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The flow behaviour of liquid metals (Sn, Pb and Sn-Pb eutectic) under different shearing conditions is investigated. Experiments were performed with two designs of concentric cylinder viscometers: rotating the inner cylinder (Searle) and rotating the outer cylinder (Couette). The latter technique is uncommon and the equipment was optimised with standard oils. The flow behaviour for the metals differs in the two systems. The curves of 'apparent' viscosity versus shear rate may be divided into two regimes: I. At lower shear rates (<200 s-1): a reduction of 'apparent' viscosity with shear was observed with both viscometers. It is suggested that the high density and high surface tension of the metals and eccentricity between the cylinders at low shear rates, leads to instabilities. Results at low shear rates were therefore discarded and further detailed analysis would be required for a fuller understanding of this behaviour. II. At higher shear rates: a steady, shear-independent behaviour of 'apparent' viscosity with shear rate is observed in the Couette system (upto 600 s-1) whereas in the Searle system the 'apparent' viscosity increases with shear rate (upto 2600 s-1). From hydrodynamic theory about Newtonian fluids, it is suggested that in the Searle type viscometer, the fluid is unstable and Taylor vortices are expected at low shear rates (~80 s-1). This gives rise to an increase in the 'apparent' viscosity with shear rate. Whereas, in the Couette type, the flow is more stable, resulting in a steady 'apparent' viscosity. This interpretation is consistent with liquid metals behaving as Newtonian fluids, but further research is required to confirm this. The author suggests further experiments, with the prime one being the investigation of the fluid with counter and co-rotation of the cylinders in order to observe more complex flows. The results are expected to have implications in the modelling of flow for liquid metal processes, especially the initiation of Taylor vortices under the unstable flow conditions produced by rotating the inner cylinder.

Tailings (mining waste) disposal is a significant consideration for the mining industry, with the majority of the ore processed in most mining operations ending up as tailings. This creates large volumes of tailings, which must be handled and stored responsibly to avoid potential environmental catastrophes. The most common form of tailings storage facility is the impoundment, where tailings are contained within a basin, with beaches forming around the perimeter of the impoundment and a pond standing in the middle. A relatively new method of tailings storage is to create a 'stack', whereby the tailings solids form a large heap, with the discharge of tailings slurry from the apex of the heap. It is of significant value for mine operators and tailings engineers to be able to predict the shape of the beach that forms in either of these disposal scenarios. The key to being able to do this relies on a method of prediction of the beach slope. The aim of this work is to develop a method of tailings beach slope prediction for tailings slurries that are sub-aerially discharged from a pipe. In this thesis a literature review is undertaken, investigating existing methods for the prediction of tailings beach slopes. These methods are validated against relevant industrial and experimental data. Two separate phases of experimental work have taken place in an effort to investigate tailings deposition behaviour, one at mine sites and the other in a laboratory on a small scale. Three new tailings beach slope prediction models are presented; a simple empirical model enabling quick approximate predictions; an a priori tailings beach slope prediction model based on existing theories of open channel flow, sediment transport and rheology, which is more powerful due to the greater degree of theory in its foundation; and a new semi-empirical model that shares some of the theoretical aspects of the a priori model but offers better predictions due to its empirical calibration to the experimental data. The experimental results, along with 3 other independently collected sets of relevant industrial and experimental data, are used to validate the beach slope prediction models found in the literature, as well as the new beach slope models presented in this thesis. Statistical evaluation of the performance of all of these models is presented to enable comparison. Finally, a new beach shape model is presented for the three dimensional geometric forecasting of the beach surface of a tailings stack. Historic tailings discharge data is run through the beach shape model, and the shapes predicted by the model are compared with aerial survey data of a real tailings stack for validation of the shape model. This work not only presents a new method of tailings stack shape prediction, but also a plausible theory for explaining the concavity of tailings beaches. The stack shape model also has the potential to be developed further for the three dimensional modelling of tailings beaches formed in other types of storage facilities, such as impoundments or valleys.

The two-body problem consists of determining the motion of two gravitationally interacting bodies with given masses and initial velocities. The problem was first solved by Isaac Newton in 1687 using geometric arguments. In this thesis, we present selected parts of Newton's solution together with an alternative geometric solution by Richard Feynman and a modern solution using differential calculus. All three solutions rely on the three laws of Newton and treat the two bodies as point masses; they differ in their approach to the the three laws of Kepler and to the inverse-square force law. Whereas the geometric solutions aim to prove some of these laws, the modern solution provides a method for calculating the positions and velocities given their initial values. It is notable that Newton in his most famous work Principia, where the general law of gravity and the solution to the two-body problem are presented, used mathematics that is not widely studied today. One might ask if today's low emphasis on classical geometry and conic sections affects our understanding of classical mechanics and calculus.

Fluid dispensing is a method by which fluid materials are delivered to the targeted boards in a controlled manner and has been extensively applied in various packaging processes in the electronics assembly industry. In these processes, the flow rate of the fluid dispensed and/or the fluid amount transferred onto a board are two important performance indexes. Due to the involvement of the compressibility and non-Newtonian behaviour of the fluid being dispensed, modeling the fluid dispensing process has proven to be a challenging task. This thesis presents a study on the modeling of the positive displacement dispensing process, in which the linear displacement of a piston is used to dispense fluid. Also, this thesis presents an evaluation of different designs of the fluid dispensing system based on the axiomatic design principles. <p>At first, the characterization of the flow behaviour of fluids used in the electronic packaging industry is addressed. Based on the previous experiments conducted in the authors lab, a 3-parameter Carreau model for the fluid Hysol FP4451 is derived for use in the present study. Then, taking into account fluid compressibility and flow behaviour, a model is developed to represent the dynamics of the flow rate of the fluid dispensed. The resulting model suggests that the dynamics of the flow rate in the positive displacement dispensing process is equivalent to that of a second order system. Based on the model developed, the influences of the fluid compressibility and the process parameters such as the dispensing time and needle temperature are investigated by simulations. <p>In the positive dispensing process, it is noticed that the fluid amount dispensed out of needle is different from the fluid amount finally transferred to the board, if the fluid amount dispensed is very small. This difference is considered one major problem affecting dispensing performance. In order to determine the fluid amount transferred to the board, a 3-step method is developed in the present study, based on existing theories of liquid bridges and Laplaces equation. Simulations are conducted based on the developed method to study the influence of surface tension and initial fluid amount on the final fluid amount transferred onto the board. <p> Finally, this thesis presents a new approach to evaluate and compare different designs of the fluid dispensing system, namely air-pressure, rotary-crew, and positive- displacement. In this approach, the axiomatic design principles, i.e., the Independence Axiom and the Information Axiom, are employed. This approach can be used not only to evaluate existing dispensing systems, but also to design new dispensing systems.

Even though fluid mechanics is well developed as a science, there are many physical phenomena that we do not yet fully understand. One of these is the deformation rates and fluid stresses generated in a boundary layer for a non-Newtonian fluid. One such non-Newtonian fluid would be a waxy crude oil flowing in a centrifugal pump. This type of flow can be numerically modeled by a rotating disk system, in combination with an appropriate constitutive equation, such as the relation for a Bingham fluid. A Bingham fluid does not begin to flow until the stress magnitude exceeds the yield stress. However, experimental measurements are also required to serve as a database against which the results of the numerical simulation can be interpreted and validated. The purpose of the present research is to gain a better understanding of the behavior of a Bingham fluid in the laminar boundary layer on a rotating disk. For this project, two different techniques were employed: numerical simulation, and laboratory investigations using Particle Image Velocimetry (PIV) and flow visualization. Both methods were applied to the flow of a Bingham fluid over a rotating disk. In the numerical investigations, the flow was characterized by the dimensionless yield stress Bingham number, By, which is the ratio of the yield and viscous stresses. Using von Kármáns similarity transformation, and introducing the rheological behavior of the fluid into the conservation equations, the corresponding nonlinear two-point boundary value problem was formulated. A solution to the problem under investigation was obtained by numerical integration of the set of Ordinary Differential Equations (ODEs) using a multiple shooting method. The influence of the Bingham number on the flow behavior was identified. It decreases the magnitude of the radial and axial velocity components, and increases the magnitude of the tangential velocity component, which has a pronounced effect on the moment coefficient, CM, and the volume flow rate, Q. In the laboratory investigations, since the waxy crude oils are naturally opaque, an ambitious experimental plan to create a transparent oil that was rheologically similar to the Amna waxy crude oil from Libya was developed. The simulant was used for flow visualization experiments, where a transparent fluid was required. To fulfill the demand of the PIV system for a higher degree of visibility, a second Bingham fluid was created and rheologically investigated. The PIV measurements were carried out for both filtered tap water and the Bingham fluid in the same rotating disk apparatus that was used for the flow visualization experiments. Both the axial and radial velocity components in the (r-z) plane were measured for various rotational speeds. Comparison between the numerical and experimental results for the axial and radial velocity profiles for water was found to be satisfactory. Significant discrepancies were found between numerical results and measured values for the Bingham fluid, especially at low rotational speeds, mostly relating to the formation of a yield surface within the tank. Even though the flow in a pump is in some ways different from that of a disk rotating in a tank, some insight about the behavior of the pump flow can be drawn. One conclusion is that the key difference between the flow of a Bingham fluid in rotating equipment from that of a Newtonian fluid such as water relates to the yield surface introduced by the yield stress of the material, which causes an adverse effect on the performance and efficiency of such equipment.

Tissue engineering is a multidisciplinary subject aimed at producing the immunologically tolerant artificial tissues/organs to repair or replace damaged ones. In this field, tissue scaffold plays a key role to support cell growth and new tissue regeneration. For fabrication of tissue scaffolds with individual external geometry and predefined inner structure, rapid prototyping (RP) systems based on fluid dispensing techniques have proved to be very promising. The present research conducted a comprehensive study on the dispensing-based fabrication process. <p>First of all, the scaffold materials are characterized in terms of their biocompatibility and flow behaviour. The biocompatibility of biomaterials of PLLA, PCL, collagen, chitosan, and gelatine is evaluated in terms of supporting neuron cells adhesion and outgrowth. Chitosan solution (2% w/v) in acetic acid is shown to be the most promising among the examined biomaterials for the fabrication of nerve tissue scaffolds. Its non-Newtonian flow behaviour is identified by using a commercial rheometer. <p>In the fabrication process, the flow rate of biomaterials dispensed, the profile of strand cross-sections, and the scaffold porosity are very important and must be precisely controlled. A model is developed to represent the flow rate of biomaterials dispensed under the assumptions that the flow is incompressible, steady, laminar, and axisymmetric. Also, the profile and size of line strands at different layers and portions are modeled based on the Young-Laplace equation. Thus the dispensing-based fabrication process can be predicted in terms of the flow rate and the scaffold porosity. <p>The effects of operation conditions on the fabrication result are identified theoretically and experimentally. Simulation result shows that a higher driving pressure, a higher temperature, and a larger needle diameter will result in a larger size of the strand cross-sections and lower scaffold porosity. The change pattern, however, is nonlinear, which is affected by the fluid surface tension and non-Newtonian flow behaviour of scaffold biomaterials. <p>To verify the effectiveness of the developed models, experiments were carried out on a commercial dispensing system (C-720, Asymtek, USA). To avoid the possible error derived from the temperature difference between the dispensing system and the rheometer, a new method is presented to characterize the fluid properties used for model predictions. Experimental results illustrate that the developed models, combined with the new identification method, are very promising to predict the dispensing-based fabrication process.

The main focus of this work is to investigate experimentally the transition to turbulence of a yield stress shear thinning fluid in Hagen-Poiseuille flow. By combining direct high speed imaging of the flow structures with Laser Doppler Velocimetry (LDV), we provide a systematic description of the different flow regimes from laminar to fully turbulent. Each flow regime is characterized by measurements of the radial velocity, velocity fluctuations, and turbulence intensity profiles. In addition we estimate the autocorrelation, the probability distribution, and the structure functions in an attempt to further characterize transition. For all cases tested, our results indicate that transition occurs only when the Reynolds stresses of the flow equals or exceeds the yield stress of the fluid, i.e. the plug is broken before transition commences. Once in transition and when turbulent, the behavior of the yield stress fluid is somewhat similar to a (simpler) shear thinning fluid. We have also observed the shape of slugs during transition and find that their leading edges to be highly elongated and located off the central axis of the pipe, for the non-Newtonian fluids examined. Finally we present a new phenomenological approach for quantifying laminar-turbulent transition in pipe flow. This criterion is based on averaging a local Reynolds number to give ReG. Our localised parameter shows strong radial variations that are maximal at approximately the radial positions where puffs first appear during the first stages of turbulent transition.

Blood is a dense suspension of flexible red blood cells. In response to a background flow, these cells distribute themselves non-uniformly throughout the vessel. As a result, material properties that are well defined in homogeneous fluids, such as viscosity, are no longer so, and depend upon the flow geometry along with the particle properties. Using a simple model that accounts for the steady-state particle distribution in vessel flow, we derive an expression for the effective viscosity of blood and the suspension flow velocity field in a pressure-driven tube flow. <br /><br /> We derive the steady-state particle distribution from a conservation equation with convective flux arising from particle deformation in the flow. We then relate the particle microstructure to the overall flow through a generalized Newtonian stress-tensor, with the particle volume fraction appearing in the expression for the local viscosity. Comparing with experimental data, we show that the model quantitatively reproduces the observed rheology of blood in tube flow. <br /><br /> We reconsider the problem in an alternate geometry corresponding to the flow between two concentric cylinders. The steady-state particle distribution, suspension velocity field and the measured effective viscosity are all very different from their counterparts in tube flow, casting serious doubt upon the practice of using data from a Couette viscometer to parameterize constitutive models applied to vascular blood flow. <br /><br /> Finally, we calculate the effect of random fluctuations in the particle velocity on the averaged behaviour of the particle conservation equation. Using a smoothing method for linear stochastic differential equations, we derive a correction to the free Einstein-Stokes diffusion coeffcient that is due to the interaction of the particles with their neighbours.

Blood is a dense suspension of flexible red blood cells. In response to a background flow, these cells distribute themselves non-uniformly throughout the vessel. As a result, material properties that are well defined in homogeneous fluids, such as viscosity, are no longer so, and depend upon the flow geometry along with the particle properties. Using a simple model that accounts for the steady-state particle distribution in vessel flow, we derive an expression for the effective viscosity of blood and the suspension flow velocity field in a pressure-driven tube flow. <br /><br /> We derive the steady-state particle distribution from a conservation equation with convective flux arising from particle deformation in the flow. We then relate the particle microstructure to the overall flow through a generalized Newtonian stress-tensor, with the particle volume fraction appearing in the expression for the local viscosity. Comparing with experimental data, we show that the model quantitatively reproduces the observed rheology of blood in tube flow. <br /><br /> We reconsider the problem in an alternate geometry corresponding to the flow between two concentric cylinders. The steady-state particle distribution, suspension velocity field and the measured effective viscosity are all very different from their counterparts in tube flow, casting serious doubt upon the practice of using data from a Couette viscometer to parameterize constitutive models applied to vascular blood flow. <br /><br /> Finally, we calculate the effect of random fluctuations in the particle velocity on the averaged behaviour of the particle conservation equation. Using a smoothing method for linear stochastic differential equations, we derive a correction to the free Einstein-Stokes diffusion coeffcient that is due to the interaction of the particles with their neighbours.