The settling of spheres in viscoplastic fluids

In this thesis, several significant contributions have been made towards the understanding of the flow behaviour of viscoplastic fluids and the settling behaviour of particles in these fluids. The attainment of this knowledge is highly crucial for the development of large-scale simulations of the movement of particles in tertiary grinding circuits, through which effective cost and resource saving strategies for the design and operation of these highly resource-demanding unit processes could be developed.To achieve the underlying objective of this thesis, the settling-sphere problem was approached using both experimental and numerical techniques. Experimentally, the flow behaviour of the viscoplastic slurries was represented by viscoplastic (aqueous) solutions of polyacrylamide. The settling behaviour of two spheres, using two different configurations of initial sphere positions, was then examined. In the first configuration, the two spheres are vertically-aligned, i.e. one sphere is released following the flow path of another sphere that has been released some time earlier into the fluid medium. In the second configuration, the two spheres are horizontally aligned, with a set distance apart, and released simultaneously into the viscoplastic solution. One of the major accomplishments achieved during the design of these experiments was the development of a stereo-photogrammetry sensor system, through which the 3D movement of spheres falling through the fluid could be determined to within ~ 1.5 mm accuracy.The numerical part of this study was conducted using Computational Fluid Dynamics (CFD) technique. Based on the Volume of Fluid (VOF) method, the settling particles were represented by fluids of very high viscosity (~ 400 – 1000 Pa.s). By implementing appropriate discretisation and approximation methods, the effects of numerical smearing and diffusion, as well as the level of deformation in the settling particles, could be minimised. A time-dependent estimation of the flow behaviour of the test fluids was then developed and implemented into this numerical scheme, using a series of User Defined Functions (UDFs).The development of the UDFs in the CFD analysis was based on the results of the rheometric assessment of the test fluids, through which it was found that these solutions possess a level of time dependency resulting from both thixotropy and elasticity. A new fluid model was thus developed, based on a scalar parameter that represents the integrity of the structural network configuration, resulting from the hydrogen bonding between the polyacrylamide and water molecules in the fluid. Although the resulting fluid model does not exclusively feature a yield stress value, the results of a series of dynamic analyses conducted on this model were found to be similar to those found experimentally, in which fluids that were initially ‘undisturbed’ or intact in structure have been found to require the application of stresses that are significantly larger in magnitude for the initiation of its deformation than in cases where the structure of the fluid is already deformed. Due to these dynamic characteristics, in which the fluid model seems to feature yield stress-like quality that dissipates once the ‘structure’ of the fluid has been deformed due to the application of shear, this fluid model was termed ‘semi-viscoplastic’.Using the analytical techniques outlined above, two significant contributions were made towards the understanding of the settling behaviour of particles in viscoplastic fluids. First, the settling velocity of particles falling in the fluid medium was found to be highly dependent on the structural condition of the fluid, i.e. whether it has recently been subjected to shear or whether sufficient time has been allowed for the fluid to recover its original viscous parameters. Based on this finding, a new generalised correlation was developed, through which predictions of the settling velocity of particles falling in fluids of various structural conditions can be made with much greater accuracy than before. The second contribution was in the understanding of the interaction tendencies between spheres that are settling in close proximity to each other. Through experimental and numerical analyses, it was found that the interaction tendencies of the particles are highly dependent on the elastic properties of the fluids. Correlations relating the tendencies of the spheres to interact with the elastic and viscous properties of the fluid were then developed. Through both of these contributions, aspects that are critical for the understanding of the motion of solid bodies in grinding circuits have been addressed

Numerical simulation of the settling behaviour of particles in thixotropic fluids

A numerical study on the settling behaviour of particles in shear-thinning thixotropic fluids has been conducted. The numerical scheme was based on the volume of fluid model, with the solid particle being likened to a fluid with very high viscosity. The validity of this model was confirmed through comparisons of the flow field surrounding a sphere settling in a Newtonian fluid with the analytical results of Stokes. The rheology model for the fluid was time-dependent, utilising a scalar parameter that represents the integrity of a “structural network,” which determines its shear thinning and thixotropic characteristics. The results of this study show that the flow field surrounding the settling sphere is highly localised, with distinct regions of disturbed/undisturbed fluids. The extension of these regions depends on the relaxation time of the fluid, as well as its shear thinning characteristics, and reflects the drag force experienced by the sphere. As the sphere settles, a region of sheared fluid that has significantly lower values of viscosity is formed above the sphere. This region slowly recovers in structure in time. As a result, a sphere that falls in a partially recovered domain (e.g., due to the shearing motion of an earlier sphere) tends to attain a greater velocity than the terminal velocity value. This was found to be true even in cases where the “resting time” of the fluid was nearly twice the relaxation time of the fluid. The results of this study could provide a framework for future analysis on the time-dependent settling behaviour of particles in thixotropic shear-thinning fluids

Phase-field modeling of planar interface electrodeposition in lithium-metal batteries

Acknowledgments This work was supported by the Aberdeen-Curtin Alliance Scholarship. This publication was also made possible in part by the Professorial Chair in Computational Geoscience at Curtin University. This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 777778 (MATHROCKS). The Curtin Corrosion Centre and the Curtin Institute for Computation kindly provide ongoing support.Peer reviewedPostprin

Dendrite formation in rechargeable lithium-metal batteries: Phase-field modeling using open-source finite element library

We describe a phase-field model for the electrodeposition process that forms dendrites within metal-anode batteries. We derive the free energy functional model, arriving at a system of partial differential equations that describe the evolution of a phase field, the lithium-ion concentration, and an electric potential. We formulate, discretize, and solve the set of partial differential equations describing the coupled electrochemical interactions during a battery charge cycle using an open-source finite element library. The open-source library allows us to use parallel solvers and time-marching adaptivity. We describe two- and three-dimensional simulations; these simulations agree with experimentally-observed dendrite growth rates and morphologies reported in the literature.Comment: Under Revie

Large expert-curated database for benchmarking document similarity detection in biomedical literature search

Document recommendation systems for locating relevant literature have mostly relied on methods developed a decade ago. This is largely due to the lack of a large offline gold-standard benchmark of relevant documents that cover a variety of research fields such that newly developed literature search techniques can be compared, improved and translated into practice. To overcome this bottleneck, we have established the RElevant LIterature SearcH consortium consisting of more than 1500 scientists from 84 countries, who have collectively annotated the relevance of over 180 000 PubMed-listed articles with regard to their respective seed (input) article/s. The majority of annotations were contributed by highly experienced, original authors of the seed articles. The collected data cover 76% of all unique PubMed Medical Subject Headings descriptors. No systematic biases were observed across different experience levels, research fields or time spent on annotations. More importantly, annotations of the same document pairs contributed by different scientists were highly concordant. We further show that the three representative baseline methods used to generate recommended articles for evaluation (Okapi Best Matching 25, Term Frequency-Inverse Document Frequency and PubMed Related Articles) had similar overall performances. Additionally, we found that these methods each tend to produce distinct collections of recommended articles, suggesting that a hybrid method may be required to completely capture all relevant articles. The established database server located at https://relishdb.ict.griffith.edu.au is freely available for the downloading of annotation data and the blind testing of new methods. We expect that this benchmark will be useful for stimulating the development of new powerful techniques for title and title/abstract-based search engines for relevant articles in biomedical research.Peer reviewe

Determination of trajectories of metallic spheres settling in non-newtonian fluids

A "videogrammetric" system to measure the trajectory of small metallic spheres falling through a slurry-filled tank has been developed to support fluid dynamics research. The system used two low-cost video cameras and a combination of commercially available and custom-built software for the image acquisition, the measurement and tracking of the spheres in the imagery and the photogrammetric operations. After a review of relevant literature and a description of the system, this paper reports on an extensive testing regime conducted to gauge the performance of the system. The results show that it achieved object space coordinate precision and accuracy better than the required figure of 1 mm. Simulation-based analyses, to quantify the sensitivity of refraction corrections in object space to the accuracy of the three refractive indices and distance parameters involved in the system, are also reported. The results of these tests demonstrated that some parameters need only be specified to about 56% of their true value whereas others must be accurate to better than 2%. Finally, results from two examples in sphere trajectory determination are presented and analysed. © Journal Compilation © 2009 Remote Sensing and Photogrammetry Society and Blackwell Publishing Ltd

The effects of fluid viscoelasticity on the settling behaviour of horizontally aligned spheres

A study on the interaction of particles settling in non-Newtonian fluids of shear-thinning, thixotropic and viscoelastic characteristics has been conducted. Key aspects of the rheological characteristics of the fluids that influence the interaction of the particles were examined by analysing the trajectories of two particles that are initially placed side-by-side in the fluid medium. The interaction of the particles was found to be highly dependent on the separation distance that is initially set between them. If the initial distance is smaller than a critical value, the spheres would tend to attract and converge. In cases where the initial distance is greater than this critical value, the two spheres would tend to diverge, resulting in a slight (~20%) increase in their separation distance over their course of settling. This tendency to diverge was found to diminish as the initial distance is increased further from the critical value. The magnitude of the critical separation distance was found to be primarily dependent on the normal stresses of the fluids. A correlation was thus proposed based on this observation. In cases where the two spheres do attract and converge, it was found that the spheres tend to follow a non-symmetrical trajectory, where one of the spheres possesses a slightly lower settling velocity than the other. As a result, the spheres appear to re-arrange themselves into a vertically aligned configuration. Once aligned, the shear-thinning and thixotropic characteristics of the fluid causes the lagging sphere to accelerate and collide with the leading sphere. © 2011 Elsevier Ltd

Numerical Simulation of the Collision of a Droplet with a Heated Solid Surface

This paper discusses the development of a model for the evaporation of a droplet on heated solid surface. Associated issues include the construction of evaporative source terms, and their implementation into a multiphase (VOF) framework. This was done in conjunction with the Level Set method (CLSVOF), allowing the evaporation at the liquid-vapour and liquid-solid interface to be characterised accurately. The validity of the model was examined through comparisons with published experimental data. The model was found to be capable of reproducing the reduced droplet spreading rate as the surface temperature is increased away from the saturation temperature. This decrease in surface wetting results from the combined effects of surface tension, viscous forces and contact line evaporation. The effects of increased pressure due to evaporation, which in some cases can be quite severe such that the liquid gets lifted-off from the surface, were also captured, in good agreement with experimental observations

Evaporation of a droplet on a heated spherical particle

© 2014 Elsevier B.V. A three-dimensional, CLSVOF-based numerical model was developed to study the hydrodynamics of water droplets of various diameters impacting a heated solid particle. The temperature of the particle was set to be above the Leidenfrost temperature of the fluid, such that the influence of several key parameters on the dynamics of film boiling of the droplet could be examined. The simulation results were validated against experimental observations, where it was found that the numerical model could satisfactorily reproduce the dynamics of the droplet. The spread of the droplets upon impact was found to be dependent on the Weber number, with surface tension and viscous forces then acting to recoil the droplet. The rate of droplet recoil was found to be highly dependent on the Reynolds number, as fluid advection tends to enhance the rate of heat transfer within the droplet and the evaporation at the solid-liquid contact line. Eventually, evaporation causes build-up of vapour pressure at the bottom of the liquid, and the droplet lifts-off from the heated particle. It was found that the onset of the droplet lift-off could be estimated through the first-order vibration of a freely oscillating droplet, particularly in cases with low values of Weber number. Finally, the rate of evaporation of the droplet was found to be highly dependent on the capillary length of the fluid and the stability of the vapour layer formation underneath the droplet

Bubble generated turbulence and direct numerical simulations

Gas–liquid two phase flows are widely encountered in industry. The design parameters include two phase pressure drop, mixing and axial mixing in both the phases, effective interfacial area, heat and mass transfer coefficients. Currently, there is a high degree of empiricism in the design process of such reactors owing to the complexity of coupled flow and reaction mechanism. Hence, we focus on synthesizing recent advances in computational and experimental techniques that will enable future designs of such reactors in a more rational manner by exploring a large design space with high-fidelity models (computational fluid dynamics) that are validated with high-fidelity measurements (hot film anemometry (HFA), Laser Doppler anemometry (LDA), particle image velocimetry (PIV), etc.) to provide a high degree of rigor. Understanding the spatial distributions of dispersed phases and their interaction during scale up are key challenges that were traditionally addressed through pilot scale experiments, but now can be addressed through advanced modelling. For practically complete knowledge of the fluid mechanical parameters, it is desirable to implement direct numerical simulations (DNS). However, the current computational power does not permit full DNS for real bubble columns. Therefore, we have been using simplified turbulence models (such as large eddy simulation, Reynolds stress, k–e, etc.) which need the knowledge of turbulence parameters. For the estimation of these parameters, currently semi-empirical procedures are being used pending the knowledge of turbulence. Further, the formulation of governing equations in all the CFD models (except DNS), the knowledge of interface forces (drag, lift, virtual mass, Basset, etc.) is needed and for their estimations empirical correlations are being employed, again pending the knowledge of fluid mechanics under turbulent conditions in bubble columns. In gas–liquid dispersions, the gas is sparged in the form of bubbles. During the bubble rise, the mechanism of wake detachment creates turbulence which can be called as wake generated turbulence. In addition, energy gets transferred from the gas phase to liquid phase. The quantitative amounts are negligible when bubble motion is not hindered and the gas–liquid dispersion is homogenous. The amounts increase with an increase in the extent of hindrance. However, in the homogenous regime, even under extreme conditions, the extent of energy transfer in the bulk gas–liquid dispersions (volume other than wake volume) is fairly limited. On contrast, in the heterogeneous regime, the rates of energy transfer become sizeable. The energy received by the liquid (in both the regimes) also creates turbulent motion and termed as bulk generated turbulence. In turbulent flows a compendium of eddies (flow structures) of different length and time scales contribute towards improved/enhanced mixing, momentum transfer, heat transfer, and mass transfer (transport phenomena). Hence, a proper understanding of the dynamics of these turbulent flow structures, and their role in the transport phenomena, can bring substantial improvement in the scale-up and design procedures. The present paper brings out the current status of knowledge on bubble generated turbulence. All the published literature in experimental measurements and DNS simulations has been critically analysed and coherently presented