The significance of early and late stages of coupled aggregation and sedimentation in the fate of nanoparticles: measurement and modelling

Despite aggregation’s crucial role in controlling the environmental fate of nanoparticles (NP), the extent to which current models can describe the progressive stages of NP aggregation/sedimentation is still unclear. In this paper, 24 model combinations of two population-balance models (PBMs) and various collision frequency and settling velocity models are used to analyse spatiotemporal variations in the size and concentration of hydroxyapatite (HAp) NP. The impact of initial conditions and variability in attachment efficiency, α, with aggregate size are investigated. Although permeability models perform well in calculating collision frequencies, they are not appropriate for describing settling velocity because of their negative correlation or insensitivity in respect to fractal dimension. Considering both early and late stages of aggregation, both experimental and model data indicate overall mass removal peaks at an intermediate ionic strength (5 mM CaCl2) even though the mean aggregate size continued to increase through higher ionic strengths (to 10 mM CaCl2). This trend was consistent when different approaches to the initial particle size distribution (PSD) were used and when a variable or constant α was used. These results point to the importance of accurately considering different stages of aggregation in modeling NP fate within various environmental conditions

Aggregation and sedimentation of shattered graphene oxide nanoparticles (SGO) in dynamic environments: a solid-body rotational approach

Nanoparticle (NP) aggregation is typically investigated in either quiescent or turbulent mixing conditions; neither is fully representative of dynamic natural environments. In groundwater, complex interacting influences of advective-diffusive transport, pore tortuosity, and the arrival of aggregates from up-gradient pores impacts the aggregation behaviour of NPs, whereas in surface waters, continuous mixing of fresh particle and aged aggregate populations amends aggregation rates. To mimic such conditions, a cylinder reactor containing shattered graphene oxide NP (5 times in the rotating system than in the static system. Later (5-13 h) aggregates collided with extensively each other, broke, and reformed on the rotating cylinder wall giving rise to larger, denser aggregates (>1 cm). These results thus shed new light on the differences in aggregation behaviour between porous media and other natural environmental systems compared to quiescent batch experiments

Parameterization and prediction of nanoparticle transport in porous media : a reanalysis using artificial neural network

The continuing rapid expansion of industrial and consumer processes based on nanoparticles (NP) necessitates a robust model for delineating their fate and transport in groundwater. An ability to reliably specify the full parameter set for prediction of NP transport using continuum models is crucial. In this paper we report the reanalysis of a data set of 493 published column experiment outcomes together with their continuum modeling results. Experimental properties were parameterized into 20 factors which are commonly available. They were then used to predict five key continuum model parameters as well as the effluent concentration via artificial neural network (ANN)-based correlations. The Partial Derivatives (PaD) technique and Monte Carlo method were used for the analysis of sensitivities and model-produced uncertainties, respectively. The outcomes shed light on several controversial relationships between the parameters, e.g., it was revealed that the trend of math formula with average pore water velocity was positive. The resulting correlations, despite being developed based on a “black-box” technique (ANN), were able to explain the effects of theoretical parameters such as critical deposition concentration (CDC), even though these parameters were not explicitly considered in the model. Porous media heterogeneity was considered as a parameter for the first time and showed sensitivities higher than those of dispersivity. The model performance was validated well against subsets of the experimental data and was compared with current models. The robustness of the correlation matrices was not completely satisfactory, since they failed to predict the experimental breakthrough curves (BTCs) at extreme values of ionic strengths

Comparison of a new mass-concentration, chain-reaction model with the population-balance model for early- and late-stage aggregation of shattered graphene oxide nanoparticles

Aggregation as an essential mechanism impacting nanoparticle (NP) functionality, fate, and transport in the environment is currently modelled using population-balance equation (PBE) models which are computationally expensive when combined with other continuum-scale reactive transport models. We propose a new simple mass-concentration-based, chain-reaction modelling (CRM) framework to alleviate computational expenses of PBE and potentially to facilitate combination with other fate, transport, and reaction models. Model performance is compared with analytical PBE solution and a standard numerical PBE technique (fixed pivot, FP) by fitting against experimental data (i.e., hydrodynamic diameter and derived count rate of dynamic light scattering used as a representative of mass concentration) for early- and late-stage, aggregation of shattered graphene oxide (SGO) NP across a broad range of solution chemistries. In general, the CRM approach demonstrates a better match with the experimental data with a mean Nash-Sutcliffe model efficiency (NSE) coefficient of 0.345 than the FP model with a mean NSE of 0.29. Comparing model parameters (aggregation rate constant and fractal dimension) obtained from fitting CRM and FP to the experimental data, similar trends or ranges are obtained between the two approaches. Computationally, the modified CRM is an order-of-magnitude faster than the FP technique, suggesting that it can be a promising modelling framework for efficient and accurate modelling of NP aggregation. However, in the scope of this study, reaction rate coefficients of the CRM have been linked to collision frequencies based on simplified and empirical relationships which need improvement in future studies

Continuum-based models and concepts for the transport of nanoparticles in saturated porous media: A state-of-the-science review

Environmental applications of nanoparticles (NP) increasingly result in widespread NP distribution within porous media where they are subject to various concurrent transport mechanisms including irreversible deposition, attachment/detachment (equilibrium or kinetic), agglomeration, physical straining, site-blocking, ripening, and size exclusion. Fundamental research in NP transport is typically conducted at small scale, and theoretical mechanistic modeling of particle transport in porous media faces challenges when considering the simultaneous effects of transport mechanisms. Continuum modeling approaches, in contrast, are scalable across various scales ranging from column experiments to aquifer. They have also been able to successfully describe the simultaneous occurrence of various transport mechanisms of NP in porous media such as blocking/straining or agglomeration/deposition/detachment. However, the diversity of model equations developed by different authors and the lack of effective approaches for their validation present obstacles to the successful robust application of these models for describing or predicting NP transport phenomena. This review aims to describe consistently all the important NP transport mechanisms along with their representative mathematical continuum models as found in the current scientific literature. Detailed characterizations of each transport phenomenon in regards to their manifestation in the column experiment outcomes, i.e., breakthrough curve (BTC) and residual concentration profile (RCP), are presented to facilitate future interpretations of BTCs and RCPs. The review highlights two NP transport mechanisms, agglomeration and size exclusion, which are potentially of great importance in controlling the fate and transport of NP in the subsurface media yet have been widely neglected in many existing modeling studies. A critical limitation of the continuum modeling approach is the number of parameters used upon application to larger scales and when a series of transport mechanisms are involved. We investigate the use of simplifying assumptions, such as the equilibrium assumption, in modeling the attachment/detachment mechanisms within a continuum modelling framework. While acknowledging criticisms about the use of this assumption for NP deposition on a mechanistic (process) basis, we found that its use as a description of dynamic deposition behavior in a continuum model yields broadly similar results to those arising from a kinetic model. Furthermore, we show that in two dimensional (2-D) continuum models the modeling efficiency based on the Akaike information criterion (AIC) is enhanced for equilibrium vs kinetic with no significant reduction in model performance. This is because fewer parameters are needed for the equilibrium model compared to the kinetic model. Two major transport regimes are identified in the transport of NP within porous media. The first regime is characterized by higher particle-surface attachment affinity than particle-particle attachment affinity, and operative transport mechanisms of physicochemical filtration, blocking, and physical retention. The second regime is characterized by the domination of particle-particle attachment tendency over particle-surface affinity. In this regime although physicochemical filtration as well as straining may still be operative, ripening is predominant together with agglomeration and further subsequent retention. In both regimes careful assessment of NP fate and transport is necessary since certain combinations of concurrent transport phenomena leading to large migration distances are possible in either case

Modified MODFLOW-based model for simulating the agglomeration and transport of polymer-modified Fe⁰ nanoparticles in saturated porous media

The solute transport model MODFLOW has become a standard tool in risk assessment and remediation design. However, particle transport models that take into account both particle agglomeration and deposition phenomena are far less developed. The main objective of the present study was to evaluate the feasibility of adapting the standard code MODFLOW/MT3D to simulate the agglomeration and transport of three different types of polymer-modified nanoscale zerovalent iron (NZVI) in one-dimensional (1-D) and two-dimensional (2-D) saturated porous media. A first-order decay of the particle population was used to account for the agglomeration of particles. An iterative technique was used to optimize the model parameters. The model provided good matches to 1-D NZVI-breakthrough data sets, with R 2 values ranging from 0.96 to 0.99, and mass recovery differences between the experimental results and simulations ranged from 0.1 to 1.8 %. Similarly, simulations of NZVI transport in the heterogeneous 2-D model demonstrated that the model can be applied to more complicated heterogeneous domains. However, the fits were less good, with the R 2 values in the 2-D modeling cases ranging from 0.75 to 0.95, while the mass recovery differences ranged from 0.7 to 6.5 %. Nevertheless, the predicted NZVI concentration contours during transport were in good agreement with the 2-D experimental observations. The model provides insights into NZVI transport in porous media by mathematically decoupling agglomeration, attachment, and detachment, and it illustrates the importance of each phenomenon in various situations

Significance of Early and Late Stages of Coupled Aggregation and Sedimentation in the Fate of Nanoparticles: Measurement and Modeling

Despite aggregation’s crucial role in controlling the environmental fate of nanoparticles (NP), the extent to which current models can describe the progressive stages of NP aggregation/sedimentation is still unclear. In this paper, 24 model combinations of two population-balance models and various collision frequency and settling velocity models are used to analyze spatiotemporal variations in the size and concentration of hydroxyapatite (HAp) NP. The impact of initial conditions and variability in attachment efficiency, α, with aggregate size are investigated. Although permeability models perform well in calculating collision frequencies, they are not appropriate for describing settling velocity because of their negative correlation or insensitivity in respect to fractal dimension. Considering both early and late stages of aggregation, both experimental and model data indicate overall mass removal peaks at an intermediate ionic strength (5 mM CaCl₂) even though the mean aggregate size continued to increase through higher ionic strengths (to 10 mM CaCl₂). This trend was consistent when different approaches to the initial particle size distribution were used and when a variable or constant α was used. These results point to the importance of accurately considering different stages of aggregation in modeling NP fate within various environmental conditions

Significance of Early and Late Stages of Coupled Aggregation and Sedimentation in the Fate of Nanoparticles: Measurement and Modeling

Despite aggregation’s crucial role in controlling the environmental fate of nanoparticles (NP), the extent to which current models can describe the progressive stages of NP aggregation/sedimentation is still unclear. In this paper, 24 model combinations of two population-balance models and various collision frequency and settling velocity models are used to analyze spatiotemporal variations in the size and concentration of hydroxyapatite (HAp) NP. The impact of initial conditions and variability in attachment efficiency, α, with aggregate size are investigated. Although permeability models perform well in calculating collision frequencies, they are not appropriate for describing settling velocity because of their negative correlation or insensitivity in respect to fractal dimension. Considering both early and late stages of aggregation, both experimental and model data indicate overall mass removal peaks at an intermediate ionic strength (5 mM CaCl₂) even though the mean aggregate size continued to increase through higher ionic strengths (to 10 mM CaCl₂). This trend was consistent when different approaches to the initial particle size distribution were used and when a variable or constant α was used. These results point to the importance of accurately considering different stages of aggregation in modeling NP fate within various environmental conditions