Fractal dimensions and their relationship to filtration characteristics
Work has been performed to characterise filtration systems according to their fractal properties and to construct agglomerates to mimic the filtration systems under scrutiny. The first objective was achieved by carrying out experiments examining the dead-end filtration of two separate mineral suspensions, namely calcite and talc. These minerals were chosen to represent typical incompressible (calcite) and compressible (talc) filtration systems, undergoing filtration using a range of pressures. The experimental apparatus produced filter cakes that could be sampled, sectioned and examined under high magnification. The second objective was met by developing a computer application that could construct simulated particle agglomerates in both two and three dimensions, using a seed agglomeration model as well as simulating filtration by means of a virtua1 filter cell. A large number of simulations were completed to mimic both the dead-end filtration and other agglomerate models. The computer application was also capable of characterising the fractal and Euclidean spatial nature of both the simulated and experimental particulate systems, using a variety of techniques. Euclidean spatial attributes such as porosity as well as fractal properties including surface roughness and a number of density fractal dimensions have been measured for both types of system and demonstrate that the conditions under which the trials were performed have a bearing on the final configuration of the structures. Results from both experimental and simulation work show that fractal dimensions offer a valid method of measuring the properties of filtration systems. Experimental results showed that as the filtering pressure was increased, the density fractal dimension for the system appeared to increase. This change in fractal dimension was also accompanied by a decrease in the porosity of the system (more so for talc than the calcite), confirming the compressibility of the materials under scrutiny. The characterisation of the sampled cakes also showed that the spatial characteristics vary within the individual slices of the sample,in agreement with modem filtration theory. Results from the simulations show that both the physical and fractal properties of the resulting structures varied with the parameters used to construct them. As a rule, as the particles in the simulations were able to move in a more diffusive manner (akin to Brownian motion), the agglomerates they formed had a more open, rugged structure. The simulation of filtration systems also showed a variation within the individual cake structures. In the case of the filtration simulations, the probability assigned to the particles' sticking to the growing agglomerate was the controlling factor. In addition, it was found that the simulated cakes had similar spatial properties to the experimental systems they were designed to replicate.