| Description |
Traditional colloidal filtration theory (CFT) predicts zero attachment when repulsion exists between colloid and filtering media (collector). Notably, repulsion is prevalent in environmental systems, e.g., riverbank filtration, and is manifested as energy barriers to attachment due to electro osmotic interactions between surfaces of the same charge. A mechanistic particle trajectory model that incorporates discrete nanoscale attractive zones (heterodomains) to account for attachment under bulk repulsive colloid-collector interactions was developed and tested against an array of direct observation experiments conducted in an impinging jet system. Retention of 0.25 to 1.95 m colloids on soda-lime glass slides was examined for 6 and 20 mM ionic strengths (IS) and average jet velocities of 1.7x10-3 to 5.94x10-3 ms-1 (equivalent pore water velocity of 1.9 and 8.2 mday-1, respectively) in order to characterize the heterodomain size distribution and surface coverage. Simulations indicate that a power law distribution of 60 and 120 nm radii heterodomains (4:1 number ratio) and 0.04% surface coverage is able to quantitatively capture observed retention across all conditions examined. Furthermore, the same heterogeneity characteristics were able to capture qualitative trends of release of colloids deposited in contact with heterodomains in response to perturbations in flow and IS relative to the loading condition, i.e., factor 25 increase in jet velocity or factor 20 decrease in IS. Finally, a correlation equation was developed to incorporate the mechanistic basis provided from the discrete heterogeneity model and calibrated from the array of experiments. The equation is a function of the colloidal number, which captures the main characteristics of the energy barrier, and the fraction of colloids that persist in the near surface fluid domain (secondary minimum) obtained from a Maxwell distribution of kinetic energies. Notably, the proposed correlation equation captures scores of experiments reported in the literature for a broad range of conditions for colloid sizes ranging from 0.06 to 3.1 m, IS from 0.1 to 300 mM, and average pore water velocities from 4 to 588 mday-1on soda-lime glass beads. The main coefficient of the correlation equation is a linear function heterodomain surface coverage, indicating that different coefficients may capture filtration across different aquifer-relevant minerals. |
