- Title
- The attachment of bubbles to composite particles
- Creator
- Gautam, Alok
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2013
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- In the processing of ores, flotation is widely used for the separation of valuable mineral from the mixture of waste materials (gangue) and desired mineral. It is necessary for the force of attachment between the bubble and the particle to be sufficient to withstand to gravitational and hydrodynamic effects in the flotation cell. The magnitude of the capillary force depends upon the contact angle, the size, and shape of particle, and the surface tension of the gas-liquid interface. Early work in this field focused primarily on theoretical models for the prediction of the capillary force of attachment between a bubble and a spherical particle. In flotation however, the particles are rarely of spherical shape, having resulted from size reduction operation, which produce particles of arbitrary shape and surface composition. A characteristic of crushed ores is the formation of sharp-edged particles, which have cracked along grain boundaries, often forming regular crystalline shapes. Analysis of the literature showed that existing solution methodology cannot be used to find the equilibrium shape of the gas-liquid interface attached to an irregular particle, whenever the interface is pinned at a corner or sharp edge. This thesis describes a study in which the aim is to develop an improved solution methodology for the calculation of the capillary force of attachment between a bubble and a solid particle of arbitrary shape and surface composition. Computational modelling is of interest since it may help in investigating the behaviour of the rough composite particle on the bubble surface. In development of the modelling methods, chemically homogenous particles with sharp edges were firstly considered. A finite element method was used to solve the Young-Laplace (Y-L) equation for particles of polyhedral shape, in the absence of contact line pinning. The simulation shows that unless the contact angle is 90 degrees, the contact line is curved, leading to increases in the perimeter. However, when the contact line becomes pinned to an edge or a corner, it is not possible to provide the boundary conditions in the form required for the solution of the Young-Laplace equation. The angle of contact has different values at different points of the three-phase contact (TPC) line, and these angles are unknown. For the first time, the sequence of events when a cubical particle is detached from an interface has been observed experimentally. As the particle moves away from the interface, the contact line first detaches from the corners while remaining pinned to sharp edges. At the edges, the angle of contact is different to the contact angle. After the contact line detaches from the corner (or an edge), the angle of contact equals the advancing contact angle. Detachment at a corner or an edge takes place within the limits of the Gibbs inequality. As the particle moves further from the plane of the gas-liquid interface at infinity, the contact line contracts until it is pinned only at the centres of the edges of the cubical object. When the line finally detaches from the remaining pinning points, it rapidly collapses inward in the form of a circle, and detaches completely from the interface. To find the shape of the gas-liquid interface and the force of attachment when pinning occurs, an energy minimisation method was used. The method has been implemented in the Surface Evolver software of Ken Brakke. The predictions were compared with the results from the experiments in which the force of attraction on a glass slide partially immersed in a gas-liquid interface was measured. Excellent agreement was found. The simulation method was then applied to a number of situations to be found in mineral flotation, including the force on regular shapes such as cubes, as well as composites where cubic or cylindrical particles of a hydrophobic mineral are embedded in a hydrophilic matrix. In this study, a new solution methodology is developed for modelling the influence of sharp edges and corners on the equilibrium shape of the gas-liquid interface near a particle. Accurate prediction of the capillary force of attachment by this model is demonstrated by comparison to the experimental results. The method developed in this study is very effective and can be used for a particle of arbitrary shape for the given physical parameters such as surface tension of liquid, the size, and shape of particle and contact angle. Theoretical and experimental investigations revealed that the angle of contact increases at sharp edges, which also results in an increased capillary force. Thus for a given displacement with respect to the gas-liquid interface at infinity, the force of attachment is greater with pinned contact lines. The same methodology was extended to compute the capillary force between a bubble and a composite particle. It is generally seen that valuable mineral is distributed in patches over the surface of such particles. The availability of hydrophobic patches as well as their distribution over the surface of a composite particle is of importance in the attachment of a particle with a bubble. A code was developed to investigate the effect of the fractional surface liberation and the distribution of hydrophobic patches on the capillary attachment force. Results show that the distribution of valuable mineral increases the attachment force. A theoretical study was conducted in which a spherical particle was placed in the interface, in which the sphere was composed of two continuous parts, one hydrophilic and the other hydrophobic. The effect of the orientation of the sphere on the attachment force was investigated. The governing equations are solved including the pinning of the contact line at an edge of the hydrophobic patch. The predicted results show that the orientation of composite particle plays an important role in determining the stability of the particle at the interface.
- Subject
- attachment of particles; composite particle; Y-L equation; hydrophobic patches
- Identifier
- http://hdl.handle.net/1959.13/1038741
- Identifier
- uon:13577
- Rights
- Copyright 2013 Alok Gautam
- Language
- eng
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| View Details Download | ATTACHMENT02 | Thesis | 8 MB | Adobe Acrobat PDF | View Details Download |