Interception History Drives Colloid Transport Variance in Porous Media

Colloid transport in porous media is traditionally predicted using the principle of constant fractional removal for each grain passed, such that concentrations decrease exponentially with transport distance. This approach successfully describes transport when repulsive barriers to attachment are absent. However, repulsive barriers characterize environmental contexts wherein attachment upon grain interception is inhibited, causing colloid concentrations to decay nonexponentially with distance from the source and thwarting prediction. The pervasiveness of these nonexponential trends across wide-ranging experiments suggests that a fundamental process is at play. Here, we propose a paradigm shift by considering constant fractional loss with each interception rather than with each grain passed. We show that by recognizing the history of grain interceptions, a pathway is revealed toward a simple and predictive framework in which nonexponential trends emerge. This shift in perspective offers the possibility of colloid transport prediction in settings that were previously infeasible using classic filtration theory, with potential applications in contexts ranging from environmental (e.g., groundwater aquifer protection) to biomedical (e.g., drug delivery).