School of Mathematics and Statistics - Theses

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End date: 2009 × Start date: 2005 × Subject: mathematics ×

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    Modelling hydrodynamic interactions between deformable droplets
    MANICA, ROGERIO ( 2007-06)
    Understanding deformations during interaction of colloidal or nano droplets. has important implications in a wide range of applications such as flotation collection and emulsion stability. The present work is important and necessary because current models are unable to properly describe recent experimental results obtained using the Atomic Force Microscope (AFM) and Surface Force Apparatus (SFA). We revisit and improve on theories involving interacting deformable droplets. A detailed theoretical model of the experiments, which accounts for surface forces, hydrodynamic interactions, droplet deformation and AFM cantilever detection, has been developed. The new feature of the model is the use of matched asymptotic expansions to derive a new boundary condition at constant volume to obtain results that are independent of the size of the computational domain. The AFM experiments provide measurements of dynamical forces between two interacting droplets as well as between a drop and a colloidal particle of micrometre radii in solution when they are driven together and then are retracted from each other. The SFA experiments measure (time dependent) surface profiles of a millimetre size mercury drop interacting with a mica surface. Different configurations have been studied including mechanical and electrical perturbations to a thin film stabilized by double layer repulsion. Interesting experimental features were observed when approaching or retracting the mica from the mercury drop.
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    Methods for assessment of probability of detection for nondestructive inspections
    Harding, Catherine Ann ( 2008)
    Assessment of the probability of detection (POD) of defects with non-destructive s inspection (NDI) is essential to integrity management of safety-critical structure, particularly in the aerospace industry. Traditionally, probability of detection is measured empirically by a POD trial, in which a number of inspections are performed under field (or simulated field) conditions on a set of specimens containing representative defects. These POD trials are very expensive and for many applications are not feasible. This thesis develops improved techniques for cost-effective measurement of POD. Methods for statistical analysis of hit/miss POD data are reviewed and the behaviour of selected methods is explored using simulations. Superior methods for applying confidence limits on POD from hit/miss data are identified, which are valid for much smaller sample sizes than traditional methods, such as that found in US military handbook, MIL-HDBK-1823 (1999). Model-assisted probability of detection assessment uses physics-based or empirical models to predict POD, which has the potential to reduce the requirement for conventional POD trials, increase the portability of POD information across related applications, and provide a basis for reliability assessment for applications where trials are not feasible. In this thesis, model-assisted POD is applied to a specific non-destructive inspection procedure developed for detection of cracks at fastener holes in the lower wing skin of Royal Australian Air Force F-111 aircraft. This application of POD modelling uses data obtained from field trials and laboratory experiments for angle-beam shear-wave ultrasonic detection of fatigue cracks at fastener holes, including human factors effects. A fully representative POD trial was not feasible for this inspevtion procedure, and so this application provides important real-world context for the development of model-assisted POD.