Modeling reactive transport of polydisperse nanoparticles: assessment of the representative particle approach

Abstract

Objective: our goal was to characterize the uncertainty in the estimates of the mobility and reactivity of polydisperse nanocolloids introduced into computations when a distribution of particle sizes is replaced with a representative particle diameter through ensemble averaging. Methods: an existing colloid and solute transport simulator was modified to account for size distribution of injected particles and was used to model the elution of dissolving silver nanoparticles in 1D porous media in both simplified (ensemble averaging) and more realistic (polydisperse) simulations. Laboratory data on nano-silver dissolution, transport, and size distribution were incorporated from the existing literature. Results: the representative particle approach (RPA) systematically underestimated silver ion speciation and elution (∼10–15% error in all RPA simulations that incorporated experimental size distribution data). RPA resulted in an underestimation of particulate silver elution in some simulated case scenarios but yielded overestimates in other cases. At a reduced interstitial velocity of 0.7 m d⁻¹, RPA underestimated silver elution in both particulate and ionic forms (an overall −6% error in total silver elution estimate). The magnitude of RPA errors was found to correlate positively with the skewness of size distribution, but exhibited a non-monotonic and less sensitive functional dependence on distribution mean. Conclusions: our analysis suggests the absolute RPA error in the particulate and total silver mobility estimates to be less than 5% under the conditions of laboratory column experiments and limited to 10% under the flow conditions of shallow sandy aquifers. For generic highly skewed and bimodal size distributions, RPA estimates fell outside a 10% error margin, demonstrating the importance of incorporating size distribution data in simulations of polydisperse nanoparticles exhibiting highly skewed and/or multi-modal size distributions for an accurate assessment of mobility and reactivity, especially under slow flow conditions typical of field-scale problems.