Abstract
The ¹⁴C-labeled few-layer graphene (FLG) nanoparticles (NPs) with unique electronic, mechanical, and optical properties have been incorporated into a range of products and industries. The soil-groundwater system is expected to be a major pathway for FLG release into the environment, and thus, investigating the mobility of FLG is necessary to identify possible exposure and adverse effects on groundwater and the food chain in terrestrial ecosystems. Mathematical models must be developed to characterize limiting kinetic processes that govern the fate and transport of NPs in the subsurface. This mathematical modeling study incorporates an existing set of effluent data for FLG-NPs transport through water-saturated quartz sand to estimate kinetic particle mobility parameters for a range of experimental (a) ionic strengths (IS) and (b) organic macromolecules (OMs) concentrations. Parameter estimation was done by implementing several NP filtration models in inverse analyses: (i) the clean-bed colloid filtration theory model (CFT), (ii) maximum retention capacity model (MRC), and (iii) two sub-classes of a two-attachment-site model (2S). It was found that as solution IS (1-100 mM NaCl) increased, the kinetic conditions for particle-collector attachment transitioned from unfavorable (i.e. fractional attachment) to favorable (i.e. diffusion-limited), and the unbounded sub-class of 2S lost the better numerical performance compared to CFT and MRC; as the difference between the normalized sum of squared residuals (NSSR) of the unbounded sub-class of 2S and CFT decreased from 20% at 1 mM to less than 1% at 100 mM NaCl suggesting the adequacy of CFT to estimate mobility parameters at high ionic strength. However, the bounded 2S which assumes the presence of surface charge heterogeneity with favorable irreversible attachment to MRC sites showed poor performance in both favorable and unfavorable conditions, which can be attributed to the preconditioning of sand material by acid-washing prior to transport experiments thereby removing the metal-oxide and oxyhydroxide based impurities from the sand surface. A model sensitivity analysis was conducted to study the possible effects of particle velocity, particle size, influent concentration, ionic strength, and sand size on particle-particle and particle-collector interactions under CFT, MRC, and 2S models. Results showed an increase of mass recovery percentages (58-88%) by all models under various particle velocities (0.82-82 m/day) and decrease of mass recovery percentages (85-41%) over the range of IS (1-10 mM). All models predicted an ascending effluent mass recovery as FLG size increased (100-1000 μm). The CFT simulation showed no sensitivity to influent concentration, however, MRC and 2S models exhibited enhancement of mass recovery percentage as FLG concentration increased from 10 to 1000 μg/l in the influent. The simulation results of all three models over a range of sand size (100-1000 μm) suggested that increasing sand size enhanced the transport of FLG in the packed sand which results in larger effluent FLG recovery. As the OMs concentrations increased from 0.8 to 50 mg total organic carbon (TOC)/l in the system, the unbounded sub-class of 2S showed the best outcomes (i.e. 𝑁𝑆𝑆𝑅2𝑆=0.0084% vs 𝑁𝑆𝑆𝑅𝑀𝑅𝐶=0.027% vs 𝑁𝑆𝑆𝑅𝐶𝐹𝑇=0.034). Simulation results from all models predicted that attachment efficiency decreases with increasing OM concentration consistent with the observed enhancement of FLG mobility at higher OM levels. FLG detachment rate coefficient slightly increased with an increase of OM concentration in the influent. The findings of this study provide additional insight on model selection for predictive simulation of the transport of FLG-NPs under IS and OMs levels representative of typical shallow freshwater aquifers. The unbounded four-parameter sub-class of 2S exhibited a numerical advantage in comparison with CFT and MRC models for estimating FLG mobility parameters at low IS (1 mM NaCl) and high OMs concentration (50 mg TOC/l). However, the CFT model yielded similar goodness of fit values very similar to 2S and MRC models at high IS (100 mM NaCl) and low OMs concentration (0.8 mg TOC/l).