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

Abstract

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 operat...

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

“…Numerous studies have reported higher aggregation rates in groundwater, surface-water and other natural environmental systems when compared to quiescent batch experiments. 34,38,58,59 The results from this study demonstrate that this effect can be understood in terms of systems where, even in the absence of hydrodynamic shear, particle suspensions are to some extent prevented from sedimentation. Such effects are simulated here by continuous rotation in a slowmoving cylinder, which models slow flow through tortuous pore networks in natural systems which are characteristic of changing flow directions and mixing of old and new particle populations.…”

“…In GW system, large aggregates attached to porous medium solid surfaces can be translated, rolled over and collide with each other, thereby aggregating in the retained phase. 32,38 They can also be detached and transported to a new pore where they can interact with new NP or aggregates, 32,38 whether in the suspended phase or in the retained phase. Likewise, in a SW system the aggregates which have already settled onto deeper depths, can be transported with sediments or be resuspended where they could encounter new particles.…”

“…[34][35][36][37] Typically, current experimental techniques investigating NP aggregation dynamics are limited to simple quiescent or turbulent mixing batch experiments which may not adequately capture aggregation conditions in real systems. 38,39 Whilst research into incorporating aggregation models within porous media transport models continues, 38,40,41 steps must be taken to validate the individual aspects of aggregation models in dynamic media. One of these impacts can be the heterogeneous or anisotropic mixing in the population of nanoaggregates induced by the environmental dynamics such as cascading/cycling conditions within GW and SW systems [27][28][29][30]32,33,36,37,[42][43][44] that can modify the particle size distribution (PSD) evolution trends under aggregation/sedimentation conditions.…”

“…The primary aim therefore is to shed light on unexpected higher aggregation rates of NP in GW systems when compared with many standard experimental and modelling results, and on how NP aggregation can be influenced by resuspension and population mixing in SW systems. 34,38,58,59 This may underpin development of new mathematical descriptions of aggregation mechanisms for a more accurate consideration of these mechanisms in models of NP fate and transport in the environment which take other complex concurrent transport/transformation phenomena into account. 38,41,60 Since the largest use of graphene nanomaterials may result from their high strength and flexibility (∼100 stronger than steel), 4 it is possible that they release into the environment as shattered graphene because they may undergo extreme physical or chemical stresses during the usage or upon entering waste streams.…”

Water Recycling via Aquifers for Sustainable Urban Water Quality Management: Current Status, Challenges and Opportunities

“…In addition to pathogen inactivation studies in relation to MAR, there is also research to quantify the retardation of microbes within the aquifer matrix due to adsorption. Modelling of microbial pathogen retardation during passage of recycled water through an aquifer has typically assumed an equilibrium adsorption approach; however, this has been shown to be inadequate [82], and new theoretical models have been developed to quantify adsorption [83].…”