Article pubs.acs.org/Langmuir
Prediction of Nanoparticle and Colloid Attachment on Unfavorable Mineral Surfaces Using Representative Discrete Heterogeneity Jacob Trauscht, Eddy Pazmino, and William P. Johnson* Department of Geology and Geophysics, University of Utah, Salt Lake City, Utah 84112, United States
Downloaded by SWINBURNE UNIV OF TECHNOLOGY on September 5, 2015 | http://pubs.acs.org Publication Date (Web): August 20, 2015 | doi: 10.1021/acs.langmuir.5b02369
S Supporting Information *
ABSTRACT: Despite several decades of research there currently exists no mechanistic theory to predict colloid attachment in porous media under environmental conditions where colloid−collector repulsion exists (unfavorable conditions for attachment). It has long been inferred that nano- to microscale surface heterogeneity (herein called discrete heterogeneity) drives colloid attachment under unfavorable conditions. Incorporating discrete heterogeneity into colloid−collector interaction calculations in particle trajectory simulations predicts colloid attachment under unfavorable conditions. As yet, discrete heterogeneity cannot be independently measured by spectroscopic or other approaches in ways directly relevant to colloid−surface interaction. This, combined with the fact that a given discrete heterogeneity representation will interact differently with differently sized colloids as well as different ionic strengths for a given sized colloid, suggests a strategy to back out representative discrete heterogeneity by a comparison of simulations to experiments performed across a range of colloid size, solution IS, and fluid velocity. This has recently been performed for interaction of carboxylate-modified polystyrene latex (CML) microsphere attachment to soda lime glass at pH 6.7 with NaCl electrolyte. However, extension to other surfaces, pH values, and electrolytes is needed. For this reason, the attachment of CML (0.25, 1.1, and 2.0 μm diameters) from aqueous suspension onto a variety of unfavorable mineral surfaces (soda lime glass, muscovite, and albite) was examined for pH values of 6.7 and 8.0), fluid velocities (1.71 × 10−3 and 5.94 × 10−3 m s−1), IS (6.0 and 20 mM), and electrolytes (NaCl, CaSO4, and multivalent mixtures). The resulting representative heterogeneities (heterodomain size and surface coverage, where heterodomain refers to nano- to microscale attractive domains) yielded colloid attachment predictions that were compared to predictions from existing applicable semiempirical expressions in order to examine the strengths and weaknesses of the discrete heterogeneity approach and opportunities for improvement.
■
with a continuum of fluid velocities ranging from zero at the grain surface to a maximum at the watershed divide separating flow fields associated with adjacent grains.7 Colloid trajectory simulations are performed by employing force/torque balances that include fluid drag, diffusion, gravity, and colloid−surface interaction forces for a variety of colloid starting positions upstream from the grain.6 These trajectory simulations determine which colloid starting locations exit the collector without interacting with the grain surface versus those that reach the near-surface fluid domain, where colloid−surface interactions extend from the grain surface (typically to approximately 200 nm).8 Near-surface colloids attach to the grain when colloid−surface interactions in the near-surface fluid domain lack significant repulsion (favorable conditions for attachment). Trajectory simulations demonstrate that the likelihood of colloid interception of the near-surface fluid domain increases with the proximity of the colloid starting location to the
INTRODUCTION The filtration of nano- and microparticles (herein referred to as colloids) in environmental granular media is the predominant process in practical environmental engineering applications such as the design of low-energy water treatment systems, e.g., river bank filtration1,2 and targeted delivery of engineered nanoparticles for subsurface remediation.3−5 A major challenge in the design of such systems is predicting the attachment of colloids to surfaces in the presence of colloid−surface repulsion that is inferred to predominate under environmental conditions. Filtration concerns colloid transport to and attachment on surfaces in a complex tortuous flow field; it is not screening (straining), which would rapidly clog the porous medium. The prediction of attachment is performed via simulation of colloid trajectories based on force and torque balances in a collector that represents a porous medium. For example, the Happel sphere-in-cell collector represents granular media as a spherical grain with a fluid envelope having a thickness corresponding to the porosity of the media being considered.6 It has a flow field impinging normal to the grain surface, creating forward and rear flow stagnation zones on the upstream and downstream sides of the grain, respectively, © 2015 American Chemical Society
Received: June 29, 2015 Revised: August 8, 2015 Published: August 11, 2015 9366
DOI: 10.1021/acs.langmuir.5b02369 Langmuir 2015, 31, 9366−9378
Article
Downloaded by SWINBURNE UNIV OF TECHNOLOGY on September 5, 2015 | http://pubs.acs.org Publication Date (Web): August 20, 2015 | doi: 10.1021/acs.langmuir.5b02369
Langmuir forward flow stagnation axis whereas diffusion and gravity may move colloids toward streamlines that intercept the nearsurface fluid domain. The fraction of all simulated colloids entering the collector that reach the near-surface fluid domain is quantified as the collector efficiency (η). The value of η is determined as a function of parameters such as porosity, colloid size, and fluid velocity.6 The predicted η well matches the observed colloid retention in simplified systems such as spherical colloids in uniform spherical porous media grains under favorable conditions.9 To provide an easily implemented mechanistically based predictive capability under favorable conditions, the mechanistic simulations are approximated by correlation equations that represent the various forces via three dimensionless quantities describing the colloid interception of the near-surface fluid domain: (a) absent diffusion and sedimentation, (b) augmented by diffusion, and (c) augmented by settling.6,11−13 Colloid−collector repulsion (unfavorable conditions for attachment) may arise from electroosmotic and steric interactions, the former arising from overlapping electric double layers as defined by the respective electrical potentials of the surfaces, as approximated by their ζ-potentials.8,9 Oppositely charged surfaces experience no electric double layer repulsion, which in the absence of steric interactions yields favorable conditions for attachment. The ζ-potential is a meanfield parameter, meaning that it represents the bulk property of the surfaces and is insensitive to nano- to microscale charge heterogeneity that may exist on surfaces.9 As such, a conventional estimation of colloid−surface repulsion using mean field ζ-potentials for like-charged surfaces (unfavorable conditions) produces colloid−collector repulsion that prevents colloid attachment in mechanistic trajectory simulations.14,16,17 Colloid attachment is, in fact, significant under unfavorable conditions,8−10,14,16,17 leading to the use of an attachment efficiency (α = ηunf/ηfav) to quantify the difference between collector efficiencies observed under unfavorable relative to favorable conditions. The prediction of colloid retention in granular media having measurable favorable surfaces (herein called macroscopic heterogeneity) can be successfully approximated using a simple linear patchwise combination of α values, where α is considered to be equal to unity for the fraction of favorable surface and zero for the fraction of unfavorable surface.5,16,17 However, this patchwise linear combination approach predicts zero colloid attachment in porous media under unfavorable conditions lacking macroscopic heterogeneity. Significant colloid attachment has been inferred in scores of column experiments packed with cleaned glass beads and quartz sand9,18−21 and has been directly observed in such media in micromodels.8,10,15 While it is reasonable to nominally expect that in natural porous media there exists sufficient macroscopic heterogeneity to support the patchwise linear approximation, reported field results from multiple locations demonstrate decreases in the attachment rate coefficient with increasing transport22,23 that are consistent with unfavorable conditions.20,21 Predominantly unfavorable conditions in natural porous media having macroscopic heterogeneity may arise from electrosteric repulsion, e.g., via adsorbed natural organic matter, on what otherwise would be favorable environmental surfaces.24−26 Colloid association with surfaces via relatively long-range van der Waals attraction that exists beyond the reach of electric double layer repulsion (typically between several tens to 200 nm) is an important influence on colloid transport behavior
under unfavorable conditions.15 Furthermore, the comparison of this longer-range attractive energy to Maxwell-based colloid kinetic energies serves as a means to estimate colloids associated with surfaces via van der Waals forces,27 which may potentially yield colloid retention over the spatial and time scales involved in colloid transport experiments in porous media.27−31 However, the relatively distant van der Waals interactions alone do not immobilize colloids.32 Absent mechanistic trajectory simulations (based on force/ torque balance) to predict colloid attachment (immobilization) under unfavorable conditions, there have been developed several semiempirical expressions for the prediction of α.19,33−35 These expressions were developed from experiments examining the retention of colloids in porous media, where the colloids were predominantly carboxylate-modified polystyrene latex (CML) microspheres and the porous medium was predominantly uniform-sized soda lime glass beads or quartz sand. The mechanism of colloid attachment on unfavorable surfaces lacking macroscopic heterogeneity is inferred to result from nano- to microscale charge heterogeneity and roughness on surfaces,10,36 which we herein refer to as discrete heterogeneity. Individual physical asperities collectively produce roughness and locally reduce the radius of curvature of the surface such that the calculated repulsion is locally reduced or eliminated,37−39 since the colloid−surface interaction force scales directly with the local radius of curvature.40 Discrete heterogeneity may also be chemical, i.e., charge heterogeneity, which reduces or eliminates the calculated repulsion if these heterodomains (herein referring to localized zones of opposite charge) comprise a sufficient portion of zone over which the colloid interacts with the collector surface.37−39,41 The incorporation of discrete heterogeneity into calculations of colloid−collector repulsion produces mechanistic trajectory simulations that predict colloid attachment under unfavorable conditions.37−39,41 Furthermore, when discrete heterogeneity is incorporated into a collector geometry that includes a grain-tograin contact,13 the various modes of colloid retention that have been observed experimentally under unfavorable conditions emerge from the mechanistic trajectory simulations,42 e.g., wedging in grain-to-grain contacts of colloids ∼ >2 μm in diameter.15 It is not currently feasible to independently directly measure heterodomains via methods directly relevant to colloid−surface interaction. This is evidenced by their insignificant influence on the measured zeta potential (ζ)14 and the relatively low resolution of volume force imaging by atomic force microscopy.43,44 Whereas spectroscopic or other independent measurement of discrete heterogeneity is a worthy pursuit, it may also be possible to constrain attributes of discrete heterogeneity by a comparison of simulations to experiments.8 This is possible because a given-sized heterodomain interacts differently with differently sized colloids or a given-sized colloid under different solution ionic strength (IS). The net colloid− surface interaction (attractive versus repulsive) at a given location depends on the extent to which the zone of colloid− surface interaction (ZOI) is occupied by heterodomains.8,39,41 The radius of the ZOI scales directly with ionic strength (IS) and colloid radius (ap)8,39,41 RZOI ≈ 2 κ −1a p 9367
(1) DOI: 10.1021/acs.langmuir.5b02369 Langmuir 2015, 31, 9366−9378
Article
Downloaded by SWINBURNE UNIV OF TECHNOLOGY on September 5, 2015 | http://pubs.acs.org Publication Date (Web): August 20, 2015 | doi: 10.1021/acs.langmuir.5b02369
Langmuir where κ−1 is the Debye length (inversely related to IS) and the net colloid−surface interaction (attractive versus repulsive) for a given-sized heterodomain depends on the colloid size and solution IS. As a result of the above-described dependence of ZOI on colloid size and IS, the net colloid−surface interaction (favorable versus unfavorable) for a given heterodomain varies with colloid size and solution conditions. This may allow backing out a representative discrete heterogeneity for a given surface by a comparison of simulations to experiments varying colloid size and solution IS. The influences of surface charge and heterogeneity are interrelated since mineral defects and surface mineral precipitants may locally influence both charge and roughness. Whereas the simulation of this effect is herein performed mechanistically in terms of charge heterogeneity, the actual discrete heterogeneity may include roughness. It is an ongoing research question as to whether such an approach effectively represents both charge and roughness mechanisms that reduce repulsion, e.g., Bendersky et al.40 The above-described approach to back out representative heterogeneity was recently reported successful by Pazmino et al.8 for soda lime glass (silica) based on the attachment of carboxylate-modified polystyrene latex microspheres (CML) under unfavorable conditions for a range of CML sizes (0.25 to 2.0 μm diameter), fluid velocities (1.71 × 10−3 to 5.94 × 10−3 m/s), and IS (6 to 20 mM NaCl) at pH 6.7. The experiments of Pazmino et al.8 were performed in a micromodel to allow direct observation of colloid attachment; however, since attachment is difficult to quantify in packed porous media micromodels (given the large observation volume relative to the depth of focus of optical microscopy) a planar impinging jet (radial stagnation point flow) system was used to allow the quantification of colloid attachment on a single plane. This array of experiments was well described with a representative discrete heterogeneity having Pareto size-distributed heterodomains (approximated with 60 and 120 nm radii) at a total surface coverage of 0.04%. The representative discrete heterogeneity not only quantitatively predicted CML retention on silica but also qualitatively predicted CML detachment from silica in response to perturbations of IS or flow.45 To our knowledge, no previously existing mechanistic colloid trajectory model has predicted both attachment and detachment using a single set of parameters. The success of the discrete heterogeneity approach for CML attachment (and detachment) on silica holds promise for expanding this construct to other unfavorable surfaces and solution chemistries that exist in natural porous media. For example, colloid transport experiments show strong influences of pH46,47 and electrolyte valence.48,49 It is an open question as to whether the representative discrete heterogeneity that successfully represented CML attachment to silica at pH 6.7 with the NaCl electrolyte will also succeed at other pH values and in the presence of other electrolytes. Furthermore, it is not clear whether CML interaction with other (nonsilica) mineral surfaces can be represented using the discrete heterogeneity approach. To explore these questions for a range of conditions expected in groundwater we performed experiments on a variety of unfavorable mineral surfaces (silica, muscovite, sodium-feldspar) at multiple solution pH values (6.7−8.0) and multiple solution electrolyte types (NaCl, CaSO4, and CaCO3-dominated synthetic groundwater) for a range of CML sizes (0.25−2.0 μm) and fluid velocities (1.71 × 10−3 to 5.94 × 10−3 m/s). Discrete heterogeneity simulations were conducted to determine whether this approach was able to capture the
experimental results and to determine whether the representative discrete heterogeneity characteristics (heterodomain size, distribution, and surface coverage) differed for different minerals, pH conditions, and electrolytes. Predictions from representative discrete heterogeneity simulations were made to applicable alternative methods for predicting α. Our comparisons highlight the strengths of the discrete heterogeneity approach and opportunities for improvement.
■
METHODS
Microsphere Suspension and Collector Properties. Carboxylate-modified polystyrene latex (CML) fluorescent (λex 505, λex 515 nm) microspheres (Molecular Probes, Inc., Eugene, OR) of three sizes (0.25, 1.1, and 2.0 μm diameter) were used in the experiments. Colloid suspensions were prepared from stock in relevant solution to the required concentrations of 5 × 106, 3.5 × 106, and 2 × 106 microspheres per milliliter for the 0.25, 1.1, and 2.0 μm colloids, respectively. The microsphere suspension concentration was determined via vacuum filtration of colloid solution (volume adjusted to ensure >20 CML per view area) on 0.1 μm polycarbonate filters (Millipore) followed by averaging counts of 25 random observation areas using wide-field fluorescence for colloid illumination and scaling this average to the area of deposition on the filter. Suspension IS was adjusted using either NaCl, CaSO4, or artificial groundwater (AGW) representing groundwater of the Snake River aquifer50 (Supporting Information Table SI-1). All solutions were buffered with 2.2 mM MOPS buffer (3-(N-morpholino) propanesulfonic acid, 4-morpholinepropanesulfonic acid; Sigma-Aldrich Corp.) with pH set to 6.7 and 8.0 using NaOH (0.5 M). The CML electrophoretic mobility (EPM) was measured in suspensions using a ζ-potential analyzer (Mobiuζ, Wyatt Technology Corp., Santa Barbara, CA). CML ζ-potentials were calculated from EPM via the Smoluchowski equation.51 CML attachment was examined on three different collector surfaces: soda lime glass (silica) microscope slides (Fisher Scientific, Inc.), synthetic muscovite sheets (H2KAI3(Si04)3) (Electron Microscopy Sciences, Hatfield, PA), and thin sections of albite (NaAlSi3O8) (prepared by the University of Utah Rock Preparation Laboratory). Values of ζ-potential for silica and muscovite in NaCl electrolyte were interpolated from values obtained from the literature52−54 as reported in the Supporting Information (Table SI-2). ζ-potential values for silica in CaSO4 and AGW electrolytes, as well as albite in NaCl, were determined from EPM measurements. EPM was measured in the filtrate (
