Interaction of micrometer-scale particles with nanotextured surfaces in shear flow

Particle dispersion through porous media with heterogeneous attractions

Porous media used in many practical applications contain natural spatial variations in composition and surface charge that lead to heterogeneous physicochemical attractions between the media and transported particles. We performed Stokesian dynamics (SD) simulations to examine the effects of heterogeneous attractions on quiescent diffusion and hydrodynamic dispersion of particles within geometrically ordered arrays of nanoposts. We find that transport under quiescent conditions occurs by two mechanisms, diffusion through the void space and intermittent hopping between the attractive wells of different nanoposts. As the attraction heterogeneity increases, the latter mechanism becomes dominant, resulting in an increase in the particle trajectory tortuosity, deviations from Gaussian behavior in the particle displacement distributions, and a decrease in the long-time particle diffusivity. Similarly, under flow conditions corresponding to low Péclet number (Pe), increased attraction heterogeneity leads to transient localization near the nanoposts, resulting in a broadening of the particle distribution and enhanced longitudinal dispersion in the direction of flow. At high Pe where advection strongly dominates, however, the longitudinal dispersion coefficient is insensitive to attraction heterogeneity and exhibits Taylor-Aris dispersion behavior. Our findings provide insight into how heterogeneous interactions may influence particle transport in complex 3-D porous media.

Interplay of physico-chemical and mechanical bacteria-surface interactions with transport processes controls early biofilm growth: A review

Biofilms initiate when bacteria encounter and are retained on surfaces. The surface orchestrates biofilm growth through direct physico-chemical and mechanical interactions with different structures on bacterial cells and, in turn, through its influence on cell-cell interactions. Individual cells respond directly to a surface through mechanical or chemical means, initiating "surface sensing" pathways that regulate gene expression, for instance producing extra cellular matrix or altering phenotypes. The surface can also physically direct the evolving colony morphology as cells divide and grow. In either case, the physico-chemistry of the surface influences cells and cell communities through mechanisms that involve additional factors. For instance the numbers of cells arriving on a surface from solution relative to the generation of new cells by division depends on adhesion and transport kinetics, affecting early colony density and composition. Separately, the forces experienced by adhering cells depend on hydrodynamics, gravity, and the relative stiffnesses and viscoelasticity of the cells and substrate materials, affecting mechanosensing pathways. Physical chemistry and surface functionality, along with interfacial mechanics also influence cell-surface friction and control colony morphology, in particular 2D and 3D shape. This review focuses on the current understanding of the mechanisms in which physico-chemical interactions, deriving from surface functionality, impact individual cells and cell community behavior through their coupling with other interfacial processes.

Review on physical and chemical factors affecting fines migration in porous media

Permeability reduction and formation damage in porous media caused by fines (defined as unconfined solid particles present in the pore spaces) migration is one of the major reasons for productivity decline. It is well accepted that particle detachment occurs under imbalanced torques arising from hydrodynamic and adhesive forces exerted on attached particles. This paper reviewed current understanding on primary factors influencing fines migration as well as mathematical formulations for quantification. We also introduced salinity-related experimental observations that contradict theoretical predictions based on torque balance criteria, such as delayed particle release and attachment-detachment hysteresis. The delay of particle release during low-salinity water injection was successfully explained and formulated by the Nernst-Planck diffusion of ions in a narrow contact area. In addition to the widely recognized explanation by surface heterogeneity and the presence of low-velocity regions, we proposed a hypothesis that accounts for the shifting of equilibrium positions, providing new insight into the interpretation of elusive attachment-detachment hysteresis both physically and mathematically. The review was finalized by discussing the quantification of anomalous salinity effect on adhesion force at low- and high-salinity conditions.

Important Role of Concave Surfaces in Deposition of Colloids under Favorable Conditions as Revealed by Microscale Visualization

This study conducted saturated column experiments to systematically investigate deposition of 1 μm positively charged polystyrene latex micro-colloids (representing microplastic particles) on negatively charged rough sand, glass beads, and soil with pore water velocities (PWV) from 4.9 × 10^-5 to 8.8 × 10^-4 m/s. A critical value of PWV was found below which colloidal attachment efficiency (AE) increased with increasing PWV. The increase in AE with PWV was attributed to enhanced delivery of the colloids and subsequent attachment at concave locations of rough collector surfaces. The AE decreased with further increasing PWV beyond the threshold because the convex sites became unavailable for colloid attachment. By simulating the rough surfaces using the Weierstrass-Mandelbrot equation, the extended Derjaguin-Landau-Verwey-Overbeek (XDLVO) interaction energy calculations and torque analysis revealed that the adhesive torques could be reduced to be comparable or smaller than hydrodynamic torques even under the favorable conditions. Interestingly, scanning electron microscopic experiments showed that blocking occurred at convex sites at all ionic strengths (ISs) (e.g., even when the colloid-colloid interaction was attractive), whereas at concave sites, blocking and ripening (i.e., attached colloids favor subsequent attachment) occurred at low and high ISs, respectively. To our knowledge, our work was the first to show coexistence of blocking and ripening at high ISs due to variation of the collector surface morphology.

DLVO Interactions between Particles and Rough Surfaces: An Extended Surface Element Integration Method

The surface element integration (SEI) method is a computationally facile technique for calculating DLVO interactions between particles and surfaces. This method yields the exact total DLVO interaction between a particle and a flat surface; however, all surfaces have some degree roughness that profoundly affects the interaction. Previously, an ad hoc approximate method has been used to extend the SEI method to interactions between particles and surfaces with arbitrary morphology. Here we derive a more rigorous approximate method based on the fundamental scaling of DLVO interactions, which approaches the exact solution as the separation distance decreases regardless of the particle or surface morphology. We verify this method by comparison to the exact van der Waals energy when roughness is present on the particle and surface. The accuracy of this method at small separations makes it well-suited for the contexts of particle adhesion and deposition in which the length scale of interaction is on the order of angstroms and nanometers, respectively.

Anionic nanoparticle and microplastic non-exponential distributions from source scale with grain size in environmental granular media

Nanoparticle and microplastic (colloid) transport behaviors impact strategies for groundwater protection and remediation. Complex colloid transport behaviors of anionic nano- and micro-sized colloids have been previously elucidated via independent experiments in chemically-cleaned and amended granular media with grain sizes in the range of fine to coarse sand (e.g., 200-1000 μm). Such experiments show that under conditions where a repulsive barrier was present in colloid-collector interactions (unfavorable conditions), the distribution of retained colloids down-gradient from their source deviates from the exponential decrease expected from compounded loss across a series of collectors (grains). Previous experiments have not examined the impact of colloid size or granular media grain size on colloid distribution down-gradient from their source, particularly in streambed-equilibrated granular media. To address this gap, a field transport experiment in constructed wetland stream beds to distances up to 20 m were conducted for colloids ranging in size from micro to nano (60 nm-7 μm) in streambed-equilibrated pea gravel and sand (4200 and 420 μm mean grain sizes, respectively). All colloid sizes showed non-exponential (hyper-exponential) distributions from source, over meter scales in pea gravel versus cm scales reported for fine sand. Colloids in the ca. 1 μm size range were most mobile, as expected from mass transfer to surfaces and interaction with nanoscale heterogeneity. The distance over which non-exponential colloid distribution occurred increased with media grain size, which carries implications for the potential mechanism driving non-exponential colloid distribution from source, and for strategies to predict transport.

Quantitative Linking of Nanoscale Interactions to Continuum-Scale Nanoparticle and Microplastic Transport in Environmental Granular Media

Quantitative linkage of fundamental physicochemical characteristics to rate coefficients used in simulations of experimentally observed transport behaviors of nanoparticles and microplastics (colloids) in environmental granular media is an active area of research. Quantitative linkage is herein demonstrated for (i) colloids ranging from nano- to microscale; in two field-based granular media of contrasting grain size, (ii) natural fine sand at the column scale; and (ii) streambed-equilibrated commercial pea gravel at the field scale. Continuum-scale rate coefficients were linked to nanoscale interactions via mechanistic pore-scale colloid trajectory simulations that predicted and defined fast- and slow-attaching subpopulations, as well as nonattaching subpopulations that either remained in the near-surface pore water or re-entrained to bulk pore water. These subfractions of the classic collector efficiency were upscaled to continuum-scale rate coefficients that produced experimentally observed colloid breakthrough-elution concentration histories and nonexponential colloid distributions from the source. The simulations explained transition from hyperexponential to nonmonotonic colloid distributions from the source as driven accumulation of mobile near-surface colloids due to relatively strong secondary minimum interaction and weak diffusion for microscale colloids. The assumption of depletion of the fast-attaching colloid subpopulation by attachment to grain surfaces produced the experimentally observed contrasting distances across which nonexponential colloid distribution from the source occurred in the fine sand versus pea gravel. Rate coefficients were quantitatively calculated from physicochemical parameters and the following three fit parameters: (i) fractional coverage by nanoscale heterogeneity; (ii) efficiency of return to the near-surface domain; and (iii) in explicit simulations, characteristic velocity for scaling transfer to near-surface pore water.

Transport of citrate-coated silver nanoparticles in saturated porous media

In this study, the influences of physical and chemical factors [e.g., ionic strength (IS), pH, and flow rate] on the fate and transport of citrate-coated silver nanoparticles (AgNPs) were investigated through experiments using saturated columns. For the transport behavior of AgNPs under various conditions, retardation was confirmed with an increase in ionic strength (IS) while early elution developed with an increase in pH and flow rate. These transport experiment outcomes were simulated through Hydrus-1D, and the observed breakthrough curves were confirmed to have a significant correlation with the fitted results. Interestingly, the AgNPs and quartz sand used in this study showed a negative charge in the investigated experimental conditions. Although the reaction between AgNPs and quartz sand was expected to be unfavorable, AgNPs were observed to have been deposited onto the sand surface during the column test. To clarify the mechanism of the deposition of AgNPs even in unfavorable conditions, the interaction energy profiles were calculated based on the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. From the results, unfavorable interactions were expected in the NP-NP and NP-sand interactions in every condition. It was concluded that the deposition of AgNPs onto the sand surface under the unfavorable conditions in this study was mainly because of the physical roughness of the sand surface. Moreover, this hypothesis was supported by the zone of influence calculation in accordance with IS, the interpretation results of the fractional sand surface coverage in accordance with concentration changes of AgNPs, and series column tests.

Understanding Interactions Driving the Template-Directed Self-Assembly of Colloidal Nanoparticles at Surfaces

Controlled deposition of colloidal nanoparticles using self-assembly is a promising technique for, for example, manufacturing of miniaturized electronics, and it bridges the gap between top-down and bottom-up methods. However, selecting materials and geometry of the target surface for optimal deposition results presents a significant challenge. Here, we describe a predictive framework based on the Derjaguin-Landau-Verwey-Overbeek theory that allows rational design of colloidal nanoparticle deposition setups. The framework is demonstrated for a model system consisting of gold nanoparticles stabilized by trisodium citrate that are directed toward prefabricated sub-100 nm features on a silicon substrate. Experimental results for the model system are presented in conjunction with theoretical analysis to assess its reliability. It is shown that three-dimensional, nickel-coated structures are well suited for attracting gold nanoparticles and that optimization of the feature geometry based on the proposed framework leads to a systematic improvement in the number of successfully deposited particles.

Interactions between nanoparticles and fractal surfaces

This study evaluated attachment of a 30-nm nanoparticle to and detachment from fractal surfaces by calculating Derjaguin-Landau-Verwey-Overbeek (DLVO) interaction energies in three-dimensional space using the surface element integration technique. The fractal surfaces were generated using the Weierstass-Mandelbrot function with varying values of fractal dimension D (2.3 ≤ D ≤ 2.7) and fractal roughness G (0.000136 ≤ G ≤ 0.136). Results show that maximum energy barrier is reduced at peak areas of a fractal surface, and hence attachment in primary minima is favored. Some nanoparticles attached in primary minima at the peak areas can be detached by decreasing ionic strength (IS) due to monotonic decrease of interaction energy with increasing separation distance at low ISs. While the attachment in primary minima at valley areas is irreversible to IS reduction, the attachment is inhibited due to enhanced maximum energy barrier at these areas. A nonmonotonic variation of attachment efficiency in primary minimum (AEPM) with IS is present at high fractal dimension (D ≥ 2.4) or low fractal roughness (G < 0.00136), whereas the AEPM decreases monotonically with decreasing IS at low fractal dimension (D < 2.4) or high fractal roughness (G ≥ 0.00136). The AEPM decreases monotonically with increasing D or decreasing G at ISs from 1 mM to 200 mM. The decrease of AEPM with D or G is much slower at 10 mM compared to other ISs. These theoretical findings can explain various experimental observations in the literature, and can have important utility to development of water filtration techniques in engineered systems and to assessment of environmental risks of nanoparticles.

DLVO Interaction Energies for Hollow Particles: The Filling Matters

A thorough knowledge of the interaction energy between a hollow particle (HP) and a surface or between two HPs is critical to the optimization of HP-based products and assessing the environmental risks of HPs and HP-associated pollutants. The van der Waals (vdW) energy between a HP and a surface is often calculated by subtracting the vdW energies of the inner and outer HP geometries. In this study, we show that this subtraction method is only valid when the interior and exterior fluids are the same, for example, for water-filled HPs (WHPs) dispersed in an aqueous solution. Expressions were developed to calculate the vdW energies for HPs whose interiors were filled with air (AHPs). The vdW energies were then calculated between a planar surface and a spherical or cylindrical WHP and AHP, and between WHPs or AHPs. The vdW attraction between a surface and a WHP was decreased at large separation distances compared to solid particles, and this reduced the depth of the secondary minimum. In contrast, the vdW attraction for AHPs and a surface was significantly reduced at all separation distances, and even became repulsive for thin shells, and this inhibited both primary and secondary minimum interactions. The vdW attraction between WHPs decreased with increasing shell thicknesses, and this reduced aggregation in both primary and secondary minima. In contrast, aggregation of AHPs was increased in both minima with decreasing shell thicknesses because of an increase in vdW attraction. Our theoretical calculations show the evolution of vdW and total interaction energies for HPs with different interior fluids and shell thicknesses. These results help explain various experimental observations such as inhibited attachment and favorable aggregation for AHPs (e.g., carbon nanotubes) and favorable bubble coalescence.

Nanoscale Functionalized Particles with Rotation-Controlled Capture in Shear Flow

Important processes in nature and technology involve the adhesive capture of flowing particles or cells on the walls of a conduit. This paper introduces engineered spherical microparticles whose capture rates are limited by their near surface motions in flow. Specifically, these microparticles are sparsely functionalized with nanoscopic regions ("patches") of adhesive functionality, without which they would be nonadhesive. Not only is particle capture on the wall of a shear-chamber limited by surface chemistry as opposed to transport, but also the capture rates depend specifically on particle rotations that result from the vorticity of the shear flow field. These particle rotations continually expose new particle surface to the opposing chamber wall, sampling the particle surface for an adhesive region and controlling the capture rate. Control studies with the same patchy functionality on the chamber wall rather than the particles reveal a related signature of particle capture but substantially faster (still surface limited) particle capture rates. Thus, when the same functionality is placed on the wall rather than the particles, the capture is faster because it depends on the particle translation past a functionalized wall rather than on the particle rotations. The dependence of particle capture on functionalization of the particles versus the wall is consistent with the faster near-wall particle translation in shearing flow compared with the velocity of the rotating particle surface near the wall. These findings, in addition to providing a new class of nanoscopically patchy engineered particles, provide insight into the capture and detection of cells presenting sparse distinguishing surface features and the design of delivery packages for highly targeted pharmaceutical delivery.

Selective Adhesive Cell Capture without Molecular Specificity: New Surfaces Exploiting Nanoscopic Polycationic Features as Discrete Adhesive Units

This work explored how molecularly non-specific polycationic nanoscale features on a collecting surface control kinetic and selectivity aspects of mammalian cell capture. Key principles for selective collector design were demonstrated by comparing the capture of two closely related breast cancer cell lines: MCF-7 and TMX2-28. TMX2-28 is a tamoxifen-selected clone of MCF-7. The collector was a silica surface, negatively-charged at pH 7.4, containing isolated molecules (~ 8 nm diameter) of the cationic polymer, poly(dimethyl-aminoethylmethacrylate), pDMAEMA. Important in this work is the non-selective nature of the pDMAEMA interactions with cells: pDMAEMA generally adheres negatively charged particles and cells in solution. We show here that selectivity towards cells results from collector design: this includes competition between repulsive interactions involving the negative silica and attractions to the immobilized pDMAEMA molecules, the random pDMAEMA arrangement on the surface, and the concentration of positive charge in the vicinity of the adsorbed pDMAEMA chains. The latter act as nanoscopic cationic surface patches, each weakly attracted to negatively-charged cells. Collecting surfaces engineered with an appropriate amount pDMAEMA, exposed to mixtures of MCF-7 and TMX2-28 cells preferentially captured TMX2-28 with a selectivity of 2.5. (This means that the ratio of TMX2-28 to MCF cells on the surface was 2.5 times their compositional ratio in free solution.) The ionic strength-dependence of cell capture was shown to be similar to that of silica microparticles on the same surfaces. This suggests that the mechanism of selective cell capture involves nanoscopic differences in the contact areas of the cells with the collector, allowing discrimination of closely related cell line-based small scale features of the cell surface. This work demonstrated that even without molecular specificity, selectivity for physical cell attributes produces adhesive discrimination.

Contribution of Nano- to Microscale Roughness to Heterogeneity: Closing the Gap between Unfavorable and Favorable Colloid Attachment Conditions

Surface roughness has been reported to both increase as well as decrease colloid retention. In order to better understand the boundaries within which roughness operates, attachment of a range of colloid sizes to glass with three levels of roughness was examined under both favorable (energy barrier absent) and unfavorable (energy barrier present) conditions in an impinging jet system. Smooth glass was found to provide the upper and lower bounds for attachment under favorable and unfavorable conditions, respectively. Surface roughness decreased, or even eliminated, the gap between favorable and unfavorable attachment and did so by two mechanisms: (1) under favorable conditions attachment decreased via increased hydrodynamic slip length and reduced attraction and (2) under unfavorable conditions attachment increased via reduced colloid-collector repulsion (reduced radius of curvature) and increased attraction (multiple points of contact, and possibly increased surface charge heterogeneity). Absence of a gap where these forces most strongly operate for smaller (<200 nm) and larger (>2 μm) colloids was observed and discussed. These observations elucidate the role of roughness in colloid attachment under both favorable and unfavorable conditions.

Transport, retention, and long-term release behavior of ZnO nanoparticle aggregates in saturated quartz sand: Role of solution pH and biofilm coating

The transport, retention, and long-term release of zinc oxide nanoparticle aggregates (denoted below as ZnO-NPs) were investigated in saturated, bare and biofilm (Pseudomonas putida) coated sand packed columns. Almost complete retention of ZnO-NPs occurred in bare and biofilm coated sand when the influent solution pH was 9 and the ionic strength (IS) was 0.1 or 10 mM NaCl, and the retention profiles were always hyper-exponential. Increasing the solution IS and biofilm coating produced enhanced retention of ZnO-NPs near the column inlet. The enhanced NPs retention at high IS was attributed to more favorable NP-silica and NP-NP interactions; this was consistent with the interaction energy calculations. Meanwhile, the greater NPs retention in the presence of biofilm was attributed to larger roughness heights which alter the mass transfer rate, the interaction energy profile, and lever arms associated with the torque balance; e.g., scanning electron and atomic force microscopy was used to determine roughness heights of 33.4 nm and 97.8 nm for bare sand and biofilm-coated sand, respectively. Interactions between NPs and extracellular polymeric substances may have also contributed to enhanced NP retention in biofilm-coated sand at low IS. The long-term release of retained ZnO-NPs was subsequently investigated by continuously injecting NP-free solution at pH 6, 9, or 10 and keeping the IS constant at 10 mM. The amount and rate of retained ZnO-NP removal was strongly dependent on the solution pH. Specifically, almost complete removal of retained ZnO-NPs was observed after 627 pore volumes when the solution pH was 6, whereas much less Zn was recovered when the eluting solution pH was buffered to pH = 9 and especially 10. This long-term removal was attributed to pH-dependent dissolution of retained ZnO-NPs because: (i) the solubility of ZnO-NPs increases with decreasing pH; and (ii) ZnO-NPs were not detected in the effluent. The presence of biofilm also decreased the initial rate and amount of dissolution and the subsequent transport of Zn(2+) due to the strong Zn(2+) re-adsorption to the biofilm. Our study indicates that dissolution will eventually lead to the complete removal of retained ZnO-NPs and the transport of toxic Zn(2+) ions in groundwater environments with pH ranges of 5-9.

Spontaneous Detachment of Colloids from Primary Energy Minima by Brownian Diffusion

The Derjaguin-Landau-Verwey-Overbeek (DLVO) interaction energy profile has been frequently used to interpret the mechanisms controlling colloid attachment/detachment and aggregation/disaggregation behavior. This study highlighted a type of energy profile that is characterized by a shallow primary energy well (i.e., comparable to the average kinetic energy of a colloid) at a small separation distance and a monotonic decrease of interaction energy with separation distance beyond the primary energy well. This energy profile is present due to variations of height, curvature, and density of discrete physical heterogeneities on collector surfaces. The energy profile indicates that colloids can be spontaneously detached from the shallow primary energy well by Brownian diffusion. The spontaneous detachment from primary minima was unambiguously confirmed by conducting laboratory column transport experiments involving flow interruptions for two model colloids (polystyrene latex microspheres) and engineered nanoparticles (fullerene C60 aggregates). Whereas the spontaneous detachment has been frequently attributed to attachment in secondary minima in the literature, our study indicates that the detached colloids could be initially attached at primary minima. Our study further suggests that the spontaneous disaggregation from primary minima is more significant than spontaneous detachment because the primary minimum depth between colloid themselves is lower than that between a colloid and a collector surface.

Equilibrium and kinetic models for colloid release under transient solution chemistry conditions

We present continuum models to describe colloid release in the subsurface during transient physicochemical conditions. Our modeling approach relates the amount of colloid release to changes in the fraction of the solid surface area that contributes to retention. Equilibrium, kinetic, equilibrium and kinetic, and two-site kinetic models were developed to describe various rates of colloid release. These models were subsequently applied to experimental colloid release datasets to investigate the influence of variations in ionic strength (IS), pH, cation exchange, colloid size, and water velocity on release. Various combinations of equilibrium and/or kinetic release models were needed to describe the experimental data depending on the transient conditions and colloid type. Release of Escherichia coli D21g was promoted by a decrease in solution IS and an increase in pH, similar to expected trends for a reduction in the secondary minimum and nanoscale chemical heterogeneity. The retention and release of 20nm carboxyl modified latex nanoparticles (NPs) were demonstrated to be more sensitive to the presence of Ca(2+) than D21g. Specifically, retention of NPs was greater than D21g in the presence of 2mM CaCl2 solution, and release of NPs only occurred after exchange of Ca(2+) by Na(+) and then a reduction in the solution IS. These findings highlight the limitations of conventional interaction energy calculations to describe colloid retention and release, and point to the need to consider other interactions (e.g., Born, steric, and/or hydration forces) and/or nanoscale heterogeneity. Temporal changes in the water velocity did not have a large influence on the release of D21g for the examined conditions. This insensitivity was likely due to factors that reduce the applied hydrodynamic torque and/or increase the resisting adhesive torque; e.g., macroscopic roughness and grain-grain contacts. Our analysis and models improve our understanding and ability to describe the amounts and rates of colloid release and indicate that episodic colloid transport is expected under transient physicochemical conditions.

Colloid release and clogging in porous media: Effects of solution ionic strength and flow velocity

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.

Cotransport of bismerthiazol and montmorillonite colloids in saturated porous media

While bismerthiazol [N,N'-methylene-bis-(2-amino-5-mercapto-1,3,4-thiadiazole)] is one of the most widely used bactericides, the transport of bismerthiazol in subsurface environments is unclear to date. Moreover, natural colloids are ubiquitous in the subsurface environments. The cotransport of bismerthiazol and natural colloids has not been investigated. This study conducted laboratory column experiments to examine the transport of bismerthiazol in saturated sand porous media both in the absence and presence of montmorillonite colloids. Results show that a fraction of bismerthiazol was retained in sand and the retention was higher at pH7 than at pH 4 and 10. The retention did not change with ionic strength. The retention was attributed to the complex of bismerthiazol with metals/metal oxides on sand surfaces through ligand exchange. The transport of bismerthiazol was enhanced with montmorillonite colloids copresent in the solutions and, concurrently, the transport of montmorillonite colloids was facilitated by the bismerthiazol. The transport of montmorillonite colloids was enhanced likely because the bismerthiazol and the colloids competed for the attachment/adsorption sites on collector surfaces and the presence of bismerthiazol changed the Derjaguin-Landau-Verwey-Overbeek (DLVO) interaction energies between colloids and collectors. The transport of bismerthiazol was inhibited if montmorillonite colloids were pre-deposited in sand because bismerthiazol could adsorb onto the colloid surfaces. The adsorbed bismerthiazol could be co-remobilized with the colloids from primary minima by decreasing ionic strength. Whereas colloid-facilitated transport of pesticides has been emphasized, our study implies that transport of colloids could also be facilitated by the presence of pesticides.

Release of colloids from primary minimum contact under unfavorable conditions by perturbations in ionic strength and flow rate

Colloid release from surfaces in response to ionic strength and flow perturbations has been mechanistically simulated. However, these models do not address the mechanism by which colloid attachment occurs, at least in the presence of bulk colloid-collector repulsion (unfavorable conditions), which is a prevalent environmental condition. We test whether a mechanistic model that predicts colloid attachment under unfavorable conditions also predicts colloid release in response to reduced ionic strength (IS) and increased fluid velocity (conditions thought prevalent for mobilization of environmental colloids). The model trades in mean-field colloid-collector interaction for discrete representation of surface heterogeneity, which accounts for a combination of attractive and repulsive interactions simultaneously, and results in an attached colloid population (in primary minimum contact with the surface) having a distribution of strengths of attraction. The model moderates equilibrium separation distance by inclusion of steric interactions. By using the same model parameters to quantitatively predict attachment under unfavorable conditions, simulated release of colloids (for all three sizes) from primary minimum attachment in response to perturbations qualitatively matched experimental results, demonstrating that both attachment and detachment were mechanistically simulated.

An explanation for differences in the process of colloid adsorption in batch and column studies

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.

Power law size-distributed heterogeneity explains colloid retention on soda lime glass in the presence of energy barriers

This article concerns reading the nanoscale heterogeneity thought responsible for colloid retention on surfaces in the presence of energy barriers (unfavorable attachment conditions). We back out this heterogeneity on glass surfaces by comparing mechanistic simulations incorporating discrete heterogeneity with colloid deposition experiments performed across a comprehensive set of experimental conditions. Original data is presented for attachment to soda lime glass for three colloid sizes (0.25, 1.1, and 1.95 μm microspheres) under a variety of ionic strengths and fluid velocities in an impinging jet system. A comparison of mechanistic particle trajectory simulations incorporating discrete surface heterogeneity represented by nanoscale zones of positive charge (heterodomains) indicates that a power law size distribution of heterodomains ranging in size from 120 to 60 nm in radius was able to explain the observed retention for all conditions examined. In contrast, uniform and random placement of single-sized heterodomains failed to capture experimentally observed colloid retention across the range of conditions examined.

Modeling microorganism transport and survival in the subsurface

An understanding of microbial transport and survival in the subsurface is needed for public health, environmental applications, and industrial processes. Much research has therefore been directed to quantify mechanisms influencing microbial fate, and the results demonstrate a complex coupling among many physical, chemical, and biological factors. Mathematical models can be used to help understand and predict the complexities of microbial transport and survival in the subsurface under given assumptions and conditions. This review highlights existing model formulations that can be used for this purpose. In particular, we discuss models based on the advection-dispersion equation, with terms for kinetic retention to solid-water and/or air-water interfaces; blocking and ripening; release that is dependent on the resident time, diffusion, and transients in solution chemistry, water velocity, and water saturation; and microbial decay (first-order and Weibull) and growth (logistic and Monod) that is dependent on temperature, nutrient concentration, and/or microbial concentration. We highlight a two-region model to account for microbe migration in the vicinity of a solid phase and use it to simulate the coupled transport and survival of species under a variety of environmentally relevant scenarios. This review identifies challenges and limitations of models to describe and predict microbial transport and survival. In particular, many model parameters have to be optimized to simulate a diversity of observed transport, retention, and survival behavior at the laboratory scale. Improved theory and models are needed to predict the fate of microorganisms in natural subsurface systems that are highly dynamic and heterogeneous.

Colloid interaction energies for physically and chemically heterogeneous porous media

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.

Role of collector alternating charged patches on transport of Cryptosporidium parvum oocysts in a patchwise charged heterogeneous micromodel

The role of collector surface charge heterogeneity on transport of Cryptosporidium parvum oocyst and carboxylate microsphere in 2-dimensional micromodels was studied. The cylindrical silica collectors within the micromodels were coated with 0, 10, 20, 50, and 100% Fe(2)O(3) patches. The experimental values of average removal efficiencies (η) of the Fe(2)O(3) patches and on the entire collectors were determined. In the presence of significant (>3500 kT) Derjaguin-Landau-Verwey-Overbeek (DLVO) energy barrier between the microspheres and the silica collectors at pH 5.8 and 8.1, η determined for Fe(2)O(3) patches on the heterogeneous collectors were significantly less (p < 0.05, t test) than those obtained for collectors coated entirely with Fe(2)O(3). However, η calculated for Fe(2)O(3) patches for microspheres at pH 4.4 and for oocysts at pH 5.8 and 8.1, where the DLVO energy barrier was relatively small (ca. 200-360 kT), were significantly greater (p < 0.05, t test) than those for the collectors coated entirely with Fe(2)O(3). The dependence of η for Fe(2)O(3) patches on the DLVO energy barrier indicated the importance of periodic favorable and unfavorable electrostatic interactions between colloids and collectors with alternating Fe(2)O(3) and silica patches. Differences between experimentally determined overall η for charged heterogeneous collectors and those predicted by a patchwise geochemical heterogeneous model were observed. These differences can be explained by the model's lack of consideration for the spatial distribution of charge heterogeneity on the collector surface.

Towards a description of particulate fouling: from single particle deposition to clogging

Particulate fouling generally arises from the continuous deposition of colloidal particles on initially clean surfaces, a process which can even lead to a complete blockage of the fluid cross-section. In the present paper, the initial stages of the fouling process (which include single-particle deposition and reentrainment) are first addressed and current modelling state-of-the-art for particle-turbulence and particle-wall interactions is presented. Then, attention is specifically focused on the later stages (which include multilayer formation, clogging and blockage). A detailed review of experimental works brings out the essential mechanisms occurring during these later stages: as for the initial stages, it is found that clogging results from the competition between particle-fluid, particle-surface and particle-particle interactions. Numerical models that have been proposed to reproduce the later stages of fouling are then assessed and a new Lagrangian stochastic approach to clogging in industrial cases is detailed. These models further confirm that, depending on hydrodynamical conditions (the flow velocity), fluid characteristics (such as the ionic strength) as well as particle and substrate properties (such as zeta potentials), particle deposition can lead to the formation of either a single monolayer or multilayers. The present paper outlines also future numerical developments and experimental works that are needed to complete our understanding of the later stages of the fouling process.

Application of DLVO energy map to evaluate interactions between spherical colloids and rough surfaces

This study theoretically evaluated interactions between spherical colloids and rough surfaces in three-dimensional space using Derjaguin-Landau-Verwey- Overbeek (DLVO) energy/force map and curve. The rough surfaces were modeled as a flat surface covered by hemispherical protrusions. A modified Derjaguin approach was employed to calculate the interaction energies and forces. Results show that more irreversible attachments in primary minima occur at higher ionic strengths, which theoretically explains the observed hysteresis of colloid attachment and detachment during transients in solution chemistry. Secondary minimum depths can be increased significantly in concave regions (e.g., areas aside of asperities or between asperities) due to sidewall interactions. Through comparing the tangential attractive forces from asperities and the hydrodynamic drag forces in three-dimensional space, we showed that attachment in secondary minima can be located on open collector surfaces of a porous medium. This result challenges the usual belief that the attachment in secondary minima only occurs in stagnation point regions of the porous medium and is absent in shear flow systems such as parallel plate flow chamber and impinging jet apparatus. Despite the argument about the role of secondary minima in colloid attachment remained, our study theoretically justified the existence of attachment in secondary minima in the presence of surface roughness. Further, our study implied that the presence of surface roughness is more favorable for attachment in secondary minima than in primary minima under unfavorable chemical conditions.

Colloid adhesive parameters for chemically heterogeneous porous media

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.

Causes and implications of colloid and microorganism retention hysteresis

Experiments were designed to better understand the causes and implications of colloid and microorganism retention hysteresis with transients in solution ionic strength (IS). Saturated packed column experiments were conducted using two sizes of carboxyl modified latex (CML) microspheres (0.1 and 1.1 μm) and microorganisms (coliphage φX174 and E. coli D21g) under various transient solution chemistry conditions, and 360 μm Ottawa sand that was subject to different levels of cleaning, namely, a salt cleaning procedure that removed clay particles, and a salt+acid cleaning procedure that removed clay and reduced microscopic heterogeneities due to metal oxides and surface roughness. Comparison of results from the salt and salt+acid treated sand indicated that microscopic heterogeneity was a major contributor to colloid retention hysteresis. The influence of this heterogeneity increased with IS and decreasing colloid/microbe size on salt treated sand. These trends were not consistent with calculated mean interaction energies (the secondary minima), but could be explained by the size of the electrostatic zone of influence (ZOI) near microscopic heterogeneities. In particular, the depth of local minima in the interaction energy has been predicted to increase with a decrease in the ZOI when the colloid size and/or the Debye length decreased (IS increased). The adhesive interaction was therefore largely irreversible for smaller sized 0.1 μm CML colloids, whereas it was reversible for larger 1.1 μm CML colloids. Similarly, the larger E. coli D21g exhibited greater reversibility in retention than φX174. However, direct comparison of CML colloids and microbes was not possible due to differences in size, shape, and surface properties. Retention and release behavior of CML colloids on salt+acid treated sand was much more consistent with mean interaction energies due to reduction in microscopic heterogeneities.

Transport of ARS-labeled hydroxyapatite nanoparticles in saturated granular media is influenced by surface charge variability even in the presence of humic acid

Hydroxyapatite nanoparticle (nHAP) is increasingly being used to remediate soils and water polluted by metals and radionuclides. The transport and retention of Alizarin red S (ARS)-labeled nHAP were investigated in water-saturated granular media. Experiments were carried out over a range of ionic strength (I(c), 0-50mM NaCl) conditions in the presence of 10 mg L(-1) humic acid. The transport of ARS-nHAP was found to decrease with increasing suspension I(c) in part, because of enhanced aggregation and chemical heterogeneity. The retention profiles (RPs) of ARS-nHAP exhibited hyperexponential shapes (a decreasing rate of retention with increasing transport distance) for all test conditions, suggesting that some of the attachment was occurring under unfavorable conditions. Surface charge heterogeneities on the collector surfaces and especially within the ARS-nHAP population were contributing causes for the hyperexponential RPs. Consideration of the effect(s) of I(c) in the presence of HA is needed to improve the efficacy of nHAP for scavenging metals and actinides in real soils and groundwater environments.

Colloid retention at the meniscus-wall contact line in an open microchannel

Colloid retention mechanisms in partially saturated porous media are currently being researched with an array of visualization techniques. These visualization techniques have refined our understanding of colloid movement and retention at the pore scale beyond what can be obtained from breakthrough experiments. One of the remaining questions is what mechanisms are responsible for colloid immobilization at the triple point where air, water, and soil grain meet. The objective of this study was to investigate how colloids are transported to the air-water-solid (AWS) contact line in an open triangular microchannel, and then retained as a function of meniscus contact angle with the wall and solution ionic strength. Colloid flow path, meniscus shape and meniscus-wall contact angle, and colloid retention at the AWS contact line were visualized and quantified with a confocal microscope. Experimental results demonstrated that colloid retention at the AWS contact line was significant when the meniscus-wall contact angle was less than 16°, but was minimal for the meniscus-wall contact angles exceeding 20°. Tracking of individual colloids and computational hydrodynamic simulation both revealed that for small contact angles (e.g., 12.5°), counter flow and flow vortices formed near the AWS contact line, but not for large contact angles (e.g., 28°). This counter flow helped deliver the colloids to the wall surface just below the contact line. In accordance with DLVO and hydrodynamic torque calculations, colloid movement may be stopped when the colloid reached the secondary minimum at the wall near the contact line. However, contradictory to the prediction of the torque analysis, colloid retention at the AWS contact line decreased with increasing ionic strength for contact angles of 10-20°, indicating that the air-water interface was involved through both counter flow and capillary force. We hypothesized that capillary force pushed the colloid through the primary energy barrier to the primary minimum to become immobilized, when small fluctuations in water level stretched the meniscus over the colloid. For large meniscus-wall contact angles counter flow was not observed, resulting in less colloid retention, because a smaller number of colloids were transported to the contact line.

Surface heterogeneity on hemispheres-in-cell model yields all experimentally-observed non-straining colloid retention mechanisms in porous media in the presence of energy barriers

Many mechanisms of colloid retention in porous media under unfavorable conditions have been identified from experiments or theory, such as attachment at surface heterogeneities, wedging at grain to grain contacts, retention via secondary energy minimum association in zones of low flow drag, and straining in pore throats too small to pass. However, no previously published model is capable of representing all of these mechanisms of colloid retention. In this work, we demonstrate that incorporation of surface heterogeneity into our hemispheres-in-cell model yields all experimentally observed non-straining retention mechanisms in porous media under unfavorable conditions. We also demonstrate that the predominance of any given retention mechanism depends on the coupled colloid-collector-flow interactions that are governed by parameters such as the size and spatial frequency of heterogeneous attractive domains, colloid size, and solution ionic strength. The force/torque balance-simulated retention is shown to decrease gradually with decreasing solution ionic strength, in agreement with experimental observations. This gradual decrease stands in sharp contrast to predictions from mean field theory that does not account for discrete surface heterogeneity.

Charge heterogeneity of surfaces: mapping and effects on surface forces

The DLVO theory treats the total interaction force between two surfaces in a liquid medium as an arithmetic sum of two components: Lifshitz-van der Waals and electric double layer forces. Despite the success of the DLVO model developed for homogeneous surfaces, a vast majority of surfaces of particles and materials in technological systems are of a heterogeneous nature with a mosaic structure composed of microscopic and sub-microscopic domains of different surface characteristics. In such systems, the heterogeneity of the surface can be more important than the average surface character. Attractions can be stronger, by orders of magnitude, than would be expected from the classical mean-field DLVO model when area-averaged surface charge or potential is employed. Heterogeneity also introduces anisotropy of interactions into colloidal systems, vastly ignored in the past. To detect surface heterogeneities, analytical tools which provide accurate and spatially resolved information about material surface chemistry and potential - particularly at microscopic and sub-microscopic resolutions - are needed. Atomic force microscopy (AFM) offers the opportunity to locally probe not only changes in material surface characteristic but also charges of heterogeneous surfaces through measurements of force-distance curves in electrolyte solutions. Both diffuse-layer charge densities and potentials can be calculated by fitting the experimental data with a DLVO theoretical model. The surface charge characteristics of the heterogeneous substrate as recorded by AFM allow the charge variation to be mapped. Based on the obtained information, computer modeling and simulation can be performed to study the interactions among an ensemble of heterogeneous particles and their collective motions. In this paper, the diffuse-layer charge mapping by the AFM technique is briefly reviewed, and a new Diffuse Interface Field Approach to colloid modeling and simulation is briefly discussed.

Numerical study on the deposition rate of hematite particle on polypropylene walls: role of surface roughness

In this paper, we investigate the deposition of nanosized and microsized particles on rough surfaces under electrostatic repulsive conditions in an aqueous suspension. This issue arises in the general context of modeling particle deposition which, in the present work, is addressed as a two-step process: first particles are transported by the motions of the flow toward surfaces and, second, in the immediate vicinity of the walls, the forces between the incoming particles and the walls are determined using the classical DLVO theory. The interest of this approach is to take into account both hydrodynamical and physicochemical effects within a single model. Satisfactory results have been obtained in attractive conditions but some discrepancies have been revealed in the case of repulsive conditions, in line with other studies which have noted differences between predictions based on the DLVO theory and experimental measurements for similar repulsive conditions. Consequently, the aim of the present work is to focus on this particular range and, more specifically, to assess the influence of surface roughness on the DLVO potential energy. For this purpose, we introduce a new simplified model of surface roughness where spherical protruding asperities are placed randomly on a smooth plate. On the basis of this geometrical description, approximate DLVO expressions are used and numerical calculations are performed. We first highlight the existence of a critical asperity size which brings about the highest reduction of the DLVO interaction energy. Then, the influence of the surface covered by the asperities is investigated as well as retardation effects which can play a role in the reduction of the interaction energy. Finally, by considering the random distribution of the energy barrier of the DLVO potential due to the random geometrical configurations, the overall effect of surface roughness is demonstrated with one application of the complete deposition model in an industrial test case. These new numerical results show that nonzero deposition rates are now obtained even in repulsive conditions, which confirms that surface roughness is a relevant aspect to introduce in general approaches to deposition.

Initial colloid deposition on bare and zeolite-coated stainless steel and aluminum: influence of surface roughness

The impact of surface roughness of bare and zeolite ZSM-5 coated stainless steel and aluminum alloy on colloid deposition has been investigated using a parallel plate flow chamber system in an aqueous environment. The metals were systematically polished to alter the surface roughness from nanoscale to microscale, with the subsequent surface roughness of both the bare and coated surfaces varying from 11.2 to 706 nm. The stainless steel and aluminum alloy surfaces are extensively characterized, both as bare and as coated surfaces. Experimental results suggest that ZSM-5 coating and surface roughness have a pronounced impact on the kinetics of the colloid deposition. The ZSM-5 coating reduced colloid adhesion compared to the corresponding bare metal surface. In general, the greater surface roughness of like samples resulted in higher colloid deposition. Primarily, this is due to greater surface roughness inducing less reduction in the attractive interactions occurring between colloids and collector surfaces. This effect was sensitive to ionic strength and was found to be more pronounced at lower ionic strength conditions. For the most electrostatically unfavorable scenario (ZSM-5 coatings in 1 mM KNO(3)), the enhanced deposition may also be attributed to inherent surface charge heterogeneity of ZSM-5 coatings due to aluminum in the crystalline structure. The two exceptions are ZSM-5 coated mirror-polished stainless steel and the unpolished aluminum surfaces, which are rougher than the other two samples of the same metal type but result in the least deposition. The reasons for these observations are discussed, as well as the effect of surface charge and hydrophobicity on the adhesion. The relative importance of surface roughness versus contributions of electrostatic interactions and hydrophobicity to the colloid deposition is also discussed.

Hysteresis of colloid retention and release in saturated porous media during transients in solution chemistry

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.