Fractals are a relatively recent development in mathematics that show promise as a foundation for models of complex systems like natural porous media. One important issue that has not been thoroughly explored is the affect of different algorithms commonly used to generate random fractal porous media on their properties and processes within them. The heterogeneous method can lead to large, uncontrolled variations in porosity. It is proposed that use of the homogeneous algorithm might lead to more reproducible applications. Computer codes that will make it easier for researchers to experiment with fractal models are provided. In Chapter 2, the application of percolation theory and fractal modeling to porous media are combined to investigate percolation in prefractal porous media. Percolation thresholds are estimated for the pore space of homogeneous random 2-dimensional prefractals as a function of the fractal scale invariance ratio b and iteration level i. Percolation in prefractals occurs through large pores connected by small pores. The thresholds increased beyond the 0.5927 porosity expected in Bernoulli (uncorrelated) networks. The thresholds increase with both b (a finite size effect) and i. The results allow the prediction of the onset of percolation in models of prefractal porous media. Only a limited range of parameters has been explored, but extrapolations allow the critical fractal dimension to be estimated for many b and i values. Extrapolation to infinite iterations suggests there may be a critical fractal dimension of the solid at which the pore space percolates. The extrapolated value is close to 1.89 -- the well-known fractal dimension of percolation clusters in 2-dimensional Bernoulli networks. The results of Chapters 1 and 2 are synthesized in an application to soil water retention in Chapter 3.

This work examines the fundamental flow behaviour of granular materials under conditions relevant to blast furnace. Such a study may have some impact on the development of new technology to improve performance of blast furnace operation. The blast furnace operation involves rich granular dynamics phenomena which currently attract a strong interest from wide scientific and engineering community. In this work, percolation phenomenon is analyzed extensively. Percolation phenomenon is one of the most significant factors which cause particle segregation and mixing. In blast furnace when sinter and coke of different size and density are charged, percolation phenomenon occurs. In this work percolation properties like percolation velocity, residence time distribution and radial dispersion are checked for different material properties of percolating particles. It was found that percolation behaviour is related to many factors. Percolation properties of a single particle and also for batches of percolating particle were examined. The effect of external forces on percolation properties is also checked. DEM simulation method was found to be suitable for analysis of percolation flow behaviour of different types of particles. It was also found that the change of packed bed conditions has a great impact on particle percolation and segregation behaviour. In a packed bed, vibration and liquid of different properties were introduced. Particle dynamics in descending packed bed condition was checked. The effect of vibration and descending velocity was measured for percolation behaviour. Both vibration frequency and amplitude are important factors for particle flow in such a packed bed. Descending velocity of packed particles combined with vibration was found to have a pronounced impact on percolation behaviour. Liquid properties like viscosity and density affect particle dynamics significantly. Particle segregation in a pile was investigated as an extension of the percolation study. The effects of diameter ratio of binary feed, initial mixing ratio, feed rate in case of central feeding on conical pile were investigated. It was found that all of those parameters affect particle flow and segregation. Flowing layer over static pile was simulated and velocity profile and mixing ratio in different layers were observed. 3-D Screening Layer model was validated by DEM and experiment. In case of multipoint feed system, a conical pile which is similar to the deadman of a blast furnace was generated and the flowing layer characteristics over this static pile was also analysed.

Thesis (M.S.- Agricultural Chemistry and Soils)--University of Arizona. / Includes bibliographical references (leaves 82-84).

Thesis (M.S. - Agricultural Chemistry & Soils)--University of Arizona. / Bibliography: leaves 53-55.

Thesis (Ph.D.) in Physics--University of Maine, 2007. / Includes vita. Includes bibliographical references (leaves 109-112).

Thesis (Ph. D.)--University of Canterbury, 2008. / Typescript (photocopy). Includes bibliographical references (p. 119-144). Also available via the World Wide Web.

Thesis (Ph. D.)--Rutgers University, 2007. / "Graduate Program in Physics and Astronomy." Includes bibliographical references (p. 71-74).

Thesis (Ph. D.)--University of Wisconsin, 1966. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.) -- Lincoln University, 2009. / Also available via the World Wide Web.

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