Image Identification

A scheme for determining the boundary of a flame in a colour image is developed. A discussion of how to fit a parallelogram to the flame follows

Minimum Particle Size for Cyclone Dust Separator

Perkins technology wish to separate small soot particles from exhaust gases, and the question posed to the study group was to determine the feasibility of using a cyclone separator to remove these particles. Soot is mostly composed of polycyclicaromatic compounds and results from the incomplete combustion of the diesel fuel in the engine. The average size of the particles formed in the engine is in the range 3 to 10 nm in diameter, but this is known to increase within the exhaust system. In the first part of this report we determine the minimum particle size that can be removed by centrifugal separation. The second part discusses the mechanisms for particle growth within the exhaust system in order to estimate the particle growth rate. In section two we estimate the minimum particle diameter that can be removed by a cyclone separator is around one micron. This estimate is consistent with current applications of hydrocyclones. The particle size measurements by Perkins Technology together with our estimates from section three, suggest that the soot particles are an order of magnitude smaller than this. Although it may be possible to remove some particles less than one micron in diameter with a well designed high-speed cyclone, we do not think it will be possible to remove a substantial proportion of 100 nm or smaller particles. The growth rate of the particles increases if the particles volume fraction or the polydispersity is increased. Therefore aggregation could be enhanced by the addition of larger particles (d > 1 µm) or water droplets (provided the water does not all vapourise) to the exhaust gas

Singular Laplacian Growth

The general equations of motion for two dimensional Laplacian growth are derived using the conformal mapping method. In the singular case, all singularities of the conformal map are on the unit circle, and the map is a degenerate Schwarz-Christoffel map. The equations of motion describe the motions of these singularities. Despite the typical fractal-like outcomes of Laplacian growth processes, the equations of motion are shown to be not particularly sensitive to initial conditions. It is argued that the sensitivity of this system derives from a novel cause, the non-uniqueness of solutions to the differential system. By a mechanism of singularity creation, every solution can become more complex, even in the absence of noise, without violating the growth law. These processes are permitted, but are not required, meaning the equation of motion does not determine the motion, even in the small.Comment: 8 pages, Latex, 4 figures, Submitted to Phys. Rev.

Electro-painting

A mathematical model for electro-painting is developed and analysed. Several sub-problems are studied analytically and numerically

Long term behaviour of geothermal reservoirs

A number of different aspects of geothermal reservoir behaviour were studied during the week. These ranged from the correct formulation of the thermo-elastic deformation equations for granite, and the possible practical methods of implementing the thermo-elastic effects within the existing large computer codes, to the generation of simple models describing the long term thermal effects. This report describes the results of simple modelling. The approach was to consider first how the rock cooled as a result of water moving through the network of cracks and then to consider second how this cooling might change the rock stresses and water viscosity, and hence the effective permeability of the cracks, thereby altering the flow pattern from inlet to outlet bore-hole

Large droplet impact on water layers

The impact of large droplets onto an otherwise undisturbed layer of water is considered. The work, which is motivated primarily with regard to aircraft icing, is to try and help understand the role of splashing on the formation of ice on a wing, in particular for large droplets where splash appears, to have a significant effect. Analytical and numerical approaches are used to investigate a single droplet impact onto a water layer. The flow for small times after impact is determined analytically, for both direct and oblique impacts. The impact is also examined numerically using the volume of fluid (VOF) method. At small times there are promising comparisons between the numerical results, the analytical solution and experimental work capturing the ejector sheet. At larger times there is qualitative agreement with experiments and related simulations. Various cases are considered, varying the droplet size to layer depth ratio, including surface roughness, droplet distortion and air effects. The amount of fluid splashed by such an impact is examined and is found to increase with droplet size and to be significantly influenced by surface roughness. The makeup of the splash is also considered, tracking the incoming fluid, and the splash is found to consist mostly of fluid originating in the layer

Void elimination in screen printed thick film dielectric pastes

The problem is to understand the mechanisms for the formation and evolution of defects in wet screen printed layers. The primary objective is to know how best to alter the properties of the paste (rather than the geometry of the screen printing process itself) in order to eliminate the defects. With these goals in mind the work done during the Study Group reported here was as follows; to describe a simple model for the closure of craters, a model for the partial closure of vias, a possible mechanism for the formation of pinholes and finally a more detailed consideration of the screen printing process

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described in [S. Tanveer, Phil. Trans. R. Soc. Lond. A 343, 155 (1993)]and [M. Siegel, and S. Tanveer, Phys. Rev. Lett. 76, 419 (1996)] as well as direct numerical computation, following the numerical scheme of [T. Hou, J. Lowengrub, and M. Shelley,J. Comp. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (non-singular) zero surface tension solutions. The effect is present even when the relevant zero surface tension solution has asymptotic behavior consistent with selection theory.Such singular effects therefore cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structually unstable flow, restoring the hyperbolicity of multifinger fixed points.Comment: 16 pages, 15 figures, submitted to Phys. Rev