Filtrations in the separation of solid-liquid mixtures have been studied for 80 years. However, the lack of a generalized set of laws for filtration has increased the difficulty of incorporating equations from one model into another. This thesis is focused on the relationship between fluid properties and cake structure on the void distribution and ultimate pressure drop during a filtration process. By comparing experimental results to those predicted from the Kozeny-Carman model/equation, we assess the utility of this equation for application to systems that include poly-disperse particles at moderate fluid pressure. We find substantial agreement between model and experiment only for systems that result in well-ordered particle packing (i.e., those that have a tight distribution of void sizes). Dramatic disagreement is observed for particle beds that exhibit wide void size distributions. The cake structure is primarily influenced by the size ratio of the particles that compose the cake; specifically, particles with a size ratio in which Rs/l is larger than 0.5 do not typically form an ordered pore structure. We propose a modified Kozeny-Carman equation, based on a bimodal void distribution, by introducing two factors: the fraction of expanded voids (κ) and the ratio of void sizes (β). Discrete Element Method (DEM) simulations of the packing of poly-disperse spheres are used to analyze the cake structure for different size ratios of binary mixtures. Based on the simulation results, void size distributions of the simulated beds can be extracted by means of a radical Delaunay tessellation. The void structure is quantified in terms of probability density functions of pore and constriction sizes. By fitting the simulated void size distributions to a bimodal (two normal) distribution, the factors κ and β can be calculated based on different mean void sizes and probability density. The predicted flow dynamics from the modified equation with factors extracted from the simulation results are found to be much more similar to the experimental flow rates than those calculated using the unmodified Kozeny-Carman equation. Therefore, the modified equation is deemed reliable at predicting the flow behavior, provided that an approximate representation of the void size distribution is available.
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