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Sphere drag data from throughout the twentieth century are available in tabular form. However, much of the data arose from experiments in small diameter cylindrical vessels, where the results might have been influenced by the wall effect. Wall effect corrections developed by others were applied to 178 of the 480 data points collected. This corrected data set is believed to be free of the influence of wall effects. Existing drag and settling velocity correlations were compared to this data set. In addition, new correlations of the same forms were developed using the corrected data. Two new correlations of sphere terminal velocity are proposed, one applicable for all Reynolds numbers less than 2ϫ10 5 , and the other designed to predict settling velocities with exceptional accuracy for terminal Reynolds numbers less than 4,000, a region that contains almost all applications of interest in environmental engineering. The trial and error solution for settling velocity using the Fair and Geyer equation for drag should be retired in favor of the direct calculation available from these new correlations.

The kinetics of flocculation of heterodisperse suspensions like those in water treatment plants are usually described by the Smoluchowski equation, which incorporates collision frequency functions for particle collisions by Brownian motion, fluid shear, and differential sedimentation. These collision‐frequency functions are based on a rectilinear view of collisions, i.e., one that ignores short‐range forces and changes in fluid motion as particles approach one another. With this rectilinear approach, the velocity gradient, G, is the principal design parameter for flocculation units. A curvilinear approach, i.e., one that accounts for short‐range effects in particle collisions, is presented as a set of corrections to the rectilinear collision frequency functions for each mechanism. The primary ramification of this curvilinear, heterodisperse approach is that G is found to be not nearly so important. Previous experimental work in which the role of G has been examined is reviewed in light of this finding.

A mathematical model (array of spheres or AOS Model) of aqueous depth filtration was developed using trajectory analysis performed on a porous media model comprised of a face-centered cubic packing of spheres. To extend removal efficiency predictions beyond the grain-size scale and take into account the presence of densely and sparsely packed regions in an actual filter bed, a parallel deficit porosity compensation scheme was developed and applied. A correlation for single collector efficiency was developed from trajectory results and, using the parallel deficit porosity compensation scheme, compared to an existing model and experimental results. Although the model discussed herein was developed with the intent of advancing the understanding of depth filtration, this work offers tools for investigating and insights into particle fate and transport in other circumstances, e.g., groundwater aquifers. This model represents the first use of a porous media model that explicitly accounts for grain contact points for trajectory modeling of aqueous depth filtration. Particle collection within the model was strongly associated with grain contact points, a phenomenon due largely to hydrodynamic forces “funneling” particles to trajectories coincident with grain contact points. In comparison to previous trajectory models, this model is less sensitive to particle size and filtration rate and much less sensitive to surface chemistry than other currently available models. At moderate to high filtration rates (on the order of 3.7 mm/s or 5.4 gpm/ft2), the AOS model represented well experimental data for removal of particles less than 5 μm. At lower filtration rates and larger particle sizes, the AOS model tends to overpredict particle removal.

Treatment of nontraditional source waters (e.g., produced water, municipal and industrial wastewaters, agricultural runoff) offers exciting opportunities to expand water and energy resources via water reuse and resource recovery. While conventional polymer membranes perform water/ion separations well, they do not provide solute-specific separation, a key component for these treatment opportunities. Herein, we discuss the selectivity limitations plaguing all conventional membranes, which include poor removal of small, neutral solutes and insufficient discrimination between ions of the same valence. Moreover, we present synthetic approaches for solute-tailored selectivity including the incorporation of single-digit nanopores and solute-selective ligands into membranes. Recent progress in these areas highlights the need for fundamental studies to rationally design membranes with selective moieties achieving desired separations.

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