Scaling bacterial filtration rates in different sized porous media

Aquifer sediments contain a wide distribution of particle sizes, but only a single collector diameter (d) can be used in a filtration equation. To establish a method for selecting a characteristic d when media are composed of different sized particles, we measured bacterial retention in columns packed with either crushed quartz sand (separated into three different size ranges) or borosilicate glass beads. The best methods for choosing d were those that produced nearly constant collision efficiencies (αs). Characteristic diameters included: d₁₀(10% of all particles were smaller), d₉₀(90% of all particles were smaller), d_a (arithmetic mean), and d_g (geometric mean), where all diameters were calculated using number, area, and volume size distributions. Bacteria αs decreased in proportion to the distance traveled in the packed bed, and were scaled by the number of bacteria-sediment collisions using a dimensionless collision number (ε). These comparisons indicated that characteristic diameters based on the smaller particles (d_a and d_g using number distributions, and d₁₀ using a volume distribution) most accurately described bacterial transport in the different-sized porous media.