The purpose of this work is to study the effects of boundaries on granular flows down vibrating inclines, on segregation in granular mixtures induced by boundary vibrations, and on flows of granular mixtures through vibrating sieves. In each case, we employ techniques borrowed from the kinetic theory to derive an appropriate set of boundary conditions, and combine them with existing flow theories to calculate the profiles of solid volume fraction, mean velocity, and granular temperature throughout the flows. The boundaries vibrate with full three-dimensional anisotropy in a manner that can be related to their amplitudes, frequencies, and phase angles in three independent directions. At impenetrable surfaces (such as those on the inclines), the conditions derived ensure that momentum and energy are each balanced at the boundary. At penetrable surfaces (such as sieves), the conditions also ensure that mass is balanced at the boundary. In these cases, the momentum and energy balances also are modified to account for particle transport through the boundary. Particular interest in all the applications considered here is in how the details of the boundary geometry and the nature of its vibratory motion affect the resulting flows. In one case, we derive conditions that apply to a monosized granular material that interacts with a bumpy, vibrating, impenetrable boundary, and predict how such boundaries affect steady, fully developed unconfined inclined flows. Results indicate that the flows can be significantly enhanced by increasing the total energy of vibration and are more effectively enhanced by normal vibration than by tangential vibration. Regardless of the direction of vibration, the bumpiness of the boundary has a profound effect on the flows. In a second case, we derive conditions that apply to a binary granular mixture that interacts with a flat, vibrating, penetrable sieve-like boundary, and predict how such boundaries affect the process in which the particles pass through the sieve. In the special case in which the particles are all the same size, the results make clear that energy is more effectively transmitted to the assemblies when either the total vibrational energy or the normal component of the vibrational energy is increased, but that an increase in the energy transferred to the material can sometimes actually decrease the flow rates through the sieve. Consequently, at any instant of time in the sieving process, there is an optimum level of vibrational energy that will maximize the flow rate. For the sieving of binary granular assemblies, the physics associated with the effects of energy transfer on the flow rates still applies. However, in these cases, the flows through the sieve are also profoundly affected by segregation that occurs while the particles reside on sieve before the pass through. For this reason, we also isolate the segregation process from the sieving process by considering the special case in which the holes in the vibrating sieve are too small to allow any particles to pass through. In this case, the results show that under most circumstances the region immediately adjacent to the vibrating surface will be populated almost entirely by the smaller particles or by the more dissipative particles if there is no size disparity, and that the reverse is true in a second region above the first.

As ligas de alumínio hipereutéticas fundidas por centrifugação apresentam a possibilidade de obtenção de um gradiente funcional de propriedades no material (Functionally Graded Material - FGM). Na fundição por centrifugação, os compostos menos densos tenderão a se concentrar no diâmetro interno de um tubo centrifugado. Como a massa específica do silício e do Mg2Si são menores do que a do alumínio, as partículas dessas fases tendem a concentrar-se na parede interna de tubos centrifugados. Em função disto, este estudo tem como objetivo dar uma contribuição ao entendimento dos mecanismos de migração das partículas de silício e de Mg2Si numa liga de alumínio hipereutética com 19% de silício e com adições de cobre e magnésio fundidas por centrifugação. Diante disto, foram obtidos tubos da liga Al-19%Si com adições de até 5% de cobre e 5% de magnésio por meio da fundição centrífuga numa rotação de 1700 rpm. A caracterização microestrutural em diversas regiões dos tubos centrifugados foi feita utilizando-se a microscopia óptica e eletrônica de varredura com sistema de análise de imagens. A fração das fases presentes e a dureza Vickers foram determinadas ao longo da parede do tubo em diversas posições de vazamento. A fundição centrífuga promove a segregação de partículas de silício primário e de Mg2Si, com massas específicas menores para a parede interna do tubo. Esta segregação é mais acentuada na região final de vazamento devido ao maior tempo de centrifugação até a solidificação. Uma retenção de partículas junto à parede externa do tubo ocorre em decorrência da mais elevada taxa de resfriamento da liga fundida em contato com a parede do molde mais frio. Esta retenção também foi maior na região do tubo de início de vazamento em relação à de final de vazamento. A adição de cobre intensificou a migração das partículas devido ao aumento da densidade do líquido. O aumento do teor de cobre na liga também inibiu a presença de dendritas de alumínio primário que ocorrem em grandes quantidades nas regiões centrais das paredes dos tubos centrifugados. O perfil de dureza ao longo da parede do tubo indicou um aumento de dureza relacionado diretamente à quantidade de partículas de silício (β) e Mg2Si. / A functionally gradient material, in terms of its properties, can be obtained with centrifugally cast hypereutectic aluminum alloys. In centrifugal casting, the less dense compounds tend to concentrate close to the inner wall of a centrifugally cast tube. Since the specific mass of silicon and Mg2Si are less than that of aluminum, particles of these phases tend to concentrate at the inner walls of centrifugally cast tubes. On the basis of this, the aim of this study was to contribute towards increased understanding of the mechanism of segregation of silicon and Mg2Si particles in a centrifugally cast hypereutectic aluminum - 19% silicon alloy to which copper and magnesium were added. Hence, tubes of Al-19%Si alloy with up to 5% copper and up to 5% magnesium were centrifugally cast at rotational speed of 1700 rpm. Microstructural examination of various regions of the centrifugally cast tubes was carried out using an optical microscope and a scanning electron microscope coupled to an image analyzer. The amount of phases that formed and the Vickers hardness were determined across the thickness of the tube at different positions. Centrifugal casting promotes segregation of primary silicon and Mg2Si particles, (with lower specific weights) towards the inner walls of the tube. This segregation was higher at regions that were last to be cast, and due to longer centrifugation until solidification. Retention of particles close to the outer wall of the tube took place due to higher cooling rate of the cast alloy in contact with the cold walls of the mold. This retention was also higher at regions of the tube that were cast first compared with those that were cast last. The addition of copper increased particle migration due to increase in density of the liquid. Increase in the amount of copper in the alloy also inhibited the presence of primary aluminum dendrites that form in large quantities at the central regions of centrifugally cast tube walls. The hardness profile along the tube wall indicated an increase in hardness and this is directly related to the quantity of (β) silicon and Mg2Si particles.

As ligas de alumínio hipereutéticas fundidas por centrifugação apresentam a possibilidade de obtenção de um gradiente funcional de propriedades no material (Functionally Graded Material - FGM). Na fundição por centrifugação, os compostos menos densos tenderão a se concentrar no diâmetro interno de um tubo centrifugado. Como a massa específica do silício e do Mg2Si são menores do que a do alumínio, as partículas dessas fases tendem a concentrar-se na parede interna de tubos centrifugados. Em função disto, este estudo tem como objetivo dar uma contribuição ao entendimento dos mecanismos de migração das partículas de silício e de Mg2Si numa liga de alumínio hipereutética com 19% de silício e com adições de cobre e magnésio fundidas por centrifugação. Diante disto, foram obtidos tubos da liga Al-19%Si com adições de até 5% de cobre e 5% de magnésio por meio da fundição centrífuga numa rotação de 1700 rpm. A caracterização microestrutural em diversas regiões dos tubos centrifugados foi feita utilizando-se a microscopia óptica e eletrônica de varredura com sistema de análise de imagens. A fração das fases presentes e a dureza Vickers foram determinadas ao longo da parede do tubo em diversas posições de vazamento. A fundição centrífuga promove a segregação de partículas de silício primário e de Mg2Si, com massas específicas menores para a parede interna do tubo. Esta segregação é mais acentuada na região final de vazamento devido ao maior tempo de centrifugação até a solidificação. Uma retenção de partículas junto à parede externa do tubo ocorre em decorrência da mais elevada taxa de resfriamento da liga fundida em contato com a parede do molde mais frio. Esta retenção também foi maior na região do tubo de início de vazamento em relação à de final de vazamento. A adição de cobre intensificou a migração das partículas devido ao aumento da densidade do líquido. O aumento do teor de cobre na liga também inibiu a presença de dendritas de alumínio primário que ocorrem em grandes quantidades nas regiões centrais das paredes dos tubos centrifugados. O perfil de dureza ao longo da parede do tubo indicou um aumento de dureza relacionado diretamente à quantidade de partículas de silício (β) e Mg2Si. / A functionally gradient material, in terms of its properties, can be obtained with centrifugally cast hypereutectic aluminum alloys. In centrifugal casting, the less dense compounds tend to concentrate close to the inner wall of a centrifugally cast tube. Since the specific mass of silicon and Mg2Si are less than that of aluminum, particles of these phases tend to concentrate at the inner walls of centrifugally cast tubes. On the basis of this, the aim of this study was to contribute towards increased understanding of the mechanism of segregation of silicon and Mg2Si particles in a centrifugally cast hypereutectic aluminum - 19% silicon alloy to which copper and magnesium were added. Hence, tubes of Al-19%Si alloy with up to 5% copper and up to 5% magnesium were centrifugally cast at rotational speed of 1700 rpm. Microstructural examination of various regions of the centrifugally cast tubes was carried out using an optical microscope and a scanning electron microscope coupled to an image analyzer. The amount of phases that formed and the Vickers hardness were determined across the thickness of the tube at different positions. Centrifugal casting promotes segregation of primary silicon and Mg2Si particles, (with lower specific weights) towards the inner walls of the tube. This segregation was higher at regions that were last to be cast, and due to longer centrifugation until solidification. Retention of particles close to the outer wall of the tube took place due to higher cooling rate of the cast alloy in contact with the cold walls of the mold. This retention was also higher at regions of the tube that were cast first compared with those that were cast last. The addition of copper increased particle migration due to increase in density of the liquid. Increase in the amount of copper in the alloy also inhibited the presence of primary aluminum dendrites that form in large quantities at the central regions of centrifugally cast tube walls. The hardness profile along the tube wall indicated an increase in hardness and this is directly related to the quantity of (β) silicon and Mg2Si particles.

Thickened tailings production and disposal continue to grow in importance in the mining industry. In particular, the transport of oil sands tailings is of interest in this study. These tailings must be in a homogeneous state (non-segregating) during pipeline flow and subsequent discharge. Tailings are often transported in an open channel or flume. Slurries containing both clay and coarse sand particles typically exhibit non-Newtonian rheological behaviour. The prediction of the flow behaviour of these slurries is complicated by the limited research activity in this area. As a result, the underlying mechanisms of solids transport in these slurries are not well understood. To address this deficiency, experimental studies were conducted with kaolin clay slurries containing coarse sand in an open circular channel.<p> A numerical model has been developed to predict the behaviour of coarse solid particles in laminar, open channel, non-Newtonian flows. The model involves the simultaneous solution of the Navier-Stokes equations and a scalar concentration equation describing the behaviour of coarse particles within the flow. The model uses the theory of shear-induced particle diffusion (Phillips et al., 1992) to provide a number of relationships to describe the diffusive flux of coarse particles within laminar flows. A sedimentation flux has been developed and incorporated into the Phillips et al. (1992) model to account for gravitational flux of particles within the flow. Previous researchers (Gillies et al., 1999) have shown that this is a significant mechanism of particle migration.<p> The momentum and concentration partial differential equations have been solved numerically by applying the finite volume method. The differential equations are non-linear, stiff and tightly coupled which requires a novel means of analysis. Specific no-flux, no-slip and no-shear boundary conditions have been applied to the channel walls and free surface to produce simulated velocity and concentration distributions. The results show that the model is capable of predicting coarse particle settling in laminar, non-Newtonian, open channel flows. The results of the numerical simulations have been compared to the experimental results obtained in this study, as well as the experimental results of previous studies in the literature.

Thickened tailings production and disposal continue to grow in importance in the mining industry. In particular, the transport of oil sands tailings is of interest in this study. These tailings must be in a homogeneous state (non-segregating) during pipeline flow and subsequent discharge. Tailings are often transported in an open channel or flume. Slurries containing both clay and coarse sand particles typically exhibit non-Newtonian rheological behaviour. The prediction of the flow behaviour of these slurries is complicated by the limited research activity in this area. As a result, the underlying mechanisms of solids transport in these slurries are not well understood. To address this deficiency, experimental studies were conducted with kaolin clay slurries containing coarse sand in an open circular channel.<p> A numerical model has been developed to predict the behaviour of coarse solid particles in laminar, open channel, non-Newtonian flows. The model involves the simultaneous solution of the Navier-Stokes equations and a scalar concentration equation describing the behaviour of coarse particles within the flow. The model uses the theory of shear-induced particle diffusion (Phillips et al., 1992) to provide a number of relationships to describe the diffusive flux of coarse particles within laminar flows. A sedimentation flux has been developed and incorporated into the Phillips et al. (1992) model to account for gravitational flux of particles within the flow. Previous researchers (Gillies et al., 1999) have shown that this is a significant mechanism of particle migration.<p> The momentum and concentration partial differential equations have been solved numerically by applying the finite volume method. The differential equations are non-linear, stiff and tightly coupled which requires a novel means of analysis. Specific no-flux, no-slip and no-shear boundary conditions have been applied to the channel walls and free surface to produce simulated velocity and concentration distributions. The results show that the model is capable of predicting coarse particle settling in laminar, non-Newtonian, open channel flows. The results of the numerical simulations have been compared to the experimental results obtained in this study, as well as the experimental results of previous studies in the literature.