn. Since A(M) = ∫M0CdM(C), then C = dA(M)/dM and the liberation function is M(C)=[(C−k1)/nk2]1(n−1). This technique worked well for the hammer-milled coal data taken at 1.4, 1.5 and 1.6 specific gravities, and enabled the calculation of the locking index for each product size (√2 screen intervals). However, the corresponding data for ball-milled coal were inconsistent, although the change of liberation with increased grinding could be shown qualitatively from plots of M/(1−φ) versus C/φ, where φ is the ash fraction of each size.

The general manner in which the liberation function must change during size reduction is described. Data from float-sink (washability) analysis of a coal is used as an illustration, and a Locking Index is defined and calculated. Ash is not distributed equally with respect to sieve size but is concentrated more in the finest sizes. On the other hand, the ash is less locked with coal in the finer sizes than in the larger sizes. Further crushing showed decreased locking in intermediate sizes, but the material in the fine sizes (produced from breakage of highly locked larger sizes) was more locked than material of the same size in the feed. Future work is also discussed.

Equations are derived for the rate of loss of mass from a screen interval when the size reduction process is an abrasion-chipping process which follows a wear law of the Bond form or the Davis form, giving cores and fragments. The treatment is extended to steady-state continuous grinding in a fully-mixed reactor, and to the case where first-order disintegrative fracture processes also occur.

A kinetic model for the prediction of the performance of a froth flotation cell is proposed. The model is based on the assumption of a free-flowing concentrate froth. The flux of bubble surface is estimated from the cell aeration rate and the specific surface of the bubbles in the froth. The specific surface in the froth is based on the mean bubble size which is estimated by off-line image processing of photographs taken of the froth during laboratory scale batch tests.A sequence of batch flotation tests in which a low-rank UK coal was demineralized, by varying the initial addition of Sodium Dodecyl Sulphate (SDS), was used to test the consistency of the model predictions with experimental data.Although all the model parameters have a physical reality, not all were able to be measured at this stage. Nevertheless, the consistency of the predictions with the experimental data was encouraging, and the potential value of extended on-line image processing as a tool for improved experimentation was apparent.

Recent work at University of Manchester Institute of Science and Technology indicates that coal may be able to be beneficiated by ultrafine grinding to below 45 μm followed by froth flotation. This was achieved under laboratory-scale test conditions. In order to develop a basis for an economic analysis of this process it is necessary to have a relationship between the extent of grinding and the degree of mineral liberation. A heavy liquid separation at 1.4 × specific gravity carried out in a centrifuge was used to characterise the liberation. This publication reports an experimental investigation of the effect of grinding on the liberation of mineral from a low-rank semibituminous UK coal and develops a mathematical model based on this data, which could be used for scale-up. It was found that the ash content could be predicted approximately by the solution of the batch grinding equation with a breakage distribution for ash different from that for total mass.

The combination of a grinding circuit simulator with a model of ball wear in a grinding mill leads to a method to calculate, with a preselected accuracy, the make-up ball charge that optimizes the operation with respect to a given objective for the grinding process. In the example shown, the best make-up ball charge, calculated with a 1% accuracy, increased the circuit capacity by 12% from the best monosized make-up ball charge.

As an extension of previous work by one author on the settling of ideal suspensions, we analyze the settling behavior of a suspension with two particle sizes. The solid flux density as a function of both particle concentrations is constructed. Using a finite difference method three initial and boundary value problems were solved showing the settling curves and the concentration profiles for each particle size. We conclude the work by extending the concept of a Kynch Sedimentation Process to a mixture of any number of ideal suspensions, each having a different particle size. An example for six particle sizes is analyzed in detail. Again the result is given as sedimentation cur-ves and concentration profiles for each particle size.

The Concha-Almendra batch-settling treatment for concentrated suspensions of single-diameter spheres has been modified. This modified version is used in the differential equations of simple batch settling of a particle size range of different density materials. The equations have been programmed for a finite difference solution, and a number of test cases have been analyzed. By cutting the settling column at a fixed fractional height, the material below this height can be treated as underflow and the material above as overflow.

The kinetics of batch grinding quartz from a feed of 600 by 425-mu-m to a product of 80% less than 10-mu-m have been determined using screening and laser diffractometer sizing for size analysis. The specific rates of breakage decreased by a factor of about three when the material became less than about 100-mu-m in size, but the primary breakage distribution function also changed to give proportionately more fine material, so that the grinding efficiency expressed as the development of surface area (B.E.T.) per unit of energy input did not decrease. Analysis of the shape of the particles in the 25 x 38-mu-m size range showed that particles of this size produced by roll crushing or by 8 minutes of grinding of a 425 x 600-mu-m feed were not different but at long grinding times the particles were rounded. This suggests that the breakage mechanism changes to give more chipping and abrasion and less disintegrative fracture. As the material approached the ultrafine size range it adhered to the mill case and there was no further size reduction. However, a technique for striking the mill case to dislodge the particles was successful in allowing further grinding to 40% by weight less than 2-mu-m.