Hierarchical approach to model multilayer colloidal deposition in porous media

Particle deposition is important in many environmental systems such as water and wastewater filtration, air pollution control, subsurface transport, biofilm formation and fouling, and thin film synthesis for use in remediation technologies. While continuum-level models have been developed to predict deposition dynamics in these systems, these models fail to explain transient dynamics of multilayer deposition from a mechanistic viewpoint. In this work, a multiscale approach has been developed to predict multiple layer irreversible colloidal deposition in the presence of interparticle electrostatic and van der Waals interactions in porous media. The approach combines the kinetic information obtained from the mesoscopic stochastic simulations of particle deposition with the macroscopic conservation equation describing colloidal transport. Sequential Brownian dynamics simulations are first performed by accounting for particle-particle (P-P) and particle-surface (P-S) interactions, and multilayered particle deposits are obtained. The available surface function quantifying the deposition kinetics is then obtained from the deposit microstructure. Deposition dynamics are studied at different ionic strengths and particle potentials that control the range and magnitude of interparticle interactions. Simulation results showed that the microstructure of the particle deposits formed under the influence of P-P and P-S electrostatic interactions exhibited significant variations with respect to ionic strength and could be qualitatively explained bythe interplay between the repulsive and attractive P-P and P-S interaction forces. The available surface function also varied significantly as a function of ionic strength. This basic understanding of the deposition dynamics at the mesoscale was then combined with the continuum-level transport equations to predict particle breakthrough curves in porous media. The approach is capable of capturing transient features of deposition dynamics, as demonstrated by the good agreement between the model predictions and the experimental observations.     

Fecal indicator bacteria transport and deposition in saturated and unsaturated porous media

Beach sediment and sand are recognized as nonpoint fecal indicator bacteria (FIB) sources capable of causing water quality and health risks for beach-goers. A comprehensive understanding of the key factors and mechanisms governing the migration and exchange of FIB between beach water column and sediment is desired to better predict FIB concentration variations and assess the associated risk. The transport and retention behavior of two model FIB Enterococcus faecalis (E. faecalis) and Escherichia coli (E. coli) was examined using packed-bed columns in both saturated and unsaturated porous media to evaluate FIB migration potentials at conditions simulating the coastal aquatic environment. Additionally, complementary cell characterization techniques were conducted to better understand the migration behaviors of both FIB strains observed in the column experiments. The mobility of the gram-positive species E. faecalis was much more sensitive to solution chemistry and column saturation level than that of the gram-negative species E. coli. Interaction energy calculations suggest that E. faecalis retention was largely governed by the combination of DLVO (Derjaguin-Landau-Verwey-Overbeek) and non-DLVO (most likely hydrophobic and/or polymer bridging) interactions in saturated porous media, while the combination of DLVO and steric interactions controlled the deposition of E. coli cells. The measured surface properties of the two FIB strains supported the distinct bacteria transport behaviors and the differences of the identified mechanisms for each strain. As a result, E. faecalis showed the least affinity to sand in freshwater and appeared to be irreversibly attached in primary energy minima at elevated salt conditions; whereas the retained E. coli cells were reversibly attached and mostly associated with the secondary energy minima at both freshwater and seawater conditions. In unsaturated porous media, E. faecalis cells seemed to prefer to attachment at air/water interface rather than sand surface, while E. coli showed a similar affinity to the two interfaces. It was proposed that the different surface characteristics of the two FIB strains resulted in the distinct transport and retention behavior in porous media. These results highlight the need for FIB management to consider variations in transport behavior between model FIB when assessing water quality and associated risks.     

Nonmonotonic variations in deposition rate coefficients of microspheres in porous media under unfavorable deposition conditions

The transport of carboxylate-modified polystyrene latex microspheres was examined in packed quartz sand under a variety of environmentally relevant ionic strength and flow conditions. The retained concentrations of microspheres in the sediment increased first, and then decreased with transport distance, indicating that the deposition rate coefficient changed nonmonotonically over the transport distance. This finding demonstrates the ubiquity of spatial variation in deposition rate coefficients under unfavorable deposition conditions, and in addition indicates that the previously recognized monotonic decrease with transport distance is not the sole form of spatial variations in deposition rate coefficients. In contrast, the deposition rate coefficients of similarly sized microspheres with different surface group densities were shown to decrease monotonically with transport distance in the same porous media, indicating that the form of spatial variation in deposition rate coefficient is highly sensitive to system conditions. The ubiquity and sensitivity of the spatial variation of deposition rate coefficients indicate that current practices that utilize log-linear extrapolation of discreet measurements of colloid attenuation to determine colloid removal with distance from source are not valid (for both biological and nonbiological colloids). The retained colloid profiles hold the promise to reveal processes governing colloid deposition under unfavorable conditions that are yet to be identified.     

Magnetic resonance imaging and quantitative analysis of particle deposition in porous media

Measurements of particle deposition and mobilization in water-saturated porous columns were performed using nuclear magnetic resonance imaging (MRI). The use of MRI enabled the acquisition of detailed, noninvasive measurements that quantify spatial and temporal evolution of particle transport patterns and porosity changes due to particle deposition. Measurements indicate that for the considered particle sizes and flow conditions significant particle deposition occurs at some distance into the column. Because identification of unique parametrizations for processes of particle straining, deposition, and detachment is complex and nonunique, a simple phenomenological model of particle deposition and porosity reduction is suggested. This model captures the essential features of the experimental measurements on spatial and temporal flow and deposition patterns.     

Role of hydrodynamic drag on microsphere deposition and re-entrainment in porous media under unfavorable conditions

Deposition and re-entrainment of 1.1 microm microspheres were examined in packed glass beads and quartz sand under both favorable and unfavorable conditions for deposition. Experiments were performed at environmentally relevant ionic strengths and flow rates in the absence of solution chemistry and flow perturbations. Numerical simulations of experimental data were performed using kinetic rate coefficients to represent deposition and re-entrainment dynamics. Deposition rate coefficients increased with increasing flow rate under favorable deposition conditions (in the absence of colloid-grain surface electrostatic repulsion), consistent with expected trends from filtration theory. In contrast, under unfavorable deposition conditions (where significant colloid-grain surface electrostatic repulsion exists), the deposition rate coefficients decreased with increasing flow rate, suggesting a mitigating effect of hydrodynamic drag on deposition. Furthermore, the re-entrainment rate was negligible under favorable conditions but was significant under unfavorable conditions and increased with increasing flow rate, demonstrating that hydrodynamic drag drove re-entrainment under unfavorable conditions. The drag torque resulting from hydrodynamic drag was found to be 1 order of magnitude or more lower than the adhesive torque based on pull-off forces from atomic force microscopy measurements. This result indicates that hydrodynamic drag was insufficient to drive re-entrainment of microspheres that were associated with the grain surface via the primary energy minimum and suggests that hydrodynamic drag drove re-entrainment of secondary-minimum-associated microspheres.     

Influence of extracellular polymeric substances on Pseudomonas aeruginosa transport and deposition profiles in porous media

The impact of cell surface extracellular polymeric substances (EPS) on bacterial transport and retention profiles was investigated in saturated columns packed with glass beads. Three genetically well-defined isogenic Pseudomonas aeruginosa strains with different EPS secretion capability and EPS composition were used to systematically examine their deposition behavior over a range of solution chemistry. The presence of EPS on nonmucoid strain PA01 and mucoid strain PD0300 significantly increased bacterial adhesion over the EPS deficient PA01 psl pel mutant strain despite their similar surface charge as indicated by the zeta potential measurements. Retained bacterial profiles show the deposition rate coefficients with various shapes and degrees of deviation from those expected from the classic filtration theory. Non-monotonic deviations from the log-linear deposition pattern with the majority of the bacteria retained downgradient of the column inlet were observed when bacterial cells were encapsuled by EPS under both high and low ionic strength conditions. In contrast, the EPS-deficient strain exhibited monotonic deviation from theory only under low ionic strength conditions. The results demonstrate that the non-monotonic deviation from filtration theory observed in this study was driven by steric interactions between extracellular polymers and glass beads. Analysis of the retained polysaccharides (carbohydrates and uronic acids) and protein profiles suggests that bacterial re-entrainment and re-entrapment may have contributed to the downgradient movement of the maximum retained bacteria. The detachment of bacteria may leave behind various constituents of EPS as their "footprints," which can be a valuable tool for tracking the trajectory of bacterial transport.     

Chemical effectors cause different motile behavior and deposition of bacteria in porous media

We tested the hypothesis whether chemically induced motility patterns of bacteria may affect their transport in porous media. Naphthalene-degrading Pseudomonas putida G7 cells were exposed to glucose, salicylate, and silver nanoparticles (AgNPs) and their motility was assessed by computer-assisted, quantitative swimming and capillary-based taxis determinations. Exposure to salicylate induced smooth movement with few acceleration events and positive taxis, whereas cells exposed to AgNPs exhibited tortuous movement and a repellent response. Although metabolized by strain G7, glucose did not cause attraction and induced a hyper-motile mode of swimming, characterized by a high frequency of acceleration events, high swimming speed (>60 μm s(-1)), and a high tortuosity in the trajectories. Chemically induced motility behavior correlated with distinct modes of attachment to sand in batch assays and breakthrough curves in percolation column experiments. Salicylate significantly reduced deposition of G7 cells in column experiments whereas glucose and AgNPs enhanced attachment and caused filter blocking that resulted in a progressive decrease in deposition. These findings are relevant for bioremediation scenarios that require an optimized outreach of introduced inoculants and in other environmental technologies, such as water disinfection and microbially enhanced oil recovery.     

Chemoeffectors decrease the deposition of chemotactic bacteria during transport in porous media

Bacterial chemotaxis enables motile cells to move along chemical gradients and to swim toward optimal places for biodegradation. However, its potentially positive effects on subsurface remediation rely on the efficiency of bacterial movement in porous media, which is often restricted by high deposition rates and adhesion to soil surfaces. In well-controlled column systems, we assessed the influence of the chemo-effectors naphthalene, salicylate, fumarate, and acetate on deposition of chemotactic, naphthalene-degrading Pseudomonas putida G7 in selected porous environments (sand, forest soil, and clay aggregates). Our data showed that the presence of naphthalene in the pore water decreased deposition of strain 67 (but not of a derivative strain, P. putida 67.C1 (pHG100), nonchemotactic to naphthalene) by 50% in sand-filled columns, as calculated by the relative adhesion efficiency (at). Similar effects were observed with P. putida G7 strain for the other chemoeffectors. Deposition, however, depended on the chemoeffector's chemical structure, its interaction with the column packing material, and concomitantly its pore-water concentration. As the presence of the chemoeffectors had no influence on the physicochemical surface properties of the bacteria, we suggest that chemotactic sensing, combined with changed swimming modes, is likely to influence the deposition of bacteria in the subsurface, provided that the chemoeffector is dissolved at sufficient concentration in the pore water.     

Transport and deposition of metabolically active and stationary phase Deinococcus radiodurans in unsaturated porous media

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.     

Effects of natural organic matter and solution chemistry on the deposition and reentrainment of colloids in porous media

The role of humic acid in the transport of negatively charged colloids through porous media was examined. Adsorption of humic acid on latex colloids and silica collectors reduced the deposition of suspended particles and enhanced the reentrainment of deposited particles in porous media. These effects are considered to arise from additional electrostatic and steric contributions to the repulsive interaction energy due to the adsorption of negatively charged humic acid on both the suspended particles and the media collectors. At low ionic strength reversible deposition in shallow secondary minima is hypothesized to be the principal attachment mechanism, independent of the presence of humic acid. It is proposed that under these solution conditions, particle deposition and reentrainment are the result of a dynamic process, in which particles are continuously captured and released from secondary minima. At higher ionic strengths, deposition may be regarded as a combination of two mechanisms: capture in the primary well and capture in the secondary minimum. Theoretical calculations of the attachment efficiency were conducted using two existing mathematical models. The first model is based on deposition in the primary well (interaction force boundary layer, IFBL), and the second model is based on the Maxwell kinetic theory and deposition in the secondary minimum (Maxwell model). Simulations conducted with the Maxwell model provide significantly better fits of the experimental results than those conducted with the IFBL model.     

Spatial distributions of Cryptosporidium oocysts in porous media: evidence for dual mode deposition

Spatial distributions of Cryptosporidium parvum oocysts in columns packed with uniform glass-bead collectors were measured over a broad range of physicochemical conditions. Oocyst deposition behavior is shown to deviate from predictions based on classical colloid filtration theory (CFT) in the presence of repulsive (unfavorable) colloidal interactions. Specifically, CFT tends to predict greater removal of oocysts (less transport) than that observed in controlled laboratory experiments. Comparison of oocyst retention with results obtained using polystyrene latex particles of similar size suggests that mechanisms controlling particle deposition are the same in both systems. At a given ionic strength, the deposition of Cryptosporidium oocysts is generally greater than that of the microspheres; however, this discrepancy is partly attributable to large differences in oocyst and microsphere zeta potentials. A dual deposition mode (DDM) model is applied which considers the combined influence of "fast" and "slow" oocyst deposition due to the concurrent existence of favorable and unfavorable oocyst-collector interactions. Model simulations of retained oocyst profiles and suspended oocyst concentration at the column effluent are consistent with experimental data. Because classic CFT does not account for the effect of dual mode deposition (i.e., simultaneous "fast" and "slow" oocyst deposition), these observations have important implications for predictions of oocyst transport in subsurface environments, where repulsive electrostatic interactions predominate. Supporting elution experiments further suggest that specific surface interactions between oocyst wall macromolecules and the glass bead collectors could retard or even completely inhibit oocyst release upon perturbation in solution chemistry.     

Transport and deposition of polymer-modified Fe0 nanoparticles in 2-D heterogeneous porous media: effects of particle concentration, Fe0 content, and coatings

Concentrated suspensions of polymer-modified Fe(0) nanoparticles (NZVI) are injected into heterogeneous porous media for groundwater remediation. This study evaluated the effect of porous media heterogeneity and the dispersion properties including particle concentration, Fe(0) content, and adsorbed polymer mass and layer thickness which are expected to affect the delivery and emplacement of NZVI in heterogeneous porous media in a two-dimensional (2-D) cell. Heterogeneity in hydraulic conductivity had a significant impact on the deposition of NZVI. Polymer modified NZVI followed preferential flow paths and deposited in the regions where fluid shear is insufficient to prevent NZVI agglomeration and deposition. NZVI transported in heterogeneous porous media better at low particle concentration (0.3 g/L) than at high particle concentrations (3 and 6 g/L) due to greater particle agglomeration at high concentration. High Fe(0) content decreased transport during injection due to agglomeration promoted by magnetic attraction. NZVI with a flat adsorbed polymeric layer (thickness ～30 nm) could not be transported effectively due to pore clogging and deposition near the inlet, while NZVI with a more extended adsorbed layer thickness (i.e., ～70 nm) were mobile in porous media. This study indicates the importance of characterizing porous media heterogeneity and NZVI dispersion properties as part of the design of a robust delivery strategy for NZVI in the subsurface.     

Fluid and porous media property effects on dense nonaqueous phase liquid migration and contaminant mass flux

The effects of fluid and porous media properties on dense nonaqueous phase liquid (DNAPL) migration and associated contaminant mass flux generation were evaluated. Relationships between DNAPL mass and solute mass flux were generated by measuring steady-state mass flux following stepwise injection of perchloroethylene (PCE) into flow chambers packed with homogeneous porous media. The effects of fluid properties including density and interfacial tension (IFT), and media properties including grain size and wettability were evaluated by varying the density contrast and interfacial tension properties between PCE and water, and by varying the porous media mean grain diameter and wettability characteristics. Contaminant mass flux was found to increase as grain size decreased, suggesting enhanced lateral and vertical DNAPL spreading with higher fluid entry pressure. Mass flux showed a slight increase as the DNAPL approached neutral buoyancy, likely due to enhanced vertical spreading above the injection point. DNAPL spatial distribution and contaminant mass flux were only minimally affected by IFT and by intermediate-level wettability changes, but were dramatically affected by wettability reversal. The relationship between DNAPL loading and flux generation became more linear as grain size decreased and density contrast between fluids decreased. These results imply that capillary flow characteristics of the porous media and fluid properties will control mass flux generation from source zones.     

Role of grain-to-grain contacts on profiles of retained colloids in porous media in the presence of an energy barrier to deposition

Deposition of 36-microm gold-coated hollow microspheres in two porous media (glass beads and quartz sand, 710-850 microm) was examined using X-ray microtomography (XMT) in the presence of an energy barrier to deposition under fluid velocity conditions representative of engineered filtration systems. XMT allowed examination of the deposition at different locations at the grain surfaces (deposition at grain-to-grain contacts versus single-contact deposition). We demonstrate that in the presence of an energy barrier to deposition, grain-to-grain contacts strongly influence colloid deposition and the spatial distribution of retained colloids in porous media. This result contrasts drastically with observations in the absence of an energy barrier to deposition, where consistency with filtration theory was observed. In the presence of an energy barrier, colloids were dominantly retained at grain-to-grain contacts, and the concentration of retained particles varied nonmonotonically with transport distance. It is proposed that the nonmonotonic profiles resulted from translation of surface-associated microspheres and subsequent immobilization at grain-to-grain contacts. This hypothesis is demonstrated using a conceptual model. The mutability and sensitivity of retained profiles to system conditions (from hyper-exponential to nonmonotonic) may reflect the interplay of different deposition mechanisms under different conditions.     

Pore-scale observation of microsphere deposition at grain-to-grain contacts over assemblage-scale porous media domains using X-ray microtomography

The prevalence of colloid deposition at grain-to-grain contacts in two porous media (spherical glass beads and angular quartz sand, 710-850 microm) was examined using X-ray microtomography (XMT) under conditions where the colloid-grain surface interaction was solely attractive (lacking an energy barrier to deposition), and under fluid velocity conditions representative of engineered filtration systems. XMT allows pore-scale observation of colloid deposition over assemblage-scale porous media domains. Colloids visible in reconstructed images were prepared by coating gold on hollow ceramic microspheres (36 microm in size) (to render densities only slightly higher than water). A significant fraction of the deposited microspheres were deposited at grain-to-grain contacts (about 20% in glass beads, 40% in quartz sand) under the conditions examined. The deposited microsphere concentrations decreased log-linearly with increasing transport distance regardless of the environment of deposition (grain-to-grain contact versus single-contact deposition). The profile shape was, therefore, consistent with filtration theory, and the observed deposition rate coefficients were also well predicted by filtration theory. The ability of filtration theory to predict the magnitude and spatial distribution of deposition demonstrates that filtration theory captures the essential elements of deposition in the absence of an energy barrier despite a lack of accounting for grain-to-grain contacts. The observed factor of 2 greater deposition at grain-to-grain contacts in quartz sand relative to equivalently sized glass beads is consistent with greater grain-to-grain contact lengths and greater fraction of small pores in the quartz sand relative to the glass beads, as determined via a pore structure analysis algorithm (medial axis algorithm).     

Evaluation of the effects of porous media structure on mixing-controlled reactions using pore-scale modeling and micromodel experiments

The objectives of this work were to determine if a pore-scale model could accurately capture the physical and chemical processes that control transverse mixing and reaction in microfluidic pore structures (i.e., micromodels), and to directly evaluate the effects of porous media geometry on a transverse mixing-limited chemical reaction. We directly compare pore-scale numerical simulations using a lattice-Boltzmann finite volume model (LB-FVM) with micromodel experiments using identical pore structures and flow rates, and we examine the effects of grain size, grain orientation, and intraparticle porosity upon the extent of a fast bimolecular reaction. For both the micromodel experiments and LB-FVM simulations, two reactive substrates are introduced into a network of pores via two separate and parallel fluid streams. The substrates mix within the porous media transverse to flow and undergo instantaneous reaction. Results indicate that (i) the LB-FVM simulations accurately captured the physical and chemical process in the micromodel experiments, (ii) grain size alone is not sufficient to quantify mixing at the pore scale, (iii) interfacial contact area between reactive species plumes is a controlling factor for mixing and extent of chemical reaction, (iv) at steady state, mixing and chemical reaction can occur within aggregates due to interconnected intra-aggregate porosity, (v) grain orientation significantly affects mixing and extent of reaction, and (vi) flow focusing enhances transverse mixing by bringing stream lines which were initially distal into close proximity thereby enhancing transverse concentration gradients. This study suggests that subcontinuum effects can play an important role in the overall extent of mixing and reaction in groundwater, and hence may need to be considered when evaluating reactive transport.     

Modelling and simulation of drop spreading on fibrous porous media

Various operations in petroleum processing, textile technology, printing and composite processing involve wetting and spreading phenomena of liquids in porous media. These phenomena are being investigated using various tools, prominent among them being the spreading of a liquid drop on a porous medium. The spreading is governed by the inertial, gravitational, viscous and capillary forces and their relative importance have been studied to understand the underlying phenomena. In this work, drop spreading on heterogeneous porous media, such as composite reinforcing fabrics, has been investigated. The liquid drop spreading has been modelled in two stages: the flow of liquid on the surface of fabric and the imbibition of the liquid into the fabric due to inter-tow and intra-tow flow of the fluid. The model equations are formulated by making a hypothetical equivalent model of the fabric. The resulting equations are solved numerically. The model is used to simulate the spreading of liquid drops on glass fabrics. The drop spreading is characterized by height, contact radius and contact angle. The front of the liquid within the porous media can also be monitored through the model. Initially, a parametric study on the effect of fabric and tow porosities, the tow radius and the droplet volume on the imbibition time is presented. Finally, the model results are compared with the experimental results from literature. It is shown that the model can capture the essential features and provide insight into drop spreading on heterogeneous porous media.     

Influence of wettability and saturation on liquid-liquid interfacial area in porous media

The knowledge of the area of interfaces between phases is important to understand and quantify many flow and transport processes in porous media. In this work, we apply the interfacial tracer technique to study the dependence of fluid-fluid interfacial area on saturation and wettability. The interfacial area between the wetting and the nonwetting phases (brine and decane) in unconsolidated porous media (glass beads) was measured using an anionic surfactant (3-phenyl decyl benzene sulfonate) as an interfacial tracer. The beads are water-wet; treating them with organosilane rendered them oil-wet. The measurements were done at a series of steady-state fractional flows, providing data at intermediate as well as residual saturations. Flow rates were kept low so that capillary forces controlled the fluid configurations. We observe significant differences in interfacial areas as a function of wetting-phase saturation as the wettability is changed from water-wet to oil-wet. During primary drainage, measured interfacial area increases monotonically with decreasing water saturation in a water-wet medium. In contrast, the interfacial area measured in the oil-wet porous medium increases with decreasing decane saturation, reaches a maximum, and decreases as the residual decane saturation is achieved. The oil-wet experiment is qualitatively consistent with theoretical results that predict the existence of a maximum in fluid-fluid interfacial area during drainage. The water-wet experiment is consistent with theoretical predictions that include the area of grains in pores that have been drained. We conclude that, in the water-wet experiments, the tracer adsorbs at the interface between the nonwetting phase and the wetting films on grains. In the oil-wet experiments, either the oil films are not sustained at high water saturation or the tracer does not adsorb at them, possibly prevented by steric hindrance. Interpretation of interfacial tracer experiments therefore requires care: for some mass transport processes, the thin films of wetting phase on grains will not behave the same as macroscopic volumes of wetting phase.     

Gravitational settling effects on unit cell predictions of colloidal retention in porous media in the absence of energy barriers

Laboratory column experiments for colloidal transport and retention are often carried out with flow direction oriented against gravity (up-flow) to minimize retention of trapped air. However, the models that underlie colloidal filtration theory (e.g., unit cell models such as the Happel sphere-in-cell and hemispheres-in-cell) typically set flow in the same direction as gravity (down-flow). We performed unit model simulations and experimental observations of retention of colloids with different size and density in porous media in the absence of energy barriers under both up-flow and down-flow conditions. Unit cell models predicted very different deposition (e.g., for large or dense colloids with gravity number N(G) > 0.01 at pore water velocity of 4 m/day) under down-flow versus up-flow conditions, which reflect underlying influences of gravity and flow on simulated colloid trajectories that resulted in very different distributions of attached colloids over the model surfaces. The Happel sphere-in-cell model showed greater sensitivity to flow orientation relative to gravity than the hemispheres-in-cell model. In contrast, experimental results were relatively insensitive to orientation of flow with respect to gravity, as a result of the variety of orientations of flow relative to gravity and to the porous media surface that exist in actual porous media. Notably, the down-flow simulations corresponded most closely to the experimental results (for near neutrally buoyant colloids); which justifies the common practice of comparing up-flow experiments to theoretical predictions developed for down-flow conditions.