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An understanding of nanobubble (NB) migration in porous media is needed for potential environmental applications. The solution chemistry is well known to be a critical factor in determining interactions of other colloids and nanoparticles with surfaces. However, little quantitative research has examined the influence of solution chemistry on NB transport. One-dimensional column experiments were therefore conducted to investigate the transport, retention, and release of NBs in glass beads under different solution chemistry conditions. NB concentrations in the effluent were reduced with an increase in ionic strength (IS) or a decrease in pH due to a reduction in the repulsive force between the glass surface and NBs, especially when the solution contained Ca2+ as compared to Na+ and for larger NBs. This result was somewhat surprising because electrostatic and van der Waals interactions for NBs were both repulsive on a homogeneous glass bead surface. NB retention on the surface was explained by ubiquitous nan...

Colloid suspensions commonly exhibit a distribution of sizes, but most transport models only consider a single colloid size. A mathematical model was therefore developed to describe the advective and dispersive transport and first-order retention and release of a stable or aggregating polydispersed colloid suspension in porous media. The colloid size distribution was described using a unimodal or a bimodal lognormal probability density function (PDF), and Brownian aggregation was considered by making lognormal PDF parameters a function of time. Filtration theory was used to predict the retention rate coefficients for the various colloid sizes. The amount of retention for a stable polydispersed suspension was highly dependent on the colloid size distribution parameters, especially for a bimodal lognormal PDF. Increasing the distribution variance produced hyper-exponential retention profiles and an increase or a decrease in colloid retention depending on whether the medium colloid size was close to the optimum size for transport. Aggregation produced a similar decrease in the breakthrough concentrations with injection time as ripening, especially when the sticking efficiency was low. Aggregation effects were much more pronounced at higher input concentration levels, which also produced retention profiles that were increasingly hyper-exponential. Simulation results indicate that the colloid size distribution of stable and aggregating polydispersed suspensions always becomes more uniform and approaches the optimum transport size with increasing distance, suggesting that consideration of polydispersed suspensions is of primary importance near the injection surface.

Although nanoscale surface roughness has been theoretically demonstrated to be a crucial factor in the interaction of colloids and surfaces, little experimental research has investigated the influence of roughness on colloid or silver nanoparticle (AgNP) retention and release in porous media. This study experimentally examined AgNP retention and release using two sands with very different surface roughness properties over a range of solution pH and/or ionic strength (IS). AgNP transport was greatly enhanced on the relatively smooth sand in comparison to the rougher sand, at higher pH, and lower IS and fitted model parameters showed systematic changes with these physicochemical factors. Complete release of the retained AgNPs was observed from the relatively smooth sand when the solution IS was decreased from 40mM NaCl to deionized (DI) water and then the solution pH was increased from 6.5 to 10. Conversely, less than 40% of the retained AgNPs was released in similar processes from the rougher sand. These observations were explained by differences in the surface roughness of the two sands which altered the energy barrier height and the depth of the primary minimum with solution chemistry. Limited numbers of AgNPs apparently interacted in reversible, shallow primary minima on the smoother sand, which is consistent with the predicted influence of a small roughness fraction (e.g., pillar) on interaction energies. Conversely, larger numbers of AgNPs interacted in deeper primary minima on the rougher sand, which is consistent with the predicted influence at concave locations. These findings highlight the importance of surface roughness and indicate that variations in sand surface roughness can greatly change the sensitivity of nanoparticle transport to physicochemical factors such as IS and pH due to the alteration of interaction energy and thus can strongly influence nanoparticle mobility in the environment.

The transport and retention behavior of polymer- (PVP-AgNP) and surfactant-stabilized (AgPURE) silver nanoparticles in carbonate-dominated saturated and unconsolidated porous media was studied at the laboratory scale. Initial column experiments were conducted to investigate the influence of chemical heterogeneity (CH) and nano-scale surface roughness (NR) arising from mixtures of clean, positively charged calcium carbonate sand (CCS), and negatively charged quartz sands. Additional column experiments were performed to elucidate the impact of CH and NR arising from the presence and absence of soil organic matter (SOM) on a natural carbonate-dominated aquifer material. The role of the nanoparticle capping agent was examined under all conditions tested in the column experiments. Nanoparticle transport was well described using a numerical model that facilitated blocking on one or two retention sites. Results demonstrate that an increase in CCS content in the artificially mixed porous medium leads to delayed breakthrough of the AgNPs, although AgPURE was much less affected by the CCS content than PVP-AgNPs. Interestingly, only a small portion of the solid surface area contributed to AgNP retention, even on positively charged CCS, due to the presence of NR which weakened the adhesive interaction. The presence of SOM enhanced the retention of AgPURE on the natural carbonate-dominated aquifer material, which can be a result of hydrophobic or hydrophilic interactions or due to cation bridging. Surprisingly, SOM had no significant impact on PVP-AgNP retention, which suggests that a reduction in electrostatic repulsion due to the presence of SOM outweighs the relative importance of other binding mechanisms. Our findings are important for future studies related to AgNP transport in shallow unconsolidated calcareous and siliceous sands.

Colloid transport and retention in porous media is a common phenomenon in nature. However, retention mechanisms are not fully revealed based on macroscale experimental observations. The pore-network model (PNM) is an effective method to account for the pore structure of a porous medium and provides a direct connection between pore-scale retention mechanisms and macroscale phenomenon. In this study, PNMs with cylindrical pore throats and spherical pore bodies are used to upscale water flow and colloid transport from pore- to macro-scales, taking into consideration surface deposition, hydrodynamic bridging, and straining. Numerical experiments were conducted to investigate the effect of colloid size, initial concentration, and flow velocity of pore water on colloid transport and retention behavior. Results show that hydrodynamic bridging and straining produce hyper-exponential retention profiles, whereas surface deposition due to nanoscale roughness and charge heterogeneity yields exponential or uniform retention profiles. Hydrodynamic bridging will not happen when the colloid size, initial concentration and flow velocity are lower than some threshold value (rp ≤ 500 nm, C0 ≤ 7.1 × 1014 Nc/m3, U0 ≤ 0.1 m/d under the conditions of this study). The relative importance of hydrodynamic bridging in comparison to surface deposition increases with an increase in the colloid size, initial concentration, and flow velocity. The PNM is a useful tool to discriminate different retention mechanisms and to predict colloid transport and retention behavior in porous media.

The concentration of nonionic surfactants like Triton X-100 (TX100) can influence the transport and fate of emerging contaminants (e.g., carbon nanotubes) in porous media, but limited research has previously addressed this issue. This study investigates the co-transport of functionalized multi-walled carbon nanotubes (MWCNTs) and various concentrations of TX100 in saturated quartz sand (QS). Batch experiments and molecular dynamics simulations were conducted to investigate the interactions between TX100 and MWCNTs. Results indicated that the concentration ratio of MWCNTs and TX100 strongly influences the dispersion of MWCNTs and interaction forces between MWCNTs and QS during the transport. Breakthrough curves of MWCNTs and TX100 and retention profiles of MWCNTs were determined and simulated in column studies. MWCNTs strongly enhanced the retention of TX100 in QS due to the high affinity of TX100 for MWCNTs. Conversely, the concentration of TX100 had a non-monotonic impact on MWCNT retention. The maximum transport of MWCNTs in the QS occurred at an input concentration of TX100 that was lower than the critical micelle concentration. This suggests that the relative importance of factors influencing MWCNTs changed with TX100 sorption. Results from interaction energy calculations and modeling of competitive blocking indicate that the predictive ability of interaction energy calculations and colloid filtration theory may be lost because TX100 mainly altered intermolecular forces between the MWCNT and porous media. This study provides new insights into the co-transport of surfactants and MWCNTs in porous media, which can be useful for environmental applications and risk management.

Transport and retention behavior of multi-walled carbon nanotubes (MWCNTs) was studied in mixtures of negatively charged quartz sand (QS) and positively charged goethite-coated sand (GQS) to assess the role of chemical heterogeneity. The linear equilibrium sorption model provided a good description of batch results, and the distribution coefficients (KD) drastically increased with the GQS fraction that was electrostatically favorable for retention. Similarly, retention of MWCNTs increased with the GQS fraction in packed column experiments. However, calculated values of KD on GQS were around 2 orders of magnitude smaller in batch than packed column experiments due to differences in lever arms associated with hydrodynamic and adhesive torques at microscopic roughness locations. Furthermore, the fraction of the sand surface area that was favorable for retention (Sf) was much smaller than the GQS fraction because nanoscale roughness produced shallow interactions that were susceptible to removal. These observations indicate that only a minor fraction of the GQS was favorable for MWCNT retention. These same observations held for several different sand sizes. Column breakthrough curves were always well described using an advective-dispersive transport model that included retention and blocking. However, depth-dependent retention also needed to be included to accurately describe the retention profile when the GQS fraction was small. Results from this research indicate that roughness primarily controlled the retention of MWCNTs, although goethite surfaces played an important secondary role.

Saturated column experiments were conducted to systematically examine the influence of hydration on the detachment of nano- and micro-sized latex colloids (35 nm and 1 μm, respectively) from sand. The colloids were attached on the sand in primary minima (PM) using high ionic strength (IS) NaCl solutions. The PM were predicted to be shallower and located farther from sand surfaces with increasing IS due to the hydration force. Consequently, a greater amount of colloid detachment occurred in deionized water when the colloids were initially deposited at a higher IS. Atomic force microscopy (AFM) examinations showed that both nanoscale protruding asperities and large wedge-like valleys existed on the sand surface. The influence of these surface features on the interaction energies/forces was modeled by approximating the roughness as cosinoidal waves and two intersecting half planes, respectively. The PM were deep and attachment was irreversible at concave regions for all ISs, even if the hydration force was included. Conversely, colloids were weakly attached at protruding asperities due to a reduced PM depth, and thus were responsible for the detachment upon IS reduction. The AFM examinations confirmed that the adhesive forces were enhanced and reduced (or even completely eliminated) at concave and convex locations of sand surfaces, respectively. These results have important implications for surface cleaning and prediction of the transport and fate of hazardous colloids and colloid-associated contaminants in subsurface environments.

Theory developed by Derjaguin, Landau, Verwey, and Overbeek (DLVO) is commonly used to interpret and predict the deposition of particles, but it was originally simplified for spherical particles. Many types of bacteria and particles in nature are not spherical. Previous literature has experimentally shown that particle shape has an effect on drug delivery, retention in porous media, self-assembly, and flotation, but the quantitative interpretation of these results has been hindered by experimental (e.g., uniform rod shaped particles and flow fields at controlled chemistries) and theoretical (e.g., consideration of rod shape particles with different surface orientations) challenges. For example, the deposition of ellipsoidal polystyrene particles has been investigated in the presence of non-DLVO interactions, due to residual poly(vinyl) alcohol, hindering the effect of shape. In our study, bare spherical and bullet-like silica particles of well-defined surface chemistry were used for deposition tests on bare silica surfaces using a Quartz Crystal Microbalance with Dissipation (QCM–D) over six ionic strengths (IS). At the same time, the DLVO theory was modified to consider particle shape and orientation of deposition. We found that particle shape had an effect on deposition at intermediate IS. A modified DLVO approach was able to interpret the deposition of bullet-like silica particles. Specifically, bullet-like silica particles of certain aspect ratio may find angles that minimize repulsive energies and overcome energy barriers so that deposition on the silica surfaces is energetically favorable. Therefore, there are conditions of water chemistry where particle shape and orientation cannot be ignored and their deposition must be systematically investigated.

The roles of graphene oxide (GO) particle geometry, GO surface orientation, surface roughness, and nanoscale chemical heterogeneity on interaction energies, aggregation, retention, and release of GO in porous media were not fully considered in previous studies. Consequently, mechanisms controlling the environmental fate of GO were incompletely or inaccurately quantified. To overcome this limitation, plate-plate interaction energies were modified to account for these factors and used in conjunction with a mathematical model to interpret the results of GO aggregation, retention, and release studies. Calculations revealed that these factors had a large influence on the predicted interaction energy parameters. Similar to previous literature, the secondary minimum was predicted to dominate on smooth, chemically homogeneous surfaces that were oriented parallel to each other, especially at higher ionic strength (IS). Conversely, shallow primary minimum interactions were sometimes predicted to occur on surfaces with nanoscale roughness and chemical heterogeneity due to adsorbed Ca2+ ions, especially when the GO particles were oriented perpendicular to the interacting surface. Experimental results were generally consistent with these predictions and indicated that the primary minimum played a major role in GO retention and the secondary minimum contributed to GO release with IS reduction. Cation exchange (Na+ replacing Ca2+) enhanced GO release with IS reduction when particles were initially deposited in the presence of Ca2+ ions. However, retained GO were always completely recovered into the excess deionized water when the sand pore structure was destroyed during excavation, and this indicates that primary minima were shallow and that the pore structure also played an important role in GO retention. Further evidence for the role of pore structure on GO retention was obtained by conducting experiments in finer textured sand and at higher input concentrations that induced greater aggregation. In both cases, greater GO retention occurred, and retention profiles became more hyperexponential in shape.

The influence of virus type (PRD1 and ΦX174), temperature (flow at 4 and 20°C), a no-flow storage duration (0, 36, 46, and 70 d), and temperature cycling (flow at 20°C and storage at 4°C) on virus transport and fate were investigated in saturated sand-packed columns. The vast majority (84-99.5%) of viruses were irreversibly retained on the sand, even in the presence of deionized water and beef extract at pH = 11. The reversibly retained virus fraction () was small (1.6 × 10 to 0.047) but poses a risk of long-term virus contamination. The value of and associated transport risk was lower at a higher temperature and for increases in the no-flow storage period due to the temperature dependency of the solid phase inactivation. A model that considered advective-dispersive transport, attachment (), detachment (), solid phase inactivation (μ), and liquid phase inactivation (μ) coefficients, and a Langmuirian blocking function provided a good description of the early portion of the breakthrough curve. The removal parameters were found to be in the order of > μ >> μ. Furthermore, μ was an order of magnitude higher than μ for PRD1, whereas μ was two and three orders of magnitude higher than μ for ΦX174 at 4 and 20°C, respectively. Transport modeling with two retention, release, and inactivation sites demonstrated that a small fraction of viruses exhibited a much slower release and solid phase inactivation rate, presumably because variations in the sand and virus surface roughness caused differences in the strength of adhesion. These findings demonstrate the importance of solid phase inactivation, temperature, and storage periods in eliminating virus transport in porous media. This research has potential implications for managed aquifer recharge applications and guidelines to enhance the virus removal by controlling the temperature and aquifer residence time.

Multi-walled carbon nanotubes (MWCNTs) are increasing used in commercial applications and may be released into the environment with anionic surfactants, such as sodium dodecylbenzenesulfonate (SDBS), in sewer discharge. Little research has examined the transport, retention, and remobilization of MWCNTs in the presence or absence of SDBS in porous media with controlled chemical heterogeneity, and batch and column scale studies were therefore undertaken to address this gap in knowledge. The adsorption isotherms of SDBS on quartz sand (QS), goethite coated quartz sand (GQS), and MWCNTs were determined. Adsorption of SDBS (MWCNTs » GQS > QS) decreased zeta potentials for these materials, and produced a charge reversal for goethite. Transport of MWCNTs (5 mg L-1) dramatically decreased with an increase in the fraction of GQS from 0 to 0.1 in the absence of SDBS. Conversely, co-injection of SDBS (10 and 50 mg L-1) and MWCNTs radically increased the transport of MWCNTs when the GQS fraction was 0, 0.1, and 0.3, especially at a higher SDBS concentration, and altered the shape of retention profile. Mathematical modeling revealed that competitive blocking was not the dominant mechanism for the SDBS enhancement of MWCNT transport. Rather, SDBS sorption increased MWCNT transport by increasing electrostatic and/or steric interactions, or creating reversible interactions on rough surfaces. Sequential injection of pulses of MWCNTs and SDBS in sand (0.1 GQS fraction) indicated that SDBS could mobilize some of retained MWCNTs from the top to deeper sand layers, but only a small amount of released MWCNTs were recovered in the effluent. SDBS therefore had a much smaller influence on MWCNT transport in sequential injection than in co-injection, presumably because of a greater energy barrier to MWCNT release than retention. This research sheds novel insight on the roles of competitive blocking, chemical heterogeneity and nanoscale roughness, and injection sequence on MWCNT retention and release.

The release and retention of in-situ colloids in aquifers play an important role in the sustainable operation of managed aquifer recharge (MAR) schemes. The processes of colloid release, retention, and associated permeability changes in consolidated aquifer sediments were studied by displacing native groundwater with reverse osmosis-treated (RO) water at various flow velocities. Significant amounts of colloid release occurred when: (i) the native groundwater was displaced by RO-water with a low ionic strength (IS), and (ii) the flow velocity was increased in a stepwise manner. The amount of colloid release and associated permeability reduction upon RO-water injection depended on the initial clay content of the core. The concentration of released colloids was relatively low and the permeability reduction was negligible for the core sample with a low clay content of about 1.3%. In contrast, core samples with about 6 and 7.5% clay content exhibited: (i) close to two orders of magnitude increase in effluent colloid concentration and (ii) more than 65% permeability reduction. Incremental improvement in the core permeability was achieved when the flow velocity increased, whereas a short flow interruption provided a considerable increase in the core permeability. This dependence of colloid release and permeability changes on flow velocity and colloid concentration was consistent with colloid retention and release at pore constrictions due to the mechanism of hydrodynamic bridging. A mathematical model was formulated to describe the processes of colloid release, transport, retention at pore constrictions, and subsequent permeability changes. Our experimental and modeling results indicated that only a small fraction of the in-situ colloids was released for any given change in the IS or flow velocity. Comparison of the fitted and experimentally measured effluent colloid concentrations and associated changes in the core permeability showed good agreement, indicating that the essential physics were accurately captured by the model.

It is essential to understand the mechanisms that control virus and bacteria removal in the subsurface environment to assess the risk of groundwater contamination with fecal microorganisms. This study was conducted to explicitly provide a critical and systematic comparison between batch and column experiments. The aim was to investigate the underlying factors causing the commonly observed discrepancies in colloid adsorption process in column and batch systems. We examined the colloid adsorption behavior of four different sizes of carboxylate-modified latex (CML) microspheres, as surrogates for viruses and bacteria, on quartz sand in batch and column experiments over a wide range of solution ionic strengths (IS). Our results show that adsorption of colloids in batch systems should be considered as an irreversible attachment because the attachment/detachment model was found to be inadequate in describing the batch results. An irreversible attachment-blocking model was found to accurately describe the results of both batch and column experiments. The rate of attachment was found to depend highly on colloid size, solution IS and the fraction of the sand surface area favorable for attachment (Sf). The rate of attachment and Sf values were different in batch and column experiments due to differences in the hydrodynamic of the system, and the role of surface roughness and pore structure on colloid attachment. Results from column and batch experiments were generally not comparable, especially for larger colloids (≥0.5μm). Predictions based on classical DLVO theory were found to inadequately describe interaction energies between colloids and sand surfaces.

Understanding the fate and transport of engineered nanoparticles (ENPs) in subsurface environments is required for developing the best strategy for waste management and disposal of these materials. In this study, the deposition and release of quantum dot (QD) nanoparticles were studied in saturated sand columns. The QDs were first deposited in columns using 100 mM NaCl or 2 mM CaC12 solutions. Deposited QDs were then contacted with deionized (DI) water and/or varying Na(+) concentrations to induce release. QDs deposited in 100 mM Na(+) were easily reversible when the column was rinsed with DI water. Conversely, QDs deposited in the presence of Ca(2+) exhibited resistance to release with DI water. However, significant release occurred when the columns were flushed with NaCl solutions. This release behavior was explained by cation exchange (Ca(2+) in exchange sites were replaced by Na(+)) which resulted in the breakdown of calcium bridging. We also studied the effect of aging time on the QD release. As the aging time increased, smaller amounts of QDs were released following cation exchange. However, deposited QDs were subsequently released when the column was flushed with DI water. The release behavior was modeled using a single first-order kinetic release process and changes in the maximum solid phase concentration of deposited QDs with transition in solution chemistry. The results of this study demonstrate that the presence of carboxyl groups on ENPs and divalent ions in the solution plays a key role in controlling ENP mobility in the subsurface environment.

A balance of applied hydrodynamic (T(H)) and resisting adhesive (T(A)) torques was conducted over a chemically heterogeneous porous medium that contained random roughness of height h(r) to determine the fraction of the solid surface area that contributes to colloid immobilization (S(f)*) under unfavorable attachment conditions. This model considers resistance due to deformation and the horizontal component of the adhesive force (F(AT)), spatial variations in the pore scale velocity distribution, and the influence of hr on lever arms for T(H) and T(A). Values of S(f)* were calculated for a wide range of physicochemical properties to gain insight into mechanisms and factors influencing colloid immobilization. Colloid attachment processes were demonstrated to depend on solution ionic strength (IS), the colloid radius (r(c)), the Young's modulus (K), the amount of chemical heterogeneity (P+), and the Darcy velocity (q). Colloid immobilization was also demonstrated to occur on a rough surface in the absence of attachment. In this case, S(f)* depended on IS, r(c), the roughness fraction (f0), h(r), and q. Roughness tended to enhance T(A) and diminish T(H). Consequently, the effect of IS on S(f)* was enhanced by h(r) relative to attachment. In contrast, the effects of r(c) and q on S(f)* were diminished by hr in comparison to attachment. Colloid immobilization adjacent to macroscopic roughness locations shares many similarities to grain-grain contact points and may be viewed as a type of straining process. In general, attachment was more important for higher IS and variance in the secondary minimum, and for smaller r(c), q, and K, but diffusion decreased these values. Conversely, straining was dominant for the opposite conditions. Discrepancies in the literature on mechanisms of colloid retention are likely due to a lack of consideration of all of these factors.

The mean and variance of the colloid interaction energy (Φ*) as a function of separation distance (h) were calculated on physically and/or chemically heterogeneous solid surfaces at the representative elementary area (REA) scale. Nanoscale roughness was demonstrated to have a significant influence on the colloid interaction energy for different ionic strengths. Increasing the roughness height reduced the magnitude of the energy barrier (Φmax*) and the secondary minimum (Φ2min*). Conversely, increasing the fraction of the solid surface with roughness increased the magnitude of Φmax* and Φ2min*. Our results suggest that primary minimum interactions tend to occur in cases where only a portion of the solid surface was covered with roughness (i.e., isolated roughness pillars), but their depths were shallow as a result of Born repulsion. The secondary minimum was strongest on smooth surfaces. The variance in the interaction energy was also a strong function of roughness parameters and h. In particular, the variance tended to increase with the colloid size, the magnitude of Φ*, the height of the roughness, and especially the size (cross-sectional area) of the heterogeneity. Nonzero values of the variance for Φ2min* implied the presence of a tangential component of the adhesive force and a resisting torque that controls immobilization and release for colloids at this location. Heterogeneity reduced the magnitude of Φ* in comparison to the corresponding homogeneous situation. Physical heterogeneity had a greater influence on mean properties of Φ* than similar amounts of chemical heterogeneity, but the largest reduction occurred on surfaces with both physical and chemical heterogeneity. The variance in Φ* tended to be higher for a chemically heterogeneous solid.

Elucidating and quantifying the transport of industrial nanoparticles (e.g. silver, carbon nanotubes, and graphene oxide) and other colloid-size particles such as viruses and bacteria is important to safeguard and manage the quality of the subsurface environment. Analytic solutions were derived for aqueous and solid phase colloid concentrations in a porous medium where colloids were subject to advective transport and reversible time and/or depth-dependent retention. Time-dependent blocking and ripening retention were described using a Langmuir-type equation with a rate coefficient that respectively decreased and increased linearly with the retained concentration. Depth-dependent retention was described using a rate coefficient that is a power-law function of distance. The stream tube modeling concept was employed to extend these analytic solutions to transport scenarios with two different partitioning processes (i.e., two types of retention sites). The sensitivity of concentrations was illustrated for the various time- and/or depth-dependent retention model parameters. The developed analytical models were subsequently used to describe breakthrough curves and, in some cases, retention profiles from several published column studies that employed nanoparticle or pathogenic microorganisms. Simulations results provided valuable insights on causes for many observed complexities associated with colloid transport and retention, including: increasing or decreasing effluent concentrations with continued colloid application, delayed breakthrough, low concentration tailing, and retention profiles that are hyper-exponential, exponential, linear, or non-monotonic with distance.

Values of the applied hydrodynamic torque ( T applied ) and the resisting adhesive torque ( T adhesion ) will determine whether a colloid will be immobilized ( T applied ≤ T adhesion ) or roll ( T applied > T adhesion ) on a solid water interface. Previous literature has demonstrated in 1–2 collector (grain) systems that the influence of T applied on colloid retention can be significant under unfavorable attachment conditions and that only a fraction of the solid surface may contribute to retention. However, many questions remain on how to obtain, analyze, and upscale information on the forces and torques that act on colloids near solid surfaces in porous media. To address some of these gaps in knowledge, high resolution pore-scale water flow simulations were conducted for sphere packs (25 spheres) over a range of Darcy velocities, grain sizes and distributions, and porosities. The spatial variability of T applied was calculated from this information, and successfully described using a lognormal cumulative density function (CDF). Linear interpolation and scaling techniques were subsequently used to predict the lognormal CDF of T applied for various colloid sizes, grain sizes and distributions, and water velocities. The lognormal CDF of T applied was then evaluated at select values of T adhesion (i.e, interaction energy) to quantify the fraction and locations on the solid surface that contributes to colloid retention ( S f ), and the theoretical maximum solid phase concentration of retained colloids ( S max ).

Saturated packed column and micromodel transport studies were conducted to gain insight on mechanisms of colloid retention and release under unfavorable attachment conditions. The initial deposition of colloids in porous media was found to be a strongly coupled process that depended on solution chemistry and pore space geometry. During steady state chemical conditions, colloid deposition was not a readily reversible process, and micromodel photos indicated that colloids were immobilized in the presence of fluid drag. Upon stepwise reduction in eluting solution ionic strength (IS), a sharp release of colloids occurred in each step which indicates that colloid retention depends on a balance of applied (hydrodynamic) and resisting (adhesive) torques which varied with pore space geometry, surface roughness, and interaction energy. When the eluting fluid IS was reduced to deionized water, the final retention locations occurred near grain-grain contacts, and colloid aggregation was sometimes observed in micromodel experiments. Significant amounts of colloid retention hysteresis with IS were observed in the column experiments, and it depended on the porous medium (glass beads compared with sand), the colloid size (1.1 and 0.5 mum), and on the initial deposition IS. These observations were attributed to weak adhesive interactions that depended on the double layer thickness (e.g., the depth of the secondary minimum and/or nanoscale heterogeneity), colloid mass transfer on the solid phase to regions where the torque and force balances were favorable for retention, the number and extent of grain-grain contacts, and surface roughness.

The coupled role of solution ionic strength (IS), hydrodynamic force, and pore structure on the transport and retention of viable Cryptosporidium parvum oocyst was investigated via batch, packed-bed column, and micromodel systems. The experiments were conducted over a wide range of IS (0.1-100 mM), at two Darcy velocities (0.2 and 0.5 cm/min), and in two sands (median diameters of 275 and 710 microm). Overall, the results suggested that oocyst retention was a complex process that was very sensitive to the solution IS, the Darcy velocity, and the grain size. Increasing IS led to enhanced retention of oocysts in the column, which is qualitatively consistent with predictions of Derjaguin-Landau-Verwey-Overbeek theory. Conversely, increasing velocity and grain size resulted in less retention of oocysts in the column due to the difference in the fluid drag force and the rates of mass transfer from the liquid to the solid phase and from high to low velocity regions. Oocyst retention was controlled by a combined role of low velocity regions, weak attractive interactions, and/or steric repulsion. The contribution of each mechanism highly depended on the solution IS. In particular, micromodel observations indicated that enhanced oocyst retention occurred in low velocity regions near grain-grain contacts under highly unfavorable conditions (IS=0.1 mM). Oocyst retention was also found to be influenced by weak attractive interactions (induced by the secondary energy minimum, surface roughness, and/or nanoscale chemical heterogeneity) when the IS=1 mM. Reversible retention of oocysts to the sand in batch and column studies under favorable attachment conditions (IS=100 mM) was attributed to steric repulsion between the oocysts and the sand surface due to the presence of oocyst surface macromolecules. Comparison of experimental observations and theoretical predictions from classic filtration theory further supported the presence of this weak interaction due to steric repulsion.

The coupled influence of input suspension concentration (Ci), ionic strength (IS), and hydrodynamics on the transport and retention of 1.1 microm carboxyl-modified latex colloids in saturated quartz sand (150 microm) under unfavorable attachment conditions (pH 10) was investigated. The percentage of retained colloids in column experiments decreased with Ci at intermediate IS conditions (31 or 56 mM) when colloids were weakly associated with the solid phase by a shallow secondary energy minima. In contrast, the effects of Ci on colloid retention were absent when IS was too low (6 mM) or too high (106 mM). The concentration effects under intermediate IS conditions were dependent on the system hydrodynamics, magnitude of Ci, and injection order of Ci, but they were largely independent of the input colloid mass. These observations were explained in part by time- and concentration-dependent filling of retention sites. Only a small fraction of the solid surface area was found to contribute to retention when IS was 31 mM, and micromodel observations indicated that colloid retention was enhanced in lower velocity regions of the pore space that occurred near grain-grain contacts. Consequently, retention profiles for IS = 31 mM conditions were increasingly nonexponential at lower values of Ci (during filling), whereas the observed concentration effect was largely eliminated as retention locations became filled. In addition, micromodel observations indicated that liquid and solid phase mass transfer of colloids to retention locations was influenced by Ci under intermediate IS conditions. Higher values of Ci are expected to produce less relative mass transfer to retention locations due to increased numbers of collisions that knock weakly associated colloids off the solid phase. Hence, the concentration effects were found to be largely independent of input colloid mass during filling of retention sites.

Our ability to accurately simulate the transport and retention of colloids in the vadose zone is currently limited by our lack of basic understanding of colloid retention processes that occur at the pore scale. This review discusses our current knowledge of physical and chemical mechanisms, factors, and models of colloid transport and retention at the interface, collector, and pore scales. The interface scale is well suited for studying the interaction energy and hydrodynamic forces and torques that act on colloids near interfaces. Solid surface roughness is reported to have a significant influence on both adhesive and applied hydrodynamic forces and torques, whereas non-Derjaguin–Landau–Verwey–Overbeek (DLVO) forces such as hydrophobic and capillary forces are likely to play a significant role in colloid interactions with the air–water interface. The flow field can be solved and mass transfer processes can be quantified at the collector scale. Here the potential for colloid attachment in the presence of hydrodynamic forces is determined from a balance of applied and adhesive torques. The fraction of the collector surface that contributes to attachment has been demonstrated to depend on both physical and chemical conditions. Processes of colloid mass transfer and retention can also be calculated at the pore scale. Differences in collector- and pore-scale studies occur as a result of the presence of small pore spaces that are associated with multiple interfaces and zones of relative flow stagnation. Here a variety of straining processes may occur in saturated and unsaturated systems, as well as colloid size exclusion. Our current knowledge of straining processes is still incomplete, but recent research indicates a strong coupling of hydrodynamics, solution chemistry, and colloid concentration on these processes, as well as a dependency on the size of the colloid, the solid grain, and the water content.

Transport of colloidal particles in porous media is governed by the rate at which the colloids strike and stick to collector surfaces. Classic filtration theory has considered the influence of system hydrodynamics on determining the rate at which colloids strike collector surfaces, but has neglected the influence of hydrodynamic forces in the calculation of the collision efficiency. Computational simulations based on the sphere-in-cell model were conducted that considered the influence of hydrodynamic and Derjaguin-Landau-Verwey-Overbeek (DLVO) forces on colloid attachment to collectors of various shape and size. Our analysis indicated that hydrodynamic and DLVO forces and collector shape and size significantly influenced the colloid collision efficiency. Colloid attachment was only possible on regions of the collector where the torque from hydrodynamic shear acting on colloids adjacent to collector surfaces was less than the adhesive (DLVO) torque that resists detachment. The fraction of the collector surface area on which attachment was possible increased with solution ionic strength, collector size, and decreasing flow velocity. Simulations demonstrated that quantitative evaluation of colloid transport through porous media will require nontraditional approaches that account for hydrodynamic and DLVO forces as well as collector shape and size.

Bioremediation is a cost-efficient cleanup technique that involves the use of metabolically active bacteria to degrade recalcitrant pollutants. To further develop this technique it is important to understand the migration and deposition behavior of metabolically active bacteria in unsaturated soils. Unsaturated transport experiments were therefore performed using Deinococcus radiodurans cells that were harvested during the log phase and continuously supplied with nutrients during the experiments. Additional experiments were conducted using this bacterium in the stationary phase. Different water saturations were considered in these studies, namely 100 (only stationary phase), 80, and 40%. Results from this study clearly indicated thatthe physiological state of the bacteria influenced its transport and deposition in sands. Metabolically active bacteria were more hydrophobic and exhibited greater deposition than bacteria in the stationary phase, especially at a water saturation of 40%. The breakthrough curves for active bacteria also had low concentration tailing as a result of cell growth of retained bacteria that were released into the liquid phase. Collected breakthrough curves and deposition profiles were described using a model that simultaneously considers both chemical attachment and physical straining. New concepts and hypotheses were formulated in this model to include biological aspects associated with bacteria growth inside the porous media.

A modeling framework is presented to determine fundamental parameters and controlling mechanisms of colloid (microbes, clays, and nanoparticles) retention and release on surfaces of porous media that exhibit wide distributions of nanoscale chemical heterogeneity, nano- to microscale roughness, and pore water velocity. Primary and/or secondary minimum interactions in the zone of electrostatic influence were determined over the heterogeneous solid surface. The Maxwellian kinetic energy model was subsequently employed to determine the probability of immobilization and diffusive release of colloids from each of these minima. In addition, a balance of applied hydrodynamic and resisting adhesive torques was conducted to determine locations of immobilization and hydrodynamic release in the presence of spatially variable water flow and microscopic roughness. Locations for retention had to satisfy both energy and torque balance conditions for immobilization, whereas release could occur either due to diffusion or hydrodynamics. Summation of energy and torque balance results over the elementary surface area of the porous medium provided estimates for colloid retention and release parameters that are critical to predicting environmental fate, including the sticking and release efficiencies and the maximum concentration of retained colloids on the solid phase. Nanoscale roughness and chemical heterogeneity produced localized primary minimum interactions that controlled long-term retention, even when mean chemical conditions were unfavorable. Microscopic roughness played a dominant role in colloid retention under low ionic strength and high hydrodynamic conditions, especially for larger colloids.

This paper examines the critical role of surface roughness (both nano- and micro-scale) on the processes of colloid retention and release in porous media under steady-state and transient chemical conditions. Nanoscale surface roughness (NSR) in the order of a few nanometers, which is common on natural solid surfaces, was incorporated into extended-DLVO calculations to quantify the magnitudes of interaction energy parameters (e.g. the energy barrier to attachment, ΔΦa , and detachment, ΔΦd , from a primary minimum). This information was subsequently used to explain the behavior of colloid retention and release in column and batch experiments under different ionic strength (IS) and pH conditions. Results demonstrated that the density and height of NSR significantly influenced the interaction energy parameters and consequently the extent and kinetics of colloid retention and release. In particular, values of ΔΦa and ΔΦd significantly decreased in the presence of NSR. Therefore, consistent with findings of column experiments, colloid retention in the primary minimum was predicted to occur at some specific locations on the sand surface, even at low IS conditions. However, NSR yielded a much weaker primary minimum interaction compared with that of smooth surfaces. Colloid release from primary minima upon decreasing IS and increasing pH was attributed to the impact of NSR on the values of ΔΦd . Pronounced differences in the amount of colloid retention in batch and column experiments indicated that primary minimum interactions were weak even at high IS conditions. Negligible colloid retention in batch experiments was attributed to hydrodynamic torques overcoming adhesive torques, whereas significant colloid retention in column experiments was attributed to nano- and micro-scale roughness which would dramatically alter the lever arms associated with hydrodynamic and adhesive torques.

Strongly sorbing chemicals (e.g., heavy metals, radionuclides, pharmaceuticals, and explosives) in porous media are associated predominantly with the solid phase, which is commonly assumed to be stationary. However, recent field- and laboratory-scale observations have shown that in the presence of mobile colloidal particles (e.g., microbes, humic substances, clays, and metal oxides), colloids can act as pollutant carriers and thus provide a rapid transport pathway for strongly sorbing contaminants. To address this problem, we developed a one-dimensional numerical model based on the HYDRUS-1D software package that incorporates mechanisms associated with colloid and colloid-facilitated solute transport in variably saturated porous media. The model accounts for transient variably saturated water flow, and for both colloid and solute movement due to advection, diffusion, and dispersion, as well as for solute movement facilitated by colloid transport. The colloid transport module additionally considers the processes of attachment/detachment to/from the solid phase and/or the air–water interface, straining, and/or size exclusion. Various blocking and depth dependent functions can be used to modify the attachment and straining coefficients. The solute transport module uses the concept of two-site sorption to describe nonequilibrium adsorption–desorption reactions to the solid phase. The module further assumes that contaminants can be sorbed onto surfaces of both deposited and mobile colloids, fully accounting for the dynamics of colloid movement between different phases. Application of the model is demonstrated using selected experimental data from published saturated column experiments, conducted to investigate the transport of Cd in the presence of Bacillus subtilis spores in alluvial gravel aquifer media. Numerical results simulating bacteria transport, as well as the bacteria-facilitated Cd transport, are compared with experimental results. A sensitivity analysis of the model to various parameters is also presented.

This study examines the volatilization behavior of binary nonaqueous phase liquid (NAPL) mixtures consisting of styrene, and toluene or tetrachloroethylene (PCE). Residual NAPL saturations were emplaced in unsaturated (residual water saturation) soil columns packed with Wagner 50-80 sand. Initial column effluent concentrations were measured for the NAPL mixtures at several pore gas phase velocities. Rate-limited volatilization occurred at higher gas phase pore velocities, and mass transfer coefficients could be reasonably predicted with a correlation developed from single component NAPL volatilization data. Long-term volatilization studies for the binary NAPL mixtures were also conducted. The effluent concentrations for both NAPL components were observed to be initially proportional to their mole fractions. After the more volatile component became depleted, a rapid drop in the effluent concentration of this component was accompanied by an increase in the mole fraction and effluent concentration of the remaining constituent to near saturated values until the free phase NAPL was volatilized. The final stage of removal was associated with a dramatic decrease in effluent concentration, attributed to reduction in the gas-NAPL interfacial area, followed by low concentration tailing. The tailing and subsequent flow interruption behavior are likely a consequence of rate-limited desorption. Equilibrium and rate-limited simulations of the long-term volatilization experiments did not provide a satisfactory description of the data. A simulation that included a fixed concentration gradient and fitted activity coefficients provided a better characterization of the volatilization data. Various potential explanations for this “fixed gradient” volatilization behavior were considered, but additional research is needed to test these hypotheses.

Colloid transport studies were conducted in water-saturated physically heterogeneous systems to gain insight into the processes controlling transport in natural aquifer and vadose zone (variably saturated) systems. Stable monodispersed colloids (carboxyl latex microspheres) and porous media (Ottawa quartz sands) that are negatively charged were employed in these studies. The physically heterogeneous systems consisted of various combinations of a cylindrical sand lens embedded in the center of a larger cylinder of matrix sand. Colloid migration was found to strongly depend on colloid size and physical heterogeneity. A decrease in the peak effluent concentration and an increase in the colloid mass removal in the sand near the column inlet occurred when the median grain size of the matrix sand decreased or the size of the colloid increased. These observations and numerical modeling of the transport data indicated that straining was sometimes an important mechanism of colloid retention. Experimental and simulation results suggest that attachment was more important when the colloid size was small relative to the sand pore size. Transport differences between conservative tracers and colloids were attributed to flow bypassing of finer-textured sands, colloid retention at interfaces of soil textural contrasts, and exclusion of colloids from smaller pore spaces. Colloid retention in the heterogeneous systems was also influenced by spatial variations in the pore water velocity. Parameters in straining and attachment models were successfully optimized to the colloid transport data. The straining model typically provided a better description of the effluent and retention data than the attachment model, especially for larger colloids and finer-textured sands. Consistent with previously reported findings, straining occurred when the ratio of the colloid and median grain diameters was >0.5%.

Numerical simulations examine the migration, entrapment, and mass recovery behavior of DNAPLs in aquifer systems with coupled textural and wettability variations. Permeability fields of varying degrees of heterogeneity (i.e., differing r 2ðkÞ ) were generated with sequential Gaussian simulation, using geostatistical parameters derived from core grain size measurements in a sandy glacial outwash aquifer. Organic-wet mass fraction, a representative metric for wettability, was correlated to porous media permeability. A multiphase flow simulator incorporating wettability-dependent constitutive relationships for capillary behavior is used to generate residual saturation distributions for tetrachloroethene (PCE) spill events in these synthetic aquifers. Simulated saturation distributions then serve as initial conditions for compositional simulations of PCE dissolution, to examine the effect of coupled wettability and permeability variations on DNAPL mass recovery. Simulations reveal considerable differences in predicted depth of organic liquid penetration, extent of vertical spreading, and magnitude of maximum entrapped saturation for the various modeled scenarios. These differences are directly linked to observable variations in effluent concentration and mass recovery predictions in the aqueous phase flushing simulations. Results suggest that mass recovery behavior may be highly realization dependent and not closely correlated with geostatistical parameters. � 2004 Elsevier Ltd. All rights reserved.

Accurately predicting the fate and transport of graphene oxide (GO) in porous media is critical to assess its environmental impact. In this work, sand column experiments were conducted to determine the effect of input concentration and grain size on transport, retention, and size perturbation of GO in saturated porous media. The mobility of GO in the sand columns reduced with decreasing grain size and almost all GO were retained in fine sand columns for all of the tested conditions. This result can be explained with colloid filtration and XDLVO theories. Input concentration also influenced the retention and transport of GO in the sand columns because of the ‘blocking’ mechanism that reduces the particle retention rate. After passing through the column, average GO sizes increased dramatically. In addition, the sizes of GO retained in the sand also increased with travel distance. These results suggested that transport through the porous media induced GO aggregation. A mathematical model based on the advection–dispersion equation coupled with the second-order kinetics to reflect the blocking effect simulated the experimental data well.

Available data from a recent study of entrapped tetrachloroethylene (PCE) dissolution (Bradford et al., 1999) reveal that soil wettability and grain size distribution characteristics can dramatically influence dissolution behavior. This paper explores the modeling of the long-term dissolution of residual nonaqueous phase liquids (NAPLs) entrapped in fractional wettability porous media. Here dissolution is modeled with a linear driving force expression, and the lumped mass transfer coefficient is represented using independent estimates of the film mass transfer coefficient and the NAPL-water interfacial area. In fractional wettability porous media the NAPL saturation is assumed to occur as both NAPL films and ganglia, and NAPL-water interfacial area is thus modeled as the sum of contributions from films and ganglia. The interfacial area model is calibrated by fitting several parameters to the available experimental data. Trends in fitted parameters suggest that (1) residual NAPL ganglia are less accessible to a flowing aqueous phase in finer textured soils; (2) the dissolution rate depends on the interfacial area in a nonlinear manner; and (3) NAPL ganglia entrapment depends on system wettability and grain size distribution. Mass transfer coefficient correlations are established from these fitted parameters. The calibrated model predicts that for a given NAPL saturation, an increasing PCE-wet sand fraction results in longer periods of high effluent concentrations, followed by increased rates of concentration reduction and more persistent subsequent low- concentration tailing. The dependence of dissolution behavior on mean grain size is also captured by this model. Simulations demonstrate a significant improvement in dissolution predictions using the proposed model in comparison with those obtained using a previously developed mass transfer correlation based upon a power law function of saturation.

Theoretical and modeling studies for the prediction of nonaqueous phase liquid (NAPL) entrapment and dissolution have largely assumed that the soil is preferentially water-wet. Many natural systems, however, have both water- and NAPL-wet solids as a result of spatial and temporal variations in fluid and soil properties. This condition is referred to as fractional wettability. This work presents long-term dissolution data for tetrachloroethylene (PCE) entrapped in porous media representing a range of grain sizes, gradations, and fractional wettabilities. Entrapment data suggest that for given wettability conditions, initial residual NAPL saturations tend to increase with decreasing soil mean grain size. In addition, residual NAPL saturations in finer-textured sands were observed to reach a minimum at intermediate wetting conditions, whereas residual saturations in coarser-textured media decreased asymptotically with increasing fraction of NAPL-wet sand. In dissolution studies, an increase in the NAPL-wet fraction tended to result in decreased PCE dissolution time, characterized by a longer period of high effluent concentrations, followed by a more rapid reduction in concentration. Increases in NAPL- wet fraction, however, were also associated with higher sorptive capacities, leading to enhanced PCE concentration tailing. The influence of fractional wettability on PCE dissolution behavior was also found to depend on media grain size distribution, particularly for more water-wet soils. Experimental observations are discussed in the context of pore-scale conceptual models of entrapment.

Organic liquids are common polluters of the subsurface environment. Once released, these nonaqueous phase liquids (NAPLs) tend to become entrapped within soils and geologic formations where they may serve as long-term contaminant reservoirs. The interphase mass transfer from such entrapped residuals will ultimately control environmental exposure levels as well as the persistence and/or remedial recovery of these contaminants in the subsurface. This paper summarizes National Institute of Environmental Health Sciencessponsored research designed to investigate and quantify NAPL entrapment and interphase mass transfer in natural porous media. Results of soil column and batch experiments are presented that highlight research findings over the past several years. These experiments explore dissolution and volatilization of hydrocarbons and chlorinated solvents in sandy porous media. Initial concentration levels and long-term recovery rates are shown to depend on fluid flow rate, soil structure, NAPL composition, and soil wetting characteristics. These observations are explained in the context of conceptual models that describe entrapped NAPL morphology and boundary layer transport. The implications of these laboratory findings on the subsurface persistence and recovery of entrapped NAPLs are discussed. -- Environ Health Perspect 106(Suppl 4):1083-1095 (1998).

A nonhydrostatic model for overland flow is developed for the purpose of providing the framework for predicting the fate and transport of chemicals under surface irrigation. The technique is based on the turbulent Navier-Stokes equations for the surface wave and the Richards equation for the movement of moisture in the underlying porous medium. The model consists of a novel two-dimensional combination of the marker-and-cell and finite-element methods and utilizes a deforming computational grid that automatically adapts to moving wave fronts in the solution. Convergence and conservation tests are performed to demonstrate the robustness of the model. Results are presented for laminar and turbulent flow cases and compared to similar computations based on traditional depth-averaged models.

Knowledge of the fluid-fluid and fluid-solid interfacial areas is important to better understand and quantify many flow and transport processes in porous media. This paper presents estimates for interfacial areas of porous media containing two or three fluids from measured capillary pressure (Pc)-saturation (S) relations. The thermodynamic treatment of two-fluid Pc−S relations presented by Morrow (1970) served as the basis for the predictions. In media containing two fluids (air-oil, air-water, oil-water), the solid-nonwetting interfacial area ( A sN ∗ ) equaled zero when the solid was completely wetted by the wetting fluid. The area under the Pc−S curve was directly proportional to the nonwetting-wetting interfacial area ( A NW ∗ ). If the solid surface was not completely wetted by one fluid, A NW ∗ and A sN ∗ were estimated by weighed partitioning of the area under the Pc−S curve. For porous media with fractional wettability, the procedure was applied separately to water- and oil-wet regions. The values of A NW ∗ and A sN ∗ were highest and lowest, respectively, in systems that were strongly wetted. In three-fluid media the wetting and spreading behavior of the liquids greatly affected the estimated interfacial areas. For a water-wet medium with a continuous intermediate oil phase, the interfacial areas were predicted from Pc−S data in a similar manner as for two-fluid media. The oil-water and oil-solid interfacial areas were estimated from the oil-water Pc−S curve, while the air-oil interfacial area was obtained from the air-oil Pc−S curve. For a fractional wettability or oil-wet medium there may be as many as six interfaces. These interfacial areas were estimated from three-fluid Pc−S relations based on previously developed methods for predicting three-fluid Pc−S relations from two-fluid data.

Knowledge of the capillary pressure-saturation (PC-S) relations of porous media is essential for the research and management of multiphase flow and transport. Indirect methods have often been used to predict PC-S curves, since the actual measurement of all PC-S curves may be cumbersome. Existing methods to predict the Pc- S relations for porous media with fractional wettability, however, are generally inadequate. This paper reports on methods to quantify PC-S curves of such media that contain two or three fluids (air, oil, and water). The prediction of oil-water PC-S relations from air-oil or air-water PC-S data through mere scaling is not possible since the oil-water capillary pressure may be positive or negative in fractional wettability media. We successfully predicted the oil-water PC-S curve using a linear transformation of air-oil PC-S data. In three-fluid media with fractional wettability the prediction of three-fluid from two-fluid PC-S relations using only Leverett's assumption is unreliable, since both water and oil act as intermediate fluid. We predicted the three-fluid oil-water Pc from two-fluid oil-water or linearly transformed air-oil PC-S data. The three-fluid air-oil Pc could be readily predicted from the two-fluid air-oil PC-S relation for a variable oil saturation and a constant water saturation. In contrast, when the water saturation was varied, at a constant oil saturation, the air-oil Pc could only be predicted using an empirical correction for the two-fluid air-oil PC-S data. The three-fluid air-water Pc is obtained as the sum of the oil-water Pc and the air-oil Pc (both water and oil pressures are measured with respect to atmospheric pressure).

Capillary pressure (P c ) - saturation (S) relationships for porous media containing three fluids are often predicted from two-fluid P c -S curves. This practice was investigated for porous media with different wettabilities. Two- and three-fluid P c -S curves were measured, using an automated setup, for sands containing air and water ; air and oil, oil and water, and air, oil, and water. Similar P c -S curves were found for air-oil systems while differences occurred for air-water or oil-water due to differences in hydrophobicity and contact angle hysteresis. Three-fluid P c -S curves could be accurately predicted for hydrophilic media from two-fluid P c -S data with scaling, using fitted contact angles and measured interfacial tensions, and Leverett's assumption. Such predictions were found to be inadequate for hydrophobic media because the intermediate fluid is presumably discontinuous.

It has been widely reported that colloids can travel faster and over longer distances in natural structured porous media than in uniform structureless media used in laboratory studies. The presence of preferential pathways for colloids in the subsurface environment is of concern because of the increased risks for disease caused by microorganisms and colloid-associated contaminants. This study presents a model for colloid transport in dual-permeability media that includes reversible and irreversible retention of colloids and first-order exchange between the aqueous phases of the two regions. The model may also be used to describe transport of other reactive solutes in dual-permeability media. Analytical solutions for colloid concentrations in aqueous and solid phases were obtained using Laplace transformation and matrix decomposition. The solutions proved convenient to assess the effect of model parameters on the colloid distribution. The analytical model was used to describe effluent concentrations for a bromide tracer and 3.2- or 1-μm-colloids that were observed after transport through a composite 10-cm long porous medium made up of a cylindrical lens or core of sand and a surrounding matrix with sand of a different grain size. The tracer data were described very well and realistic estimates were obtained for the pore-water velocity in the two flow domains. An accurate description was also achieved for most colloid breakthrough curves. Dispersivity and retention parameters were typically greater for the larger 3.2-μm-colloids while both reversible and irreversible retention rates tended to be higher for the finer sands than the coarser sand. The relatively small sample size and the complex flow pattern in the composite medium made it difficult to reach definitive conclusions regarding transport parameters for colloid transport.

A simple modeling approach was developed to calculate colloid adhesive parameters for chemically heterogeneous porous media. The area of the zone of electrostatic influence between a colloid and solid-water interface (A(z)) was discretized into a number of equally sized grid cells to capture chemical heterogeneity within this region. These cells were divided into fractions having specific zeta potentials (e.g., negative or positive values). Mean colloid adhesive parameters such as the zeta potential, the minimum and maximum in the interaction energy, the colloid sticking efficiency (α), and the fraction of the solid surface area that contributes to colloid immobilization (S(f)) were calculated for possible charge realizations within A(z). The probability of a given charge realization in A(z) was calculated using a binomial mass distribution. Probability density functions (PDFs) for the colloid adhesive parameters on the heterogeneous surface were subsequently calculated at the representative elementary area (REA) scale for a porous medium. This approach was applied separately to the solid-water interface (SWI) and the colloid, or jointly to both the SWI and colloid. To validate the developed model, the mean and standard deviation of the interaction energy distribution on a chemically heterogeneous SWI were calculated and demonstrated to be consistent with published Monte Carlo simulation output using the computationally intensive grid surface integration technique. Our model results show that the PDFs of colloid adhesive parameters at the REA scale were sensitive to the size of the colloid and the heterogeneity, the charge and number of grid cells, and the ionic strength.

[1] We are grateful for this opportunity to address the comment of Johnson et al. [2009] on our manuscript. Their comment concerns the nature of colloid association with solid surfaces via the secondary energy minimum. There are currently different opinions in the literature on this topic. Johnson et al. [2007] have assumed that colloids associated with collector surfaces via the secondary minimum are ‘‘freely mobile’’ in the presence of fluid drag and can therefore only be immobilized in stagnation regions. In contrast, we have applied a torque balance approach to determine locations where colloid retention is theoretically possible when the driving (hydrodynamic) torque is less than the resisting (adhesive) torque [Bradford et al., 2007; Torkzaban et al., 2007, 2008]. Each of these points of view will be discussed below.

The transport and deposition behavior of Escherichia coli O157: H7 was investigated in saturated packed-bed columns and micromodel systems over a range of ionic strength (IS) (1, 10, and 100 mM) and pH (5.8, 8.4, and 9.2) conditions. At a given IS, elevated solution pH resulted in decreased deposition as a result of the increase in the measured zeta potential of the quartz sand. This deposition trend was consistent with predictions from classic Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Conversely, the E. coil O157:H7 deposition was inversely proportionalto IS (1-100 mM) at high pH conditions (8.4 and 9.2), whereas no effect of IS was observed at pH 5.8. This deposition trend was not consistent with DLVO theory, but could be explained by pH-associated electrosteric stabilization. This phenomenon is driven by the pH-dependent protonated state of functional groups on E. coil O157:H7 surface macromolecules and the corresponding conformational state of the bacterial polymers. Results from this study demonstrate that retention of E. coil O157:H7 cells in porous media is a complex process that depends on the solution chemistry, cell-cell interactions, and pore structure. The findings in this study also imply that previous work conducted at lower pH and IS conditions may underestimate E. coli O157:H7 travel distance in higher salt and pH groundwater environments.

The transport of solutes and colloids in porous media is influenced by a variety of physical and chemical nonequilibrium processes. A combined physical-chemical nonequilibrium (PCNE) model was therefore used to describe general mass transport. The model partitions the pore space into "mobile" and "immobile" flow regions with first-order mass transfer between these two regions (i.e, "physical" nonequilibrium or PNE). Partitioning between the aqueous and solid phases can either proceed as an equilibrium or a first-order process (i.e, "chemical" nonequilibrium or CNE) for both the mobile and immobile regions. An analytical solution for the PCNE model is obtained using iterated Laplace transforms. This solution complements earlier semi-analytical and numerical approaches to model solute transport with the PCNE model. The impact of selected model parameters on solute breakthrough curves is illustrated. As is well known, nonequilibrium results in earlier solute breakthrough with increased tailing. The PCNE model allows greater flexibility to describe this trend; for example, a closer resemblance between solute input and effluent pulse. Expressions for moments and transfer functions are presented to facilitate the analytical use of the PCNE model. Contours of mean breakthrough time, variance, and spread of the colloid breakthrough curves as a function of PNE and CNE parameters demonstrate the utility of a model that accounts for both physical and chemical nonequilibrium processes. The model is applied to describe representative colloid breakthrough curves in Ottawa sands reported by Bradford et al. (2002). An equilibrium model provided a good description of breakthrough curves for the bromide tracer but could not adequately describe the colloid data. A considerably better description was provide by the simple CNE model but the best description, especially for the larger 3.2-microm colloids, was provided by the PCNE model.

[1] Experimental and theoretical studies were undertaken to explore the coupled effects of chemical conditions and pore space geometry on bacteria transport in porous media. The retention of Escherichia coli D21g was investigated in a series of batch and column experiments with solutions of different ionic strength (IS) and ultrapure quartz sand. Derjaguin–Landau–Verwey–Overbeek (DLVO) calculations and results from batch experiments suggested that bacteria attachment to the sand surface was negligible when the IS was less than or equal to 50 mM. Breakthrough data from column experiments showed significant cell retention and was strongly dependent on the IS. This finding indicates that cell retention was dependent on the depth of the secondary energy minimum which increases with IS. When the IS of the influent bacteria-free solution was decreased to 1 mM, only a small fraction of the retained bacteria was released from the column. The remaining retained bacteria, however, were recovered from the sand, which was excavated from the column and suspended in a cell-free electrolyte having the original IS. These observations suggest that the solution chemistry is not the only parameter controlling bacteria retention in the porous media. Computational simulations of flow around several collector grains revealed the retention mechanism, which is dependent on both the solution chemistry and the pore space geometry. Simulations demonstrate that the pore space geometry creates hydrodynamically disconnected regions. The number of bacterial cells that may be transported to these relatively “immobile” regions will theoretically be dependent on the depth of the secondary energy minimum (i.e., the IS). Once bacteria are trapped in these immobile regions, reduction of the secondary energy minimum does not necessarily release the cells owing to hydrodynamic constraints.

Profiles of retained colloids in porous media have frequently been observed to be hyper-exponential or non-monotonic with transport depth under unfavorable attachment conditions, whereas filtration theory predicts an exponential profile. In this work we present a stochastic model for colloid transport and deposition that allows various hypotheses for such deviations to be tested. The model is based on the conventional advective dispersion equation that accounts for first-order kinetic deposition and release of colloids. One or two stochastic parameters can be considered in this model, including the deposition coefficient, the release coefficient, and the average pore water velocity. In the case of one stochastic parameter, the probability density function (PDF) is characterized using log-normal, bimodal log-normal, or a simple two species/region formulation. When two stochastic parameters are considered, then a joint log-normal PDF is employed. Simulation results indicated that variations in the deposition coefficient and the average pore water velocity can both produce hyper-exponential deposition profiles. Bimodal formulations for the PDF were also able to produce hyper-exponential profiles, but with much lower variances in the deposition coefficient. The shape of the deposition profile was found to be very sensitive to the correlation of deposition and release coefficients, and to the correlation of pore water velocity and deposition coefficient. Application of the developed stochastic model to a particular set of colloid transport and deposition data indicated that chemical heterogeneity of the colloid population could not fully explain the observed behavior. Alternative interpretations were therefore proposed based on variability of the pore size and the water velocity distributions.

Packed column and mathematical modeling studies were conducted to explore the influence of water saturation, pore-water ionic strength, and grain size on the transport of latex microspheres (1.1 microm) in porous media. Experiments were carried out under chemically unfavorable conditions for colloid attachment to both solid-water interfaces (SWI) and air-water interfaces (AWI) using negatively charged and hydrophilic colloids and modifying the solution chemistry with a bicarbonate buffer to pH 10. Interaction energy calculations and complementary batch experiments were conducted and demonstrated that partitioning of colloids to the SWI and AWI was insignificant across the range of the ionic strengths considered. The breakthrough curve and final deposition profile were measured in each experiment indicating colloid retention was highly dependent on the suspension ionic strength, water content, and sand grain size. In contrast to conventional filtration theory, most colloids were found deposited close to the column inlet, and hyper-exponential deposition profiles were observed. A mathematical model, accounting for time- and depth-dependent straining, produced a reasonably good fit for both the breakthrough curves and final deposition profiles. Experimental and modeling results suggest that straining--the retention of colloids in low velocity regions of porous media such as grain junctions--was the primary mechanism of colloid retention under both saturated and unsaturated conditions. The extent of stagnant regions of flow within the pore structure is enhanced with decreasing water content, leading to a greater amount of retention. Ionic strength also contributes to straining, because the number of colloids that are held in the secondary energy minimum increases with ionic strength. These weakly associated colloids are prone to be translated to stagnation regions formed at grain-grain junctions, the solid-water-air triple point, and dead-end pores and then becoming trapped.

[1] Considerable research suggests that colloid deposition in porous media is frequently not consistent with filtration theory predictions under unfavorable attachment conditions. Filtration theory was developed from an analysis of colloid attachment to the solid-water interface of a single spherical grain collector and therefore does not include the potential influence of pore structure, grain-grain junctions, and surface roughness on straining deposition. This work highlights recent experimental evidence that indicates that straining can play an important role in colloid deposition under unfavorable attachment conditions and may explain many of the reported limitations of filtration theory. This conclusion is based upon pore size distribution information, size exclusion, time- and concentration-dependent deposition behavior, colloid size distribution information, hyperexponential deposition profiles, the dependence of deposition on colloid and porous medium size, batch release rates, micromodel observations, and deposition at textural interfaces. The implications of straining in unsaturated and heterogeneous systems are also discussed, as well as the potential influence of system solution chemistry and hydrodynamics. The inability of attachment theory predictions to describe experimental colloid transport data under unfavorable conditions is demonstrated. Specific tests to identify the occurrence and/or absence of straining and attachment are proposed.

Capillary pressure/saturation data are often difficult and time consuming to measure, particularly for non-water-wetting porous media. Few capillary pressure/saturation predictive models, however, have been developed or verified for the range of wettability conditions that may be encountered in the natural subsurface. This work presents a new two-phase capillary pressure/saturation model for application to the prediction of primary drainage and imbibition relations in fractional wettability media. This new model is based upon an extension of Leverett scaling theory. Analysis of a series of DNAPL/water experiments, conducted for a number of water/intermediate and water/organic fractional wettability systems, reveals that previous models fail to predict observed behavior. The new Leverett-Cassie model, however, is demonstrated to provide good representations of these data, as well as those from two earlier fractional wettability studies. The Leverett-Cassie model holds promise for field application, based upon its foundation in fundamental scaling principles, its requirement for relatively few and physically based input parameters, and its applicability to a broad range of wetting conditions.

Two-dimensional multiphase flow and transport simulators were refined and used to numerically investigate the entrapment and dissolution behavior of tetrachloroethylene (PCE) in heterogeneous porous media containing spatial variations in wettability. Measured hydraulic properties, residual saturations, and dissolution parameters were employed in these simulations. Entrapment was quantified using experimentally verified hydraulic property and residual saturation models that account for hysteresis and wettability variations. The nonequilibrium dissolution of PCE was modeled using independent estimates of the film mass transfer coefficient and interfacial area for entrapped and continuous (PCE pools or films) saturations. Flow simulations demonstrate that the spatial distribution of PCE is highly dependent on subsurface wettability characteristics that create differences in PCE retention mechanisms and the presence of subsurface capillary barriers. For a given soil texture, the maximum and minimum PCE infiltration depth was obtained when the sand had intermediate (an organic-wet mass fraction of 25%) and strong (water- or organic-wet) wettability conditions, respectively. In heterogeneous systems, subsurface wettability variations were also found to enhance or diminish the performance of soil texture-induced capillary barriers. The dissolution behavior of PCE was found to depend on the soil wettability and the spatial PCE distribution. Shorter dissolution times tended to occur when PCE was distributed over large regions due to an increased access of flowing water to the PCE. In heterogeneous systems, capillary barriers that produced high PCE saturations tended to exhibit longer dissolution times.