in Wiley Online Library (wileyonlinelibrary.com).The longitudinal (D L ) and transverse (D T ) dispersion coefficients in two-dimensional (2-D) randomly packed beds of circular particles in a laminar flow regime are derived. A 2-D discrete system of particles is divided into cells using modified Voronoi diagrams. The relationship between the variation of the stream function and the averaged vorticity is obtained from computational fluid dynamics (CFD) simulations. The whole flow pattern is then obtained by using the principle of energy dissipation rate minimization. The obtained values of D L agree well with 3-D experimental data for all velocities investigated. At very high velocities, D T in 2-D appears to be higher than 3-D experimental data. In addition, the effects of particle-size distributions, packing structure, and porosity on the D L and D T were studied. One result was that an increase in the width of the particle-size distribution resulted in higher values of D L and D T at high velocities.

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The longitudinal (D L ) and transverse (D T ) dispersion coefficients for flow through randomly packed beds of discrete monosized spherical particles are studied. The three-dimensional (3-D) porous-medium model consists of thousands of spherical particles that are divided into cells using Voronoi diagrams. The relationship between the variation of the dual stream function and the vorticity between neighboring particles is derived using Laurent series. The whole flow pattern at low particle Reynolds number is then obtained by minimization of the dissipation rate of energy with respect to the dual stream function. The

Sorption by active filter media can be a convenient option for phosphorus (P) removal and recovery from wastewater for on-site treatment systems. There is a need for a robust laboratory method for the investigation of filter materials to enable a reliable estimation of their longevity. The objectives of this study were to (1) investigate and (2) quantify the effect of hydraulic loading rate and influent source (secondary wastewater and synthetic phosphate solution) on P binding capacity determined in laboratory column tests and (3) to study how much time is needed for the P to react with the filter material (reaction time). To study the effects of these factors, a 22 factorial experiment with 11 filter columns was performed. The reaction time was studied in a batch experiment. Both factors significantly (α = 0.05) affected the P binding capacity negatively, but the interaction of the two factors was not significant. Increasing the loading rate from 100 to 1200 L m−2 d−1 decreased P binding capacity from 1.152 to 0.070 g kg−1 for wastewater filters and from 1.382 to 0.300 g kg−1 for phosphate solution filters. At a loading rate of 100 L m−2 d−1, the average P binding capacity of wastewater filters was 1.152 g kg−1 as opposed to 1.382 g kg−1 for phosphate solution filters. Therefore, influent source or hydraulic loading rate should be carefully controlled in the laboratory. When phosphate solution and wastewater were used, the reaction times for the filters to remove P were determined to be 5 and 15 minutes, respectively, suggesting that a short residence time is required. However, breakthrough in this study occurred unexpectedly quickly, implying that more time is needed for the P that has reacted to be physically retained in the filter.

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