The mixing of powders and liquids is a process ubiquitous to many industrial, research and household applications, from the production of foodstuffs, pharmaceutical and cosmetic products to the preparation of hot drinks or cement. The final mixed state of powders and liquids can be broadly split into two distinct regimes identified respectively as having low- and high volume fraction, ∅. Low-∅ systems are typified by flowing suspensions whereas samples prepared with high-∅, beyond some threshold value, produce solid agglomerates which are unable to flow. These two regimes are the focus of two separate scientific disciplines; suspension rheology and granulation. Within the field of suspension rheology there has been recent advances in the understanding of a phenomena known as shear thickening, which describes the increase in a suspension's viscosity with increasing applied stress. In this thesis we aim to unify the phenomena of shear thickening and granulation within this new theoretical framework. We study shear thickening and granulation using a well characterised model system developed for this purpose, comprising polydisperse glass particles with a mean diameter of ≃ 7 μm and a glycerol-water mixture (90:10 %vol). We measured the rheological behaviour as a function of applied stress, σ, of suspensions at various volume fractions. We observed shear thickening behaviour, with divergences in the low-stress viscosity, η1(∅), and the high-stress viscosity, η2(∅), at ∅RCP = 0:662 and ∅m = 0:572 respectively. These divergences mark the transition between continuous shear thickening, discontinuous shear thickening and a state in which flow is not possible, with increasing volume fraction. Using a recently developed theory of shear thickening (Wyart and Cates, 2014), we were able to fit our rheological data quantitatively. The WC theory predicts a stress-dependent crossover in the fraction of contacts which are frictional in nature, following a stretched exponential function. In order to improve numerical agreement between our data and the model, we developed a method taking into account the volume-weighted contribution of particle sizes in our polydisperse system. Bulk mixing of the same model system in a custom-built high-shear mixer also exhibited three different mixing regimes with the change in behaviour coinciding with the location of the viscosity divergences, ∅m and ∅RCP, measured in the rheology experiments. For ∅ < ∅m suspensions are formed at both high and low stress; for ∅ ≥ ∅RCP granules are formed at all stresses; for ∅m ≤ ∅ < ∅RCP transient granules are formed, which are solid at high stresses, but can relax to a flowing suspension state at low stress. This transient behaviour is reversible with the application of high stress. This coincidence of viscosity divergence in the rheology measurements and mixing behaviour change in the high-shear mixing strongly suggests that the two phenomena are related. Thus we used the stress-dependent jamming volume fraction, ∅J(σ), predicted by the WC theory, to define the transition between the formation of suspensions and granules. We were able to calculate a quantitative phase diagram, with which the regions of the ∅-σ phase space in which granules or suspensions are formed can be easily identified, in agreement with our high-shear mixer data. Thus, using small-scale rheological measurements, requiring relatively small volumes of sample, we are able to define the parameter space in which granules can be prepared, thus eliminating the need for trial and error granulation experiments in order to define this space. We measured the volume-weighted mean granule size as a function of ∅ in the range ∅m → ∅ ≃ 0:85. Based on our observations of granule structure and measurements of granule size distributions, we modelled the granules as an ensemble of core-shell agglomerates with a log-normal size distribution. The packing in the granule cores was assumed to be ∅J(σ ), i.e. ∅m at high stress and ∅RCP at low stress. Appealing to conservation of mass arguments, our model predicts that the mean granule size decreases with increasing volume fraction and stress, in quantitative agreement with experimental data.

Channelling and compression in batch and continuous gravity sedimentation systems have been investigated using an electrical impedance imaging technique. The accuracy of such a system is shown to be a function of a number of variables, in particular particle morphology. Not all materials were found to be suitable to this form of imaging. Three primary materials, aragonite, calcite and talc were used, each exhibited random channelling, i.e. channel formation was not due to the presence of foreign bodies or externally induced. Channels in this type of channelling form within a zone which grows and propagates upwards into a suspension. Through visual observations this region has been sub-divided into hard and soft zones. Superposition of zone propagation on characteristic (loci of concentration) plots has yielded information on the conditions required for channel formation and growth and has led to a revised set of conclusions on the nature of random channelling.

O espessamento é uma operação unitária que tem como finalidade separar, por diferença de massa específica entre o sólido e o líquido, sólidos suspensos em meio fluido, pela ação da gravidade. É bastante empregado industrialmente em processos contínuos no adensamento de polpas e minérios, em unidades com reação de precipitação e no tratamento de efluentes, dentre outros. Os equipamentos que realizam esta operação, chamados espessadores, são, em geral, tanques abertos de formato cilíndrico, instalados no eixo vertical com a entrada da suspensão na parte superior central, de fundo ligeiramente cônico para a retirada da polpa espessada e calha circulando o topo para descarga do líquido clarificado. As várias técnicas de projeto destas unidades contínuas são comumente baseadas em ensaios de bancada com provetas. Não é raro ocorrerem para os mesmos dados experimentais, áreas de projeto com desvios superiores a 50%. O presente trabalho visou verificar a validade das técnicas de seleção de TALMADGE-FITCH, ROBERTS e FLUXO DE SÓLIDOS, para o dimensionamento de espessadores industriais com salmoura e lodo biológico. Foram realizados para este fim, ensaios de espessamento em provetas com as próprias suspensões industriais, calculadas as áreas pelas técnicas supracitadas e comparadas com os resultados das secções dos equipamentos contínuos industriais. Os desvios médios dos diâmetros para cada técnica em relação ao espessadores industriais apresentaram contra a segurança dos equipamentos um valor de 42% para o método de Talmadge-Fitch, 45,5% para Roberts e 43,5% para o método do Fluxo de sólidos. Concluiu-se, para as condições estudadas, que os métodos de provetas utilizados forneceram valores na mesma ordem de grandeza e que requerem um fator de escala para o dimensionamento das unidades industriais contínuas. / Thickening is a unit operation that has the goal of solid-liquid separation. The principle of this separation is the difference of specific weight between solid and liquid. This unit operation is used in mineral industries, to ore concentrate, wastewater, and others. The tanks called thickeners are usually open, with the feed on the top of the equipment. The solids discharge is done trough the bottom in a conical shape. The most techniques of sizing thickeners are based on graduated cylinders, and it is a common get result that has a difference area in about 50%. This happens because security coefficient, difficulties for results interpretation and scales factors. This research has the goal to apply the techniques of selection of Solids Flux, Roberts and Talmadge-Fitch in graduated cylinders. These methods are classical for thickener sizing. A comparison has been made between the results by those methods with the data obtained from continuous industrial units for salt solution and biological brine. The shunting line for the techniques obtained was 42% for Talmadge-Fitch, 45,5% for Roberts and 43,5% for Solid Flux in the relationship with industrial thickeners. In conclusion, for the studied condition, all methods showed values in the same order and requires a scale factors to sizing the continuous thickeners.

Abstract In order to improve the optimisation of mineral processing operations the rheological properties of slurries must be determined as accurately as possible under the conditions that closely resemble actual site conditions. The rheology of particles suspended in Newtonian fluids is well documented. However, the rheology of particles in non-Newtonian fluids has not been the subject of much investigation till now. The work conducted here attempts to fill this gap in knowledge. The rheological properties of slurries are heavily dependent on the solids concentrations and particle-solid interaction. At low solids concentrations, constant viscosity and Newtonian behaviour is observed, but as solids concentration increases the rheological behaviour becomes increasingly complex and non-Newtonian with viscosity becoming dependent on the shear rate. The nature of the non-Newtonian behaviour depends on the solid concentration, particle shape, particle size, particle size distribution and the suspending liquid rheological properties. The suspension/slurry may develop a yield stress and become time dependent in nature as structures develop within the fluid at higher solids concentrations. This study however, is primarily focused on the measurement of the rheological properties, where it is assumed that the fluid will be fully sheared and that the rheological properties will be unlikely to change with time. Shear thickening behaviour of slurries was the focus of this work. The aim was to investigate the slurry concentration region where shear thickening occurs. The first objective of the project was to develop a fluid analogue which will have similar rheological behaviour to that of concentrated tailings from gold mines so that it can be used as a test material to simulate the flow behaviour of the tailings in a pipe. The second objective of this project was to enable the prediction of flow behaviour in the pipe loop under certain conditions using the fluid analogue for slurry from Sunrise dam. In order to achieve the objectives, experiments were carried out to obtain a fluid analogue of a shear thickening slurry. CSL 500 and SR 200 rheometers were used for the characterisation of different fluid analogues and shear thickening mineral slurries. Malvern Sizer, model: mastersizerX v1.1, was used to obtain particle size distributions. A mini pipe loop system, located in the laboratory of the Rheology and Materials Processing Centre (RMPC) was used to get pipe line flow data for comparison with the rheometer data. A few fluid analogues with different suspending medium and different concentrations of glass spheres was tested before finally using, 48 vol% glass spheres in 1.8 wt% CMC solution as a fluid analogue for the mineral tailings obtained from Sunrise dam, WA. For comparison between the pipe line and rheometer data, all pipe line data (in the form of 8V/D) were converted to rheometer data (in the form of du/dr) using the Robinowitsch-Mooney equation. The above comparison indicated that it is possible to produce fluid analogue to simulate the flow behaviour of Sunrise dam slurry using a shear thinning suspending medium with high concentration of glass particles. Shear thickening flow behaviour was clearly observed in the rheometer while it was less predominant in a pipe line flow.

O espessamento é uma operação unitária que tem como finalidade separar, por diferença de massa específica entre o sólido e o líquido, sólidos suspensos em meio fluido, pela ação da gravidade. É bastante empregado industrialmente em processos contínuos no adensamento de polpas e minérios, em unidades com reação de precipitação e no tratamento de efluentes, dentre outros. Os equipamentos que realizam esta operação, chamados espessadores, são, em geral, tanques abertos de formato cilíndrico, instalados no eixo vertical com a entrada da suspensão na parte superior central, de fundo ligeiramente cônico para a retirada da polpa espessada e calha circulando o topo para descarga do líquido clarificado. As várias técnicas de projeto destas unidades contínuas são comumente baseadas em ensaios de bancada com provetas. Não é raro ocorrerem para os mesmos dados experimentais, áreas de projeto com desvios superiores a 50%. O presente trabalho visou verificar a validade das técnicas de seleção de TALMADGE-FITCH, ROBERTS e FLUXO DE SÓLIDOS, para o dimensionamento de espessadores industriais com salmoura e lodo biológico. Foram realizados para este fim, ensaios de espessamento em provetas com as próprias suspensões industriais, calculadas as áreas pelas técnicas supracitadas e comparadas com os resultados das secções dos equipamentos contínuos industriais. Os desvios médios dos diâmetros para cada técnica em relação ao espessadores industriais apresentaram contra a segurança dos equipamentos um valor de 42% para o método de Talmadge-Fitch, 45,5% para Roberts e 43,5% para o método do Fluxo de sólidos. Concluiu-se, para as condições estudadas, que os métodos de provetas utilizados forneceram valores na mesma ordem de grandeza e que requerem um fator de escala para o dimensionamento das unidades industriais contínuas. / Thickening is a unit operation that has the goal of solid-liquid separation. The principle of this separation is the difference of specific weight between solid and liquid. This unit operation is used in mineral industries, to ore concentrate, wastewater, and others. The tanks called thickeners are usually open, with the feed on the top of the equipment. The solids discharge is done trough the bottom in a conical shape. The most techniques of sizing thickeners are based on graduated cylinders, and it is a common get result that has a difference area in about 50%. This happens because security coefficient, difficulties for results interpretation and scales factors. This research has the goal to apply the techniques of selection of Solids Flux, Roberts and Talmadge-Fitch in graduated cylinders. These methods are classical for thickener sizing. A comparison has been made between the results by those methods with the data obtained from continuous industrial units for salt solution and biological brine. The shunting line for the techniques obtained was 42% for Talmadge-Fitch, 45,5% for Roberts and 43,5% for Solid Flux in the relationship with industrial thickeners. In conclusion, for the studied condition, all methods showed values in the same order and requires a scale factors to sizing the continuous thickeners.

The crystallization behavior of bisphenol-A polycarbonate (BAPC) was studied, focusing on the initial stage of crystallization and the secondary stage of crystallization. Bisphenol-A polycarbonate was the polymer chosen for this study because of its slow crystallization rate. With slow crystallization kinetics, the polymer morphology does not change when quenched below its glass transition temperature, enabling the study of different stages of crystallization through the frozen morphology. The study of the initial stages of crystallization pertained to crystallization times prior to the growth of detectable crystallinity. This study employed BAPC because of the long induction period, a direct result of the slow crystallization kinetics. During the induction period of polycarbonate crystallized at 190°C there was no evidence of polymer chain ordering that was seen in literature for other polymers. The length of the induction period determined by differential scanning calorimetry and wide-angle X-ray diffraction varied by over 6 hours because differential scanning calorimetry can detect a smaller amount of crystallinity than wide-angle X-ray diffraction. Signs of pre-ordering in the literature could be a result of experimental sensitivity. The study of the secondary crystallization dealt with the isothermal lamellar thickening of BAPC crystals during annealing, after crystallization for an extended period of time. Small-angle X-ray scattering and differential scanning calorimetry experiments were performed on bisphenol-A polycarbonate samples crystallized near 190°C for 8 days and annealed at either 223°C or 228°C for various times. The Gibbs-Thomson relationship, which can be defined using the experiments mentioned, yielded two thermodynamic constants, the equilibrium melting temperature and the surface free energy. Including data from literature in the determination of the constants, the equilibrium melting temperature and surface free energy of BAPC is 303°C and 36.6mJ/m2, respectively. Comparing the lamellar thickness measurements by small-angle X-ray diffraction with direct measurements by microscopy was difficult because the morphology of the polymer was not easily seen in the bulk using atomic force microscopy or scanning electron microscopy. Etching the sample was the most promising technique for future investigations of revealing the bulk morphology for direct lamellar thickness measurements. Crystallizing thin films of polycarbonate on calcite substrates allowed the measurement of lamellar thickness using scanning electron microscopy because the lamellae grow epitaxially to the substrate. The measurement of the long spacing in thin film samples was comparable to that of bulk samples. / Master of Science

The present study consists of the development of a MATLAB version of computer program (FORTRAN) developed by Papanicolaou (1992) to solve the governing small strain consolidation equation of second order non-linear transit partial differential equation of parabolic type. This program is modified to integrate the settling and consolidation processes together in order to provide continuous results from start to end of the process in a single run of MATLAB program. The study also proposes a method to calculate the batch curve by considering the variation of solids concentration in the suspension region. Instead of the graphical approach available in the literature, the program uses numerical approach (Newton-Raphson method) to calculate the solids concentration in suspension region at the interface of suspension and sedimentation regions. This method uses the empirical relationship between solids flux and solids concentration. The study also proposes a method to calculate the solids concentration, throughout the settling column, using the concept of characteristic. The present work also simulates the large strain consolidation model (Gutierrez, 2003). The results of present work closely match with the results of small strain model (Diplas & Papanicolaou, 1997) available in literature. / Master of Science

Transport properties of concentrated suspensions are of interest to many industries. Mineral slurries at higher solids concentrations have shown some rheologically interesting characteristics such as shear thickening, the increase of viscosity of a multi-phase mixture with increasing shear rate. The general literature on the rheology of suspensions records the presence of yield stresses, shear thinning and normal stress differences. Little is said specifically about shear thickening behaviour except for colloidal suspensions. The aim of this study is to examine the behaviour of coarse shear thickening suspensions and determine the causes of this phenomenon. The study intended to achieve the following objectives to; develop the appropriate techniques for rheometric studies of shear thickening suspensions; investigate the nature of particle-fluid interaction; develop a model of shear thickening behaviour as it occurs in non-colloidal suspensions and to develop a method of applying the rheology results to flows and flow geometries of practical relevance. The effects of wall slip dominate much of the literature of shear thickening materials. To investigate this aspect a significant portion of the experimental work examined the effect of shear thickening on torsional flow. The rheogram produced from parallel plate rheometry was reassessed as a non-controlled flow and a rheology model dependant analysis demonstrated that the effects of slip are considerably more problematic for shear thickening suspensions, particularly as wall slip is an increasing function of shear stress. As a consequence of the rheometric method described above it was observed that the rate of change of the first normal stress difference, N1, with shear rate changes as shear thickening commences for non-colloidal suspensions. N1 is initially negative and is increasingly negative at low shear rates. Additional rheometric analysis examined the transient effects in the behaviour of a non-colloidal shear thickening suspension. By employing large angle oscillating strain tests the strain required to initiate a shear thickening response was determined. Coherent back scattering of laser light experiments were able to show the change in orientation of the particles with respect to its rotation around the vorticity axis. After a viscosity minimum was reached the orientation became more random as particle rotation and lamina disruption occurred. This was considered to be the cause of the measured shear thickening. A model of shear thickening in concentrated, non-colloidal suspensions of non-spherical particles was developed. Based on hydrodynamic interaction in the Stokes flow regime, the flow of interstitial fluid subjected the adjacent particles to lubricating and Couette type forces, acting as a couple. When a series of force balances on a particle contained between two moving laminae are conducted as a time sequence, the particle orientation and motion can be observed. The model has qualitative agreement with several aspects of the experimentally observed behaviour of shear thickening suspensions, such as viscosity change with shear rate and concentration, and the first normal stress difference increasing with shear rate. Pipe line flow experiments were conducted on the model suspension. Particle settling produces unusual patterns in shear thickening suspensions, with an annulus of delayed settling near the wall.

No description available.

A particulate suspension under shear is a classic example of a system driven out of equilibrium. While it is possible to predict the equilibrium phase behaviour of a quiescent suspension, linking microscopic details to bulk properties under flow remains an open challenge. Our current understanding of sheared suspensions is restricted to two disparate regimes, the colloidal regime, for particle sizes d < 1 μm and the granular regime, for d > 50 μm. The physics of the industrially-relevant intermediate size regime, 1 μm ≲ d ≲ 50 μm, is unclear and has not been explored previously. In this thesis, we use conventional rheometry on a range of model spheres to develop the foundations of a predictive understanding of suspension flow across the entire size spectrum. In the first part of the thesis, we show that in repulsive particulate systems the rheology is characterised by two viscosity "branches" diverging at different volume fractions φRCP and φm, which represent states of flow with lubricated (frictionless) and frictional interactions between particles. In the intermediate size regime, there is a transition between these two branches above a critical onset stress σ* which manifests as shear thickening. This σ* is related to a barrier (invariably due to the charge or steric stabilisation) keeping particle surfaces apart. Our data are quantitatively fit by the Wyart and Cates theory for frictional thickening [1] if we assume that probability distribution of forces in the system is similar to in dry granular media. The onset stress for shear thickening is found to decrease with the inverse square of the particle size σ* / d ̄ 2 for diverse systems. We show that it is the competition between the scaling of σ*(d) and the size dependence of the entropic stress scale (~ d ̄ 3) that controls the crossover from colloidal to granular rheology with increasing size. Granular systems are "always shear thickened" under typical experimental conditions, while colloidal systems are always in a frictionless state. In the second part of the thesis, we explore the validity of the frictional framework for shear thickening. Although it quantitatively predicts our steady-state rheology, the frictional framework contradicts traditional fluid-mechanical thinking and has yet to be rigorously tested experimentally. In fact, there is a large body of literature that attributes thickening to purely hydrodynamic effects. Using dimensional analysis and simple physical arguments we examine possible physical origins for thickening and show that previously-proposed mechanisms can be subdivided into three types: two-particle hydrodynamic thickening, many-particle hydrodynamic thickening ("hydroclusters") and frictional-contact driven thickening. Many of these mechanisms can are inconsistent with the experimental two-branch phenomenology and can be disregarded. We further narrow down possible causes of thickening using the technique of flow reversal, which disentangles the relative contributions of contact and hydrodynamic forces to the viscosity. Consistent with recent simulations [2] and theory [1], we find that in each case thickening is dominated by the formation of frictional contacts and that hydrodynamic thickening, if present, is subdominant.