The settling of spheres in viscoplastic fluids
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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.
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