<p>The Particle Level set method is a successful extension to Level set methods to improve thevolume preservation in fluid simulations. This thesis will analyze how sparse volume data structures can be used to store both the signed distance function and the particles in order to improve access speed and memory efficiency. This Particle Level set implementation will be evaluated against Digital Domains current Particle Level set implementation. Different degrees of quantization will be used to implement particle representations with varying accuracy. These particles will be tested and both visual results and error measurments will be presented. The sparse volume data structures DB-Grid and Field3D will be evaluated in terms of speed and memory efficiency.</p>

The Particle Level set method is a successful extension to Level set methods to improve thevolume preservation in fluid simulations. This thesis will analyze how sparse volume data structures can be used to store both the signed distance function and the particles in order to improve access speed and memory efficiency. This Particle Level set implementation will be evaluated against Digital Domains current Particle Level set implementation. Different degrees of quantization will be used to implement particle representations with varying accuracy. These particles will be tested and both visual results and error measurments will be presented. The sparse volume data structures DB-Grid and Field3D will be evaluated in terms of speed and memory efficiency.

The process of froth flotation relies on using air bubbles to collect desired mineral particles dispersed in aqueous media on the surface, while leaving undesirous mineral particles behind. For a particle to be collected on the surface of a bubble, the thin liquid films (or wetting films) of water formed in between must rupture. According to the Frumkin-Derjaguin isotherm, it is necessary that wetting films can rupture when the disjoining pressures are negative. However, the negative disjoining pressures are difficult to measure due to the instability and short lifetimes of the films. In the present work, two new methods of determining negative disjoining pressures have been developed. One is to use the modified thin film pressure balance (TFPB) technique, and the other is to directly determine the interaction forces using the force apparatus for deformable surfaces (FADS) developed in the present work. The former is designed to obtain spatiotemporal profiles of unstable wetting films by recording the optical interference patterns. The kinetic information derived from the spatiotemporal profiles were then used to determine the disjoining pressures using an analytical expression derived in the present work on the basis of the Reynolds lubrication theory. The technique has been used to study the effects of surface hydrophobicity, electrolyte (Al3+ ions) concentration, and bubble size on the stability of wetting films. Further, the geometric mean combining rule has been tested to see if the disjoining pressures of the wetting films can be predicted from the disjoining pressures of the colloid films formed between two hydrophobic surfaces and the disjoining pressures of the foam films formed between two air bubbles. The FADS is capable of directly measuring the interaction forces between air bubble and solid surface, and simultaneously monitoring the bubble deformation. The results were analyzed using the Reynolds lubrication theory and the extended DLVO theory to determine both the hydrodynamic and disjoining pressures. The FADS was used to study the effects of surface hydrophobicity and approach speeds. The results show that hydrophobic force is the major driving force for the bubble-particle interactions occurring in flotation. / Ph. D.