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

Tools and rules for modelling uptake and bioaccumulation of nanomaterials in invertebrate organisms

Quantification of the uptake and elimination of nanomaterials (NMs) by organisms is key in assessing the environmental risks of NMs.</p

Mathematical modeling the transport of few-layer graphene in saturated porous media

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 ionic strengths (IS) and 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 subclasses 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 subclass 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 subclass 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.As the OMs concentrations increased from 0.8 to 50 total organic carbon (mg (TOC)/L) in the system, the unbounded subclass of 2S showed the best outcomes. 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. The FLG detachment rate coefficient slightly increased with an increase of OM concentration in the influent. The unbounded four-parameter subclass 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)