Mathematical Modeling of the Transport and Dissolution of Citrate-Stabilized Silver Nanoparticles in Porous Media

A one-dimensional mathematical model is developed and implemented to describe the coupled transport of citrate-stabilized silver nanoparticles (nAg) and dissolved silver ions in porous media. This hybrid numerical simulator employs an Eulerian finite difference (FD) method to model the reactive transport of dissolved constituents and a Lagrangian (random-walk particle-tracking (RWPT)) approach to capture the transport and differential aging of nanoparticles. Model performance is demonstrated by comparison of simulations with data obtained from a series of nAg transport and dissolution column experiments. A three pore volume pulse of a citrate-stabilized nAg suspension (ca. 3 mg/L) was introduced into a 12 or 16 cm long column packed with water-saturated quartz sand at a pore-water velocity of ca. 7.6 m/day and pH 4 or 7. While low retention levels (ca.17%) and no dissolution were observed for the pH 7 column, analysis of column effluent samples for pH 4 conditions indicated that ca. 88% of the injected silver mass was retained in the column, while 6% was eluted as particles (nAg) and 6% as dissolved ions (Ag+). Hybrid model simulations, employing a lumped nAg dissolution coefficient of (3.45 ± 0.35) × 10–2/h, are shown to accurately capture measured nAg transport and Ag+ release behavior. A model sensitivity analysis explores the influence of flow velocity and particle size on nAg transport and fate, indicating that as velocity and particle size decrease, nAg dissolution and Ag+ transport processes increasingly dominate silver mobility