Abstract: The degradation of coarse aggregates under shear stresses and its influence on the shear strength is studied, considering the energy consumption by particle breakage during shearing. An analytical model is developed relating the deviator stress ratio, dilatancy, friction angle and particle breakage under triaxial loading. Large-scale triaxial testing of latite basalt has been conducted, and the extent of particle breakage during shearing has been quantified. The breakage of particles under monotonic triaxial loading has been considered within the scope of this paper, and the modelling of particle breakage of aggregates under cyclic loading will be presented in a follow-up paper. The results show that the breakage of particles continues to increase beyond the peak deviator stress. The energy consumption by particle breakage is non-linearly related to the particle breakage index. The model also evaluates the effect of particle breakage on the friction angle of ballast. This study sheds further light on the basic angle of friction, which is independent of the breakage of particles during shearing.

Abstract: An approach for the quantitative characterisation of feed materials in impact grinding is presented. With the help of dimensional reasoning and a fracture mechanic model two material parameters can be derived which describe the breakage probability quantitatively. The influence of stress intensity (impact energy), stress number, initial particle size and material are separated clearly. The two derived material parameters can be determined by single particle impact experiments with narrow size fractions of the feed material. A single mastercurve for the selection function of five different polymers, limestone and glass describes the breakage behaviour for two decades of initial particle size. The procedure using narrow feed size fractions can be simplified by using feed material with a broad particle size distribution. Then the appropriate population balance has to be inverted in order to determine the particle properties. Both, the population balance and the inversion are presented and validated with experimental results.

Abstract: There are three main mechanisms of breakage in Autogenous Grinding (AG) and Semi-Autogenous Grinding (SAG) mills: (i) Abrasion,(ii) Chipping, and (iii) Crushing. Abrasion is a surface event in which small grains of particles are removed. Chipping can also be classified as surface event in which surface "features" are removed. During both events cracks are not propagated through the main body of the rock and therefore can be classified as surface breakage. However, In crushing cracks propagate through the body of the rock. In modelling breakage is described by using a so-called appearance/breakage function which historically has made use of size-average breakage parameters (Herbst and Fuerstenau (1968); Austin and Luckie (1971); Leung (1987)), ie rock strength is assumed to be independent of size. In addition these parameters typically do not consider the mode of breakage or as in the case of Leung do so in an arbitrary manner. Given that in AG/SAG mills the feed size distribution is usually -250 mm and the product size P80 can be as low as 50 microns the assumption of sizeinvariant strength is likely to have a significant impact on the model's accuracy. To rectify the current lack of appropriate definition in the way that rock breakage is described in existing AG/SAG mill models, a research program was undertaken via the AM IRA POL project. This thesis describes the resultant model which Incorporates the effect of particle size for the two main regimes of breakage, namely surface and crushing, and unifies them in a single, mechanistically sound, description of breakage. To quantify surface breakage at different energy levels, a range of equipment was developed. This equipment allows the fragments generated for each breakage event to be extracted. Using four different mill diameters, the effect of input energy and particle size on mass of fines produced was determined. The results showed that under very low Input energy conditions, which produce chipping and abrasion breakage, the resultant product size and quantity of broken products are affected by the size of the particles. As expected, the coarser particles tend to generate more fragments than the smaller ones. Although the common method of relating the amount of fragments produced during breakage is by the use of mass specific input energy, due to the fact that abrasion and chipping is related to surface conditions, the data were found to be correlated to surface specific input energy instead. A drop weight tester was used to quantify the effect of particle strength on the particle size distribution obtained under higher energy impact breakage conditions (eg as observed in crushing). A wide range of particle sizes was tested under a wide range of input energies. As in the case of surface breakage, the results showed that coarser particles tend to be inherently weaker than smaller ones. In view of the fact that during crushing cracks propagate through the body of the rock, the effect observed was modelled based on the volumetric specific input energy. The above descriptions of "surface" (eg abrasion and chipping) and "body" (eg crushing) breakage were integrated into a single description of breakage for use in AG/SAG mill modelling. To do so the size distributions of products from these two types of breakage were combined using a weighting function. To determine the weighting, the Hopkinson Pressure Bar (HPB) was used to further characterise the rocks. The data from the HPB was modelled using the log-normal distribution. The approach provides a probability distribution that allows the determination of the proportion of the material that will break either by body or surface breakage under a given input energy. The breakage model has been incorporated in a prototype version of a new AG/SAG mill model. Evaluation of the model has shown that it can mimic expected trends during SAG mill operation. Similar simulation studies were carried out using the current (Leung's) appearance function technique and the results showed that the trends obtained are in contradiction to operational experience. This apparent discrepancy further highlights the limitation of the current techniques for describing breakage.

Abstract: The endosperm and bran of a wheat grain have different mechanical properties and break differently under the same stresses. Stress-strain analysis was used to model the factors affecting wheat kernel breakage during milling using fluted rolls. The planes of principal compressive and tensile stress and the maximum shear stresses, along which the kernel is most likely to be broken, were calculated for a sharp-to-sharp roll disposition. With the occurrence of compressive stress in the horizontal direction and shear stress in the vertical direction, a kernel tends to break along a principal tensile stress plane because the tensile strength of the endosperm is much smaller than its compressive strength. The model presented quantifies the mathematical relationship of three design and operational factors affecting the principal stresses and the maximum shear stresses: roll gap, differential, and roll diameter. High-speed video was used to observe wheat breakage events during milling; the results show consistency with the theoretical analysis.

Abstract: An experimental apparatus to study the breaking process of axisymmetric liquid bridges has been developed, and the breaking sequences of a large number of liquid bridge configurations at minimum-volume stability limit have been analyzed. Experimental results show that very close to the breaking moment the neck radius of the liquid bridge varies as t1/3, where t is the time to breakage, irrespective of the value of the distance between the solid disks that support the liquid column.

Abstract: The objective of this study is to develop and evaluate a new Monte-Carlo simulation method to predict the hydrodynamics of rotating disc contactors (RDC) with continuous flows of liquid phases and with drop breakage. This method has the advantage of using individual drops controlled by breakage phenomenological parameters of probability of breakage, number of generated drops and their size distribution. Drop coalescence is ignored due to the very low hold-up and the high interfacial tension of the chemical system. The Monte Carlo stochastic method is applied by using the elements of generated vectors of random numbers having given distribution and with sequences of repeatable or non-repeatble. The limiting values are obtained from correlations that are based on single drop experiments. A stage-wise explicit calculation method with the use of a population balance is employed to follow the steady flow of dispersed phase. The generated results are compared with the experimental results obtained from a pilot RDC and a good agreement is observed. The changes of local hold-up and mean drop size along the column are also described reasonably.

Abstract: The characteristics of ultrasonic breakage are investigated quantitatively by measuring the particle size of a dye dispersion subjected to ultrasound radiation. The breakage of dye particles strongly depends on the liquid medium temperature, the ultrasound intensity, and the dye dispersion volume. The degree of breakage is also determined by the total sonic energy per unit volume radiated to the dye dispersion, regardless of factors such as ultrasound radiation intensity, dye dispersion volume, and ultrasound radiation time. There exists a temperature at which the breakage rate reaches a maximum.

Abstract: This paper presents the breakage and wetting parameters of calcite mineral obtained experimentally and establishes a correlation between these characteristic parameters. The breakage parameter obtained from the different feed sizes of grinding is the specific rate of breakage (Si). The wettability parameter, obtained from surface chemistry-based processes such as contact angle measurements or flotation methods, is the critical surface tension of wetting of a solid or mineral (γc). Calcite mineral, studied for the determination of the above parameters and their correlations, was ground in a laboratory-size ceramic ball mill with dry, wet and chemically aided grindings and tested extensively to determine the γc values by using a contact angle goniometer and a newly designed micro-column flotation cell. The highest Si value obtained was 0.35 min−1 for sodium dodecyl sulfate (SDDS)-aided grinding, and the lowest Si value was 0.26 min−1 for dry grinding of the −600+425 feed in the mill. The γc values for calcite were obtained as 34.0–34.9 mN/m for SDDS-treated calcite surfaces, 29.9–31.4 mN/m for sodium oleate-treated surfaces and >72 mN/m for both dry and wet ground products whose surfaces were not treated chemically. Some correlations were established between the Si and γc parameters; as the Si increases, γc decreases, indicating that relatively more hydrophobic surfaces are broken faster for the largest sizes, resulting in higher Si values with more fines (lower γ of Bi, j) in the finer size distribution region (i.e. −150 μm).

Abstract: A mathematical model has been developed to describe the size and settling rate of aggregates formed by flocculation in thickeners/clarifiers used in the mineral processing industry. The aggregation process was simulated with a population balance model, which calculates the aggregate size distribution through time as a function of the competing processes of aggregation and breakage. The population balance was written specifically to describe aggregation by high molecular weight polymer flocculants that have now largely replaced coagulant salts in mineral processing operations, and the model includes terms to describe flocculant/slurry mixing and irreversible aggregate breakage (Table 1). The model was written to form part of a full computational fluid dynamics (CFD) model of a thickener/clarifier, allowing the eventual simulation and optimisation of the full-scale unit. In addition to the effects of fluid shear and residence time normally described by population balance models, additional process variables have been considered, with the model correctly accounting for changes in the flocculant dosage, primary particle size and solid fraction. The model has also been extended to describe the hindered settling rate under the same range of conditions, considerably increasing its usefulness by forming a link between the aggregation kinetics in the feedwell and the subsequent setting rate as the aggregates enter the settling zone of the thickener. The model was fitted to experimental data from a turbulent pipe reactor. A variety of pipe sizes, lengths, and flow rates were used to give a range of fluid shear rates and mean residence times, with the aggregate size distribution measured by an on-line sizing probe placed at the end of the pipe, immediately before a settling column. Experimental data was collected under a sparse matrix of experimental conditions, with the fluid shear rate (G), flocculant dosage (θf), primary particle size (dp) and solid fraction (φ) varied independently away from a common baseline. Additional data was collected from conditions in the gaps of the experimental matrix, and was used to check the predictivity of the model. The population balance model is based on the discretised balance by Hounslow et al. (1988) and Spicer and Pratsinis (1996), in this case using 35 channels covering the size 4 range: 0.2-3500 μm. The aggregation rate is described by Saffman and Turner’s (1956) turbulent collision kernel, used in conjunction with a capture efficiency term. The capture efficiency is initially taken to be zero (no successful collisions) before flocculant addition, but increases to unity (all collisions successful) as described by a flocculant-suspension mixing term. The breakage rate is described as a function of the aggregate size, energy dissipation rate, suspension viscosity and effective flocculant surface coverage. The effective flocculant coverage is taken to decrease through time, reflecting the loss of flocculant activity caused by repeated aggregation/breakage. Aggregate porosity is also included, using fractal geometry, and is used to calculate the aggregate capture radius and effective suspension solid volume fraction. The solid volume fraction is used to determine the suspension viscosity, accounting for experimental data showing the pressure drop in the pipe is a function of the aggregate size. The model equations were solved numerically as an initial value problem with a commercial dynamic simulation package (gPROMS), which was also used to estimate the unknown model parameters. The model was found to be robust and stable, and gave good predictions of the additional experimental data sets. The extension of the model to also describe the hindered settling rate allowed a dynamic optimisation to give the maximum settling flux, and hence unit throughput. Various optimisation strategies were investigated, in particular the use of recycle to find the optimal feed solid fraction. The inclusion of the model within a full CFD simulation will allow further optimisation strategies to be investigated, in particular changes to the feedwell geometry to give good mixing but without subjecting fully formed aggregates to regions of destructive high fluid shear.

Abstract: PROBLEM TO BE SOLVED: To facilitate the prediction of breakage and collapse of ground and enhance the reliability of the prediction. SOLUTION: Two or more profile lines differed in length are set in a prediction subject area GA where the ground is predicted to be unstable, electrodes 1 are set on both sides thereof, and the ground potential difference is measured between the electrodes 1 and 1, respectively. The measured ground potential difference data are recorded every fixed time by a data logger 2, and transmitted to a personal computer 7 set in an observation station or the like through a data transmitting means 3, where necessary processing such as noise removal or the like is performed to evaluate a collapse or breakage precursory phenomenon of the ground of the area GA.

Abstract: PROBLEM TO BE SOLVED: To provide a process for highly precise estimation of the surface strength of coke SOLUTION: In a process for estimating the surface breakage strength of coke from the characteristics of coal, a degree of void filling at the softening of charcoals defined by the formula: degree of void filling at the softening of coal (-) = specific volume at the softening of coal (cm3/g) × bulk density of charcoals when charged in the coke oven (g/cm3), and the relationship between the degree of void filling at the softening of coal and the surface breakage strength of the coke are determined Subsequently, the surface breakage strength of the coke is estimated from the specific volume of the coal to be used at the softening of coal and the bulk density of coal when charged in the coke oven

Abstract: monitoring of technological processes in electrometallurgy, possibly in aluminum production, namely testing of state of aluminum cell hearth at operation. SUBSTANCE: method comprises steps of measuring with use of instruments physical parameters of construction members of hearth for detecting zones of local breakage according to fluctuation of those parameters relative to standard values of production process; measuring electric current load of all cathode rods and determining zones and degree of hearth breakage according to value of decreasing electric current load from standard one for cathode rod or group of cathode rods; measuring in addition temperature of all cathode rods for more accurately defining zones and degree of hearth breakage according to lowered temperature of cathode rod or group of cathode rods relative to standard value of technological process. EFFECT: lowered consumption of materials and labor for liquidation of hearth breakage and for preventing aluminum cell failure. 2 cl, 1 dwg, 1 tbl