Abstract: Granular materials forming part of embankments, foundations and pavement structures are subjected to both static and dynamic loads. As a result, total or partial particle breakage occurs. Particle breakage causes settlements and a reduction in hydraulic conductivity (Fragaszy & Voss, 1986). Previous research has indicated that granular materials undergoing crushing exhibit a non-linear Mohr-Coulomb failure envelope if the envelope is constructed with the peak values of shear resistance. Therefore the angle of shearing resistance decreases as a consequence of particle crushing (Bolton, 1986; Feda, 2002). On the other hand, recent ring shear tests on carbonate sand presented by Coop et al. (2004) showed crushing without loss of residual angle of internal friction. It seems that crushable granular materials experience a reduction in the internal friction angle as a consequence of particle breakage prior to achieving a constant value of residual strength. The main focus of this study is to understand and produce a visualisation of the evolution of crushing in a weak granular material subjected to a direct shear test. The results from direct shear tests conducted on sugar, and a computer simulation using the discrete element method, are presented. (A)

Abstract: The objective of this paper is to investigate the predictability of the warp breakage rate from a sizing yarn quality index using a feed-forward back-propagation network in an artificial neural network system. In order to achieve the objective, a series of trials is conducted. An eight-quality index (size add-on, abrasion resistance, abrasion resistance irregularity, hairiness beyond 3 mm, breaking strength, breaking strength irregularity, breaking elongation, and breaking elongation irregularity) and warp breakage rates are rated in controlled conditions. A good correlation between predicted and actual warp breakage rates indicates that warp breakage rates can be predicted by neural networks. A model with a single sigmoid hidden layer with four neurons is able to produce better predictions than the other models of this particular data set in the study.

Abstract: An experimental and computational investigation of the effects of local fluid shear rate on the aggregation and breakage of approximately 10 microm latex spheres suspended in an aqueous solution undergoing turbulent Taylor-Couette flow was carried out. First, computational fluid dynamics (CFD) simulations were performed and the flow field predictions were validated with data from particle image velocimetry experiments. Subsequently, the quadrature method of moments (QMOM) was implemented into the CFD code to obtain predictions for mean particle size that account for the effects of local shear rate on the aggregation and breakage. These predictions were then compared with experimental data for latex sphere aggregates (using an in situ optical imaging method). Excellent agreement between the CFD-QMOM and experimental results was observed for two Reynolds numbers in the turbulent-flow regime.

Abstract: The emulsification of dodecane oil was studied in a standard stirred vessel filled with distilled water. The in situ size distribution of the drops was measured at certain time intervals by using a particle size analyzer while stirring. The results showed that an increase in the stirring time and stirring rate resulted in a decrease in the mean drop size of drops and shifted the drop size distribution toward smaller sizes. The minimum droplet size in the turbulent flow was found to be proportional to amin∼(WD)−1.75. Normalization of data exhibited that the size distribution of drops is self‐preserving. The distribution of mean drop size and distribution functions of drops were determined by using models developed from the Focker‐Plank equation regarding size distribution of particles in turbulent flows. The evaluation of droplet breakage with time in isotropic turbulent flow showed that the size distribution can be represented by the summation of log‐normal distribution function in series. It was found th...

Abstract: Through experimental results on the compaction breakage of loose rock blocks,some breaking laws are obtained. The results show that the majority of blocks are broken before the relative load reaches 0.5 or 0.6 compared to unixial compressive strength. When the stress exceeds such level,the broken rate of blocks is very small. Therefore,the grading of granular tends to keep constant even if the exerted load is increased. For soft rock, e.g.,coal,the ultimate fine particles have a greater percentage. However,for hard rock,e.g.,sand stone,the difference of ingredient of each class of particle is not apparent. For rock blocks with different strengths,the curves of grading of granular have strong similarity and relativity and can be described by polynomial.

Abstract: In this paper, the degree of breakage of glass filament yarns during the weft knitting process is studied. A quantitative method used for assessing the degree of glass filament breakage is proposed, and the effects of different factors such as cam setting, knitted structures and yarn parameters are analysed. The experimental results show that an optimum cam setting exists at which the degree of filament breakage is minimum.

Abstract: It is well known that the fragmentation equation admits self-similar solutions for evolving particle-size distributions (PSD); i.e., if the shape of PSD is independent of time after an initial transient period. Although an analytical derivations of the self-similar PSD cases have been studied extensively, results for cases requiring numerical solutions are rare. The aim of the present work is to fill this gap for the case of homogeneous breakage functions. The known analytical and approximate solutions for the self-similar PSD are reviewed and a general algorithm for the numerical solution is proposed. Results for a broad range of breakage functions (kernel and rate) are presented. Further, the work is focused on the sensitivity of the relation between self-similar PSD and breakage kernel and its influence on the inverse breakage problem, i.e., that of estimating the breakage kernel from experimental self-similar PSDs. Useful suggestions are made for tackling the inverse problem.

Abstract: The population balance equation for the evolution of drop size distributions in fully developed turbulent flow of a liquid−liquid dispersion in a circular pipe has been solved “exactly” using spectral expansion of the self-adjoint diffusion operator with a radially varying diffusion coefficient to obtain the number density at any location in the pipe. The breakage frequency is allowed to vary with position, although the size distribution of broken fragments is assumed to satisfy a form of similarity assumed in the work of Narsimhan et al. (AIChE J. 1980, 26, 991; 1984, 30, 457) that rids it of explicit spatial dependence. Of course, insofar as numerical methods are used to calculate the spectral data (eigenvalues and eigenvectors), such an exact solution is still to be regarded as approximate. Furthermore, because the solution is expressed in terms of a transient well-mixed batch dispersion evolving by breakage, the actual number density may be obtained by any of the methods for solving population balance...

Abstract: This paper presents the breakage behavior of a zeolite granulate in compression tests. The compression behavior of this granulate is described by means of a force-displacement curve, the application of Hertz-Huber contact theory, and continuum mechanics. The effects of granulate size and stressing velocity on the breakage force and contact stiffness during elastic and elastic-plastic deformation are examined. It is shown that the zeolite granulates with elastic-plastic behavior have viscous properties as well. The breakage probability is approximated by the Weibull distribution function. The behavior of the granulates during compression under conditions of repeated loading-unloading was investigated.

Abstract: The strength of coal is usually determined by the tumbler tests and shatter tests. The strength index is an empirical and its numerical value cannot be used to predict the extent of breakage in a bulk handling circuit. A new drop test procedure has been developed to measure the strength of the coal based on the extent of the breakage due to repeatedly drop from a predetermined height. The lump size coal breaks in the tumbler drum by volume breakage and surface breakage; the extent of one affects the extent of other. Tumbler index is not directly related to any fundamental material property but depends on the number of lifters in the drum and material parameters, which include particle size and strength. The rate of degradation is higher on larger lump sizes coal compare to smaller lump size. At small drop heights, the stress of impact experienced by the sample sizes is comparatively smaller and resulting in a much lower extend of volume breakage and increase the significant of surface breakage.

Abstract: Using a kinetic approach to the breakage of solids, a two-stage model of breakage is constructed. The model is invariant for objects of various scale. A physical approach to forecasting the final stage of macroscopic breakage is developed. The applicability of the methods devised is tested on laboratory samples, industrial constructions, and large-scale objects.

Abstract: The general binary breakage problem with power-law breakage functions and two families of symmetric and asymmetric breakage kernels is studied in this work. A useful transformation leads to an equation that predicts self-similar solutions in its asymptotic limit and offers explicit knowledge of the mean size and particle density at each point in dimensionless time. A novel moving boundary algorithm in the transformed coordinate system is developed, allowing the accurate prediction of the full transient behaviour of the system from the initial condition up to the point where self-similarity is achieved, and beyond if necessary. The numerical algorithm is very rapid and its results are in excellent agreement with known analytical solutions. In the case of the symmetric breakage kernels only unimodal, self-similar number density functions are obtained asymptotically for all parameter values and independent of the initial conditions, while in the case of asymmetric breakage kernels, bimodality appears for high degrees of asymmetry and sharp breakage functions. For symmetric and discrete breakage kernels, self-similarity is not achieved. The solution exhibits sustained oscillations with amplitude that depends on the initial condition and the sharpness of the breakage mechanism, while the period is always fixed and equal to ln 2 with respect to dimensionless time.

Abstract: Aeration experiments were conducted for a gelatin solution and a food emulsion. The change in the overrun (the amount of air incorporated into the continuous medium) was monitored, and the bubble size distribution was measured using the advanced image analysis technique for various stages of the aeration process. The aeration process consists of two regimes: the incorporation of large bubbles into the continuous medium and the breakage of the incorporated bubbles. The bubble dynamics during the aeration process were modeled using the population balance equation. The breakage frequency and coalescence rate (which is required to solve the population balance equation) are obtained from the modification of the formula derived by Vennerkar et al. (AIChE J. 2002, 48, 673). The sizes of the broken bubbles (daughter bubbles) are calculated with consideration of the breakage of the bubbles inside the aerating vessel as a result of the Rayleigh−Taylor instability phenomenon. The energy consumption rate, which is t...

Abstract: There is anecdotal experience which suggests that rocks get softer or damaged as a result of incremental impacts even if they do not appear to break. This thesis aims to develop an understanding of the incremental damage caused in rocks after multiple impacts. It is believed that after a non-breakage impact event that the energy imparted on the particle is not wasted, but causes internal fracture and crack propagation, thus weakening the particle. Despite this however, it is suggested that there is a minimum energy for each particle below which no damage at all will occur. A literature review of breakage mechanisms, multiple impact testing and abrasion mill testing is presented. Based on the findings of the literature review the following hypotheses were determined. After impact cumulative damage occurs to rock particles even though they may not appear to be ‘broken’. This is due to internal stresses and crack lengthening. It is believed that by conducting test work with the JK Drop Weight tester that cumulative damage in rock particles can be modelled with respect to the effective comminution energy and progeny size. It is believed that the energy absorbed by a particle after a non-breakage impact event can be quantified using the Hopkinson Pressure Bar and that this will help to explain the cumulative damage occurring from multiple impacts. The rate of abrasion in a mill can be analysed based on testwork in a laboratory sized abrasion mill. The specific rate of abrasion combined with mill power can be used to design large scale mills for a particular ore. The data from laboratory mill tests can be used with discrete element modelling combined with the results from the multiple impact testwork to analyse impacting efficiencies in the mills. The drop weight tester will be used to produce energy and product size distribution data for particles that have been incrementally damaged with low energy impacts. The test will involve three size fractions being impacted with three different energies. The energies to be imparted will be 30%, 40% and 50% of the minimum energy to cause a breakage with one impact. This energy was determined to be 0.0804kWh/t. The Hopkinson pressure bar will be used to analyse the energy absorption of particles during these low energy impacts. The abrasion mill testwork was performed to determine the specific rate of grinding for different loading situations and to model the data in a discrete element model. One of the model outputs is the impact energies experienced by individual rocks in the mill. These values can be compared to the results of the impact testing with the drop weight. A model analysing the size-energy relationship with respect to low energy multiple impacts was successfully fitted to the experimental data. The model contains a parameter for the energy threshold below which no damage will occur to a particle as seen below; where the size distribution of the progeny is expressed as the percentage of the progeny particles less than ten percent of the original size by mass. The energy is expressed in kWh/t and the energy threshold is 0.016kWh/t. It was also shown that a parent rock particle size parameter should be included in the model, however applying this to the model was beyond the scope of thesis. An analysis of the energy required to break a particle to a specific size distribution with respect to single and multiple impacting was performed. It was determined that using low energy multiple impacting is less energy efficient than using a higher energy single breakage impact to achieve the same progeny size. This is in part explained by the increased loss of energy repeatedly required to overcome the energy threshold with each hit in multiple impact testing. If this becomes understood further then industrial applications could follow by applying the knowledge to a milling environment. The Loveday grinding mill was used to perform tests with three different mill loadings. The mass of each pebble was recorded before and after each test and the progeny flowing out of the mill was collected in two minute intervals. The data obtained from this test was used to determine the specific rate of mass loss as well as the mill power for the different conditions. The progeny sizings can be used for comparison with the drop weight test abrasion data produced from the single impact testing. The data produced by the mill will be used in a discrete element model which has the capabilities of determining the impact energy history of every pebble in the mill. This model was not available prior to the completion of this thesis, however, the data will be used and the impact energies on the pebble will be compared to the results from the multiple impact testing. This will analyse how efficient the rock breakage was in the mill for the three tests. The major outcome of this thesis was the creation of a model of the multiple impact breakage with respect to progeny size and effective comminution energy. It was also shown that single breakage impacting is more energy efficient than multiple impacting for a given progeny size distribution. In order to learn more about impact breakage energy efficiency it is recommended that in the future more work be conducted in this area of research particularly with different ore types.

Abstract: The particle size distribution of fine chemicals in the solid state, like active pharmaceutical ingredients, is often a critical parameter. To achieve the desired particle size distribution, milling of such materials is usually the method of choice. Since these chemicals are often scarcely available, experimental optimization of milling is not possible. Therefore, a model to predict the milling conditions has been developed. The model estimates the rate of breakage function, and needs mechanical properties like hardness and yield strength as input to calculate the rate of breakage function. This paper attempts to check the validity of the model by a series of experiments. A comparison of the experimental results with the outcomes of the model using five different model compounds has been performed. It appears that the rate of breakage function can be estimated by: S-I 5.85 (+/- 1.78) 10(8) E-kin E-fract root P-V/rho/V H root x(i) K-1c . The model is able to rank the compounds by degree of fracture as an effect of milling. It was also possible to perform a quantitative prediction of the impact of milling pressure on the milling behavior. Finally, it appeared that the prediction of the large particles in the distribution was significantly better than small ones. Because the oversized material is usually the most critical parameter, the conclusion is that the model has acceptable practical applicability.