Langmuirian Blocking of Irreversible Colloid Retention: Analytical Solution, Moments, and Setback Distance

Soil and aquifer materials have a finite capacity for colloid retention. Blocking of the limited number of available retention sites further decreases the rate of retention with time and enhances risks (e.g., pathogens or colloid-associated contaminants) or benefits (e.g., remediation by microorganisms or nanoparticles) of colloid migration. Our objective was to use a straightforward procedure, based on variable transformation and Laplace transform, to solve the problem of advective colloid transport with irreversible retention and Langmuirian blocking for a pulse-type condition. Formulas for the mean breakthrough time and retardation factor were obtained using zero- and first-order time moments of the breakthrough curves. Equations for the time and position (setback distance) for a particular colloid concentration were obtained from this information. D21 g breakthrough curves and retention profiles in fine sand at four ionic strengths were well described by the model when parameters were optimized. Illustrative simulations demonstrated that blocking becomes more important for smaller retention capacity () and for larger retention rate coefficient (), input concentration (), and pulse duration. Blocking tended to delay colloid arrival time at a particular location relative to a conservative tracer, and produced larger setback distances for smaller and /.