A Unified Force and Torque Balance for Colloid Transport: Predicting

Article Cite This: Langmuir 2019, 35, 9061−9070

pubs.acs.org/Langmuir

A Unified Force and Torque Balance for Colloid Transport: Predicting Attachment and Mobilization under Favorable and Unfavorable Conditions Kurt VanNess, Anna Rasmuson, Cesar A. Ron, and William P. Johnson* Department of Geology & Geophysics, University of Utah, 115 South 1460 East, Salt Lake City, Utah 84112, United States

Downloaded via BUFFALO STATE on July 28, 2019 at 09:50:43 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

S Supporting Information *

ABSTRACT: Colloid attachment and detachment behaviors concern a wide range of environmental contexts but have typically been mechanistically predicted exclusive of one another despite their obvious coupling. Furthermore, previous mechanistic prediction often addressed packed column contexts, wherein specific forces and torques on the colloid could not be well-constrained, preventing robust predictions. These weaknesses were addressed through direct observation experiments under conditions where perfect sink assumptions fail and allow calibration of the contact between the colloid and collector. Attachment and flow perturbation experiments in the presence of colloid−collector attraction (favorable conditions) permitted calibration of contact parameters without the complexity that comes with colloid−collector repulsion (unfavorable conditions). Combining calibrated contact parameters with discrete representative nanoscale heterogeneity, developed to predict unfavorable attachment, provided an independent means to predict unfavorable detachment. The result was mechanistic prediction of colloid attachment and detachment that quantitatively agreed with experimental observation for both ionic strength and flow perturbation results, improving significantly upon previous qualitative prediction.

■

INTRODUCTION Contexts of Interest for Colloid Attachment and Detachment. A range of transport contexts drive the need to understand how changes in solution conditions affect colloid attachment and detachment. For example, targeted delivery of novel nano- and microparticles to surfaces is of interest in drug delivery, wherein encapsulated pharmaceuticals are directed to particular organs, as well as in subsurface environmental cleanup, wherein nanoparticles are delivered to contaminated locales for contaminant sequestration (e.g., activated carbon nanoparticles) or degradation (e.g., nanozero valent iron). In another transport context linking environment and health, the association between heavy rainfall and waterborne disease outbreaks1,2 suggests that increased pathogen transport can stem from remobilization of immobilized pathogens (increased detachment) or from a reduction in attenuation of pathogens (decreased attachment) in response to heavy rainfall. Shortcomings of Past Colloid Attachment and Detachment Investigations. Colloid detachment involves a force and torque balance (Figure 1c), wherein detachment occurs when the mobilizing torque (from hydrodynamic drag) exceeds the arresting torque (from adhesion).3 A torque balance is less frequently applied to colloid attachment, since it is often bypassed using a perfect sink boundary condition to approximate the torque balance. However, the same forces and torques that determine detachment also govern attachment, © 2019 American Chemical Society

wherein immobilization (attachment) is permitted only when the arresting torque exceeds the mobilizing torque. Given that the same torque balance underlies both attachment and detachment, it is surprising that existing work often focuses on predicting solely attachment4−7 or solely detachment,8−11 as if these two processes occur independently. The approach has been further fragmented by treating detachment with different theories depending on the type of perturbation: physical or chemical.3 That colloid arrest and mobilization depend on the same torque balance requires that predictions be tested against attachment and detachment experiments (under both physical and chemical perturbations) to test whether essential elements governing both processes are captured and to create a unified theory predicting colloid transport. Another weakness of existing literature regarding colloid detachment from surfaces is the heavy reliance of existing work on breakthrough-elution curves and retention profiles from porous media packed columns.12−16 Characterization of the arresting and mobilizing torques requires knowledge of colloidscale adhesive forces and near-surface fluid velocities, which are poorly constrained in porous media packed columns. Received: March 27, 2019 Revised: June 2, 2019 Published: June 10, 2019 9061

DOI: 10.1021/acs.langmuir.9b00911 Langmuir 2019, 35, 9061−9070

Article

Langmuir

Figure 1. (a) An example of the resultant flow field generated in COMSOL Multiphysics for the impinging jet flow cell. Hot and cold colors indicate high and low fluid velocities, respectively. (b) Within the jet radius, tangential fluid velocities near the surface increase moving outward from the jet axis. Comparing mobilizing torque (blue arrow) to arresting torque (red arrow) determines colloidal attachment or detachment. (c) The arresting torque (red) is composed of the adhesive force acting on a lever arm generated from the colloid−collector contact area radius. The mobilizing torque (blue) is composed of the drag force acting on an effective lever arm generated from the forces and torques due to the fluid shear and colloid translation and rotation in the fluid.

Figure 2. Favorable (blue) and unfavorable (red) colloid−surface interaction energy curves using bulk surface zeta potentials. Including a steric repulsive force (b) significantly reduces the magnitude of the primary energy minimum for favorable conditions and eliminates the minimum for unfavorable conditions, while the secondary energy minimum is unaffected (inset).

Furthermore, a range of retention modes exists in porous media, including arrest either on the open grain surface or in grain-to-grain contacts, as well as retention without attachment via strong secondary minimum interactions (explained below) and/or in low fluid velocity domains.7,15,17,18 The distribution of near-surface fluid velocities in packed columns ranges greatly across each grain surface from forward to rear flow stagnation zones,15 preventing direct comparison of breakthrough-elution curves and retention profiles to predictions of arrest and mobilization based on forces and torques. Energies Defining Colloid Attachment and Detachment. The arresting torque is largely defined by colloid− collector surface interactions that include attractive van der Waals (vdW) and electric-double layer (EDL) interactions. The EDL interactions may be attractive or repulsive depending on whether colloid and collector surfaces are opposite- versus like-charged, respectively. Other colloid−surface interactions may also be significant such as Born (atomic-scale repulsion),

Lewis acid−base (LAB) (electron donor/acceptor interactions), and steric forces (e.g., hydration repulsion, solvation). Because the various interactions persist over varying distances, the net interaction may shift from net attractive to repulsive over small changes in colloid−collector separation distance (Figure 2). A primary difficulty in predicting colloid attachment to, and detachment from, surfaces stems from conditions in which colloid−surface EDL repulsion exists, which is the prevalent condition for colloidal transport in the environment and other contexts where the interacting surfaces are like-charged (both positive or both negative). For conditions where EDL repulsion is absent (oppositely charged surfaces), so-called favorable conditions, there is a single energy minimum (typically within 1−2 nm separation distance), called the primary minimum (Figure 2a, blue line). For conditions where EDL repulsion is present, so-called unfavorable conditions, two energy minima exist: (1) a primary minimum typically within 9062

DOI: 10.1021/acs.langmuir.9b00911 Langmuir 2019, 35, 9061−9070

Article

Langmuir

fraction of the ZOI to generate a net attractive interaction. The ZOI size is proportional to colloid size and Debye length,26,31 such that, for given colloid and heterodomain sizes, high ionic strength favors net attraction, and low ionic strength favors net repulsion. In the absence of steric interactions such as solvation and hydration forces emanating from solvent interaction, as well as structural interactions32 (e.g., roughness), atomic-scale Born repulsion force alone counteracts vdW attraction to set the limit on primary minimum depth. However, insurmountable barriers to detachment that contradict experimental observations result (Figure 2a), unless the Born collision parameter is increased from the generally accepted value of 0.5 nm, for example, to 2.0 nm,21 or unless other forms of steric repulsion are included22 (Figure 2b). In the absence of known justification for increasing the Born collision parameter, this work utilizes steric repulsion to reduce the insurmountable barrier to detachment. Objectives. Previous studies (as described above) employed parameters to simulate poorly constrained, underdetermined systems. This study utilized highly constrained directly observed attachment of spherical colloids on smooth surfaces under favorable conditions in a known impinging jet flow field to recalibrate otherwise difficult to constrain parameters to predict both attachment and detachment under unfavorable conditions, wherein neither were previously quantitatively predictable. To achieve this, we incorporated new understanding of nanoscale heterogeneity on bulk repulsive surfaces (DRNH), as well as repulsive interactions operating at larger-than-Born scales (steric interactions). We do this for both favorable and unfavorable conditions for the following reasons. Favorable conditions lack complication from repulsive EDL interactions, thereby obviating impacts of nanoscale heterogeneity and allowing steric impacts on colloid arrest and mobilization to be discerned. Unfavorable conditions include repulsive EDL interactions and the influence of nanoscale heterogeneity. With steric interactions resolved under favorable conditions, unfavorable conditions provide the opportunity for DRNH22,28,33 to predict colloid attachment and detachment under unfavorable conditions using the same set of parameters. We show that these predictions are greatly improved relative to those previously reported using steric parameters that were not independently constrained.22

1−2 nm separation distance; and (2) a shallow secondary minimum typically at several tens of nanometers separation distance derived from the longer range of vdW interactions relative to EDL (Figure 2a, red line). The repulsive energy barrier separating these minima is defined by the EDL interaction between the like-charged surfaces. The barriers to colloid attachment in, or detachment from, primary minima are therefore set by the differences between the height of the repulsive barrier and the depth of the secondary minimum, or primary minimum, respectively (Figure 2a, red line). Likewise, the barrier to colloid reentrainment from secondary minima is the secondary minimum depth, where the term “reentrainment” is used rather than “detachment”, since secondary minimum-associated colloids are not immobilized.18,19 Diffusion energy may be sufficiently strong to drive colloid detachment from an energy minimum if the detachment energy barrier is no larger than ∼10 kT.20 For larger barriers, perturbations such as increased kinetic energy via fluid flow (increased mobilizing torque via fluid drag) or reduced solution ionic strength (decreased arresting torque via increased repulsion) are required for detachment.21,22 Under unfavorable conditions, the barrier to attachment in, as well as to detachment from, primary minima are typically insurmountable (Figure 2a, red line), when predicted from measured bulk surface parameters.23 The contradiction between the insurmountable calculated barrier to detachment (under constant potential) and the observed detachment of colloids in response to ionic strength reduction led some11,24,25 to conclude that colloid retention preceding colloid mobilization occurred in secondary minima, since ionic strength reduction may eliminate the barrier to detachment from secondary minima but not primary minima, according to calculations considering bulk surface parameters. While secondary minimum elimination with reduced ionic strength qualitatively explains observed detachment, it cannot explain the observed immobilization of colloids in zones of high fluid drag, where colloids are often delivered to, and arrested on, grain surfaces.18,26 Influence of Chemical Heterogeneity and Steric Interactions on Energies of Interaction. The presence of strong energy barriers impeding colloid delivery to the primary energy minimum leads to prediction of no colloid attachment despite clear experimental observation to the contrary. This discrepancy is resolved by inclusion of discrete representative nanoscale heterogeneity (DRNH) comprised by heterodomains26−29 (e.g., nanoscale zones of opposite charge to bulk surface). It is not necessary to attribute all nanoscale heterogeneity to charge, since it is likely that variation in other surface chemical properties may exist (e.g., Hamaker constant, LAB characteristics, etc.). Furthermore, physical roughness is another form of nanoscale heterogeneity.30 The current inability to distinguish the various forms of physical and chemical heterogeneity at nanoscales leads us to utilize roughness and charge as the primary surrogates for these various forms of heterogeneity. In DRNH, a colloid may encounter heterodomains as it moves over a surface in response to the imposed forces26 (drag, Brownian, colloid−surface, gravity, etc.). The colloid− surface interaction at any given moment ranges from net repulsive to attractive depending on whether the effective zone of colloid−surface interaction31 (ZOI) lies over a heterodomain(s) and whether heterodomains occupy a sufficient

■

EXPERIMENTAL SECTION

Microsphere Solution. Experiments examined 7.0 μm diameter aminated polystyrene latex fluorescent microspheres (Magsphere). Colloid suspensions were diluted from stock in pure water (Milli-Q) to the desired concentration of 2.5 × 105 microspheres per milliliter. The pH was set to 2.0 using HCl (1.3 M), and ionic strength was increased using NaCl (50 mM) to guarantee the colloid−collector attraction (favorable attachment conditions) necessary to constrain steric interactions and contact mechanics (discussed below). Colloid electrophoretic mobility was measured using a ζ-potential analyzer (Zetasizer Nano, Malvern Instruments Ltd. Worcestershire, U.K.). ζpotential was calculated to be 1.9 ± 1.1 mV from the electrophoretic mobilities via the Smoluchowski equation.34 Collector Surface. Deposition on microscope soda-lime glass (herein referred to as glass) slides (Fisher Scientific, Inc.) was examined for the impinging surface in the impinging jet flow cell. Glass slides were cleaned via the SC-1 procedure35 prior to every experiment. Glass slide ζ-potential was estimated to be −10 mV from representative values reported in the literature.36 Streaming potential measurement of the collector surface ζ-potential would likely not 9063

DOI: 10.1021/acs.langmuir.9b00911 Langmuir 2019, 35, 9061−9070

Article

Langmuir

Figure 3. Experimental images showing the decrease in colloid retention radius as a function of flow rate (4.7, 21, 43 mL/min). Upper and lower panels indicate retention radii under loading and flow perturbation conditions, respectively. Red circles indicate approximate retention radii. surface interactions are highly significant). This contrast yields contrasting colloid residence times in the near surface fluid domain, which ranges from negligible to dominant under favorable to unfavorable conditions, respectively.29,33 We therefore use η to quantify attachment under favorable and unfavorable conditions to avoid misperception regarding the role of transport under favorable versus unfavorable conditions. An additional reason that we do not utilize α to quantify attachment herein is that our goal is to explore conditions wherein η even under favorable conditions is not correctly predicted by the commonly used perfect sink boundary condition that by-passes full force and torque balance. It is under these favorable conditions, with high fluid velocity, that steric and contact mechanics parameters are constrained. Whereas the constrained parameters are demonstrated to yield improved prediction under unfavorable conditions, the primary contrast herein is between perfect sink versus full force and torque balance predictions under favorable conditions. Using η consistently to quantify attachment reinforces focus on that contrast. Experimental conditions included flow rates of 4.7, 13, 21, 32, 43, and 57 mL/min. These flow rates, while greater than environmentally relevant, yielded a laminar flow field, and allowed determination of contact mechanics parameters that greatly improved prediction of attachment and mobilization at lower flow rates under unfavorable conditions, as described below. Flow perturbation experiments were conducted following initial colloid loading onto a clean slide with 4.7 mL/min flow rate. Incremental increases in flow rate (4.7, 13, 21, 43 mL/min) led to the observed detachment and corresponding step decreases in retention radius (Figures 3, SI-2). Attachment and detachment of 7 μm colloids under flow conditions that shifted the torque balance between arrest and mobilization in direct observation experiments were examined to constrain steric parameters and the loading hysteresis factor (both described below). Favorable conditions were chosen for calibration to avoid additional complications that arise in estimating the colloid− collector interaction under unfavorable conditions. Retention radii (Figure 3) and associated error were objectively determined via decreased areal colloid concentrations as a function of radial coordinate. Radially symmetric annuli of identical width (25 μm) were examined to determine the areal concentration as a function of radius from the jet axis (Figures SI-1 and SI-2). For each flow rate, the upper bound of the loading retention radius was indicated by the smallest annulus with near-zero areal concentration, whereas the lower bound of the loading retention radius was indicated by the largest annulus with near-maximum areal concentration (Figure SI-1). For each increase in flow rate, the upper bound of the perturbation retention radius was indicated by the smallest annulus with significant decrease (>20%) in areal concentration,

improve this value, and furthermore the results of this work are not strongly sensitive to bulk ζ -potential on the collector surface. Impinging Jet Experiments. A custom-made stainless-steel impinging jet flow cell (radially symmetric) was used to observe colloid retention and mobilization as in previous studies.26,30 The jet (cell inlet) was 500 μm in radius, and the impinging surface was located 1.25 mm from the jet, perpendicular to the jet axis. To ensure an evenly radial distribution of the flow across the cell, four outlets were evenly spaced in a circular array at a radial distance 10 mm from the jet axis. Colloids were experimentally observed using a 10x objective (Nikon, Japan) utilizing wide-field fluorescence with a bandpass filter for excitation (478−493 nm) and a (405/488/543 nm) dichroic filter for emission (Chroma Technology Corp., Bellows Falls, VT). Images were acquired via a CoolSNAP HQ CCD camera (Photometrics, Tucson, AZ) and processed using image analysis software (MetaMorph, Universal Imaging Corp., Downingtown, PA). A detailed description of the optical setup is provided in previous publications.26,28,30,36 The flow field in a confined impinging jet is radially symmetric such that tangential fluid velocities at the surface of the collector initially increase moving outward from the jet axis before decreasing beyond the radius of the jet (Figures 1, SI-6). Utilizing this flow field, circular domains of colloid retention centered on the jet axis (retention rings) formed (Figures 3, SI-1, SI-2), inside which tangential flow was sufficiently low to allow retention. Irregularities in the experimentally observed circular retention rings are attributed to small-scale irregularities in the flow field, on the collector surface, and possibly in the colloid population, which are beyond our current scope of characterization. Despite these irregularities, the retention rings were well indicated by observed dramatic decreases in colloid areal concentrations as a function of proximity to the jet axis (Figures SI-1 and SI-2). The outer radius of these domains indicated the radius at which the two opposing torques were equal and opposite (retention radius), thereby constraining the steric parameters. Favorable colloid retention experiments were conducted by injecting colloidal suspensions in the flow cell after 10 min of equilibration with colloid-free solution and quantified by the collector efficiency (η = number attached/number injected) and by the radius of colloid retention. Collision efficiency (α), the ratio of collector efficiency under unfavorable versus favorable conditions, respectively, is traditionally used to represent colloid attachment under unfavorable conditions. This tradition generalizes α as reflecting “chemical surface interaction” processes and η as reflecting “physical transport” processes. However, this generalization is misleading, since both α and η reflect transport; η reflects colloid transport in the bulk fluid (where colloid−surface interactions are insignificant), and α reflects colloid transport in the near-surface fluid domain (where colloid− 9064

DOI: 10.1021/acs.langmuir.9b00911 Langmuir 2019, 35, 9061−9070

Article

Langmuir

Torque Balance in Contact with Collector Surface. Upon contact with the collector surface, force and torque balances were applied to the colloid. The force balance determined the equilibrium colloid−collector separation distance, and the balance of arresting and mobilizing torques determined arrest versus rolling on the collector surface. The mobilizing torque is composed of a hydrodynamic drag force that acts on an effective lever arm created using the ratio of the torque to force37,44 (Figure 1). τ lever arm = a p + i Fi (4)

whereas the lower bound was indicated by the largest annulus with negligible change ( More Information & Downloads.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (801) 585-5033. Fax: (801) 581-7065. ORCID

William P. Johnson: 0000-0003-3126-3877 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research was supported by the National Science Foundation Hydrologic Science Program (1547533). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We are also grateful for the technical and facility support provided at the Center for High Performance Computing at the Univ. of Utah.

■

REFERENCES

(1) Curriero, F. C.; Patz, J. A.; Rose, J. B.; Lele, S. The Association between Extreme Precipitation and Waterborne Disease Outbreaks in the United States, 1948−1994. Am. J. Public Health 2001, 91 (8), 1194−1199. (2) Auld, H.; MacIver, D.; Klaassen, J. Heavy Rainfall and Waterborne Disease Outbreaks: The Walkerton Example. J. Toxicol. Environ. Health, Part A 2004, 67 (20−22), 1879−1887. (3) Ryan, J. N.; Elimelech, M. Colloid Mobilization and Transport in Groundwater. Colloids Surf., A 1996, 107 (95), 1−56. (4) Rajagopalan, R.; Tien, C. Trajectory Analysis of Deep-Bed Filtration with the Sphere-in-Cell Porous Media Model. AIChE J. 1976, 22 (3), 523−533. (5) Tufenkji, N.; Elimelech, M. Correlation Equation for Predicting Single-Collector Efficiency in Physicochemical Filtration in Saturated Porous Media. Environ. Sci. Technol. 2004, 38 (2), 529−536. (6) Nelson, K. E.; Ginn, T. R. New Collector Efficiency Equation for Colloid Filtration in Both Natural and Engineered Flow Conditions. Water Resour. Res. 2011, 47 (5), 1−17. (7) Ma, H.; Pazmino, E.; Johnson, W. P. Surface Heterogeneity on Hemispheres-in-Cell Model Yields All Experimentally-Observed NonStraining Colloid Retention Mechanisms in Porous Media in the Presence of Energy Barriers. Langmuir 2011, 27 (24), 14982−14994. 9069

DOI: 10.1021/acs.langmuir.9b00911 Langmuir 2019, 35, 9061−9070

Article

Langmuir Nanoscale Electrostatic Heterogeneity. J. Colloid Interface Sci. 2008, 326 (1), 18−27. (28) Trauscht, J.; Pazmino, E.; Johnson, W. P. Prediction of Nanoparticle and Colloid Attachment on Unfavorable Mineral Surfaces Using Representative Discrete Heterogeneity. Langmuir 2015, 31 (34), 9366−9378. (29) Ron, C. A.; VanNess, K.; Rasmuson, A.; Johnson, W. P. How Nanoscale Surface Heterogeneity Impacts Transport of Nano- to Micro-Particles on Surfaces under Unfavorable Attachment Conditions. Environ. Sci.: Nano 2019, No. 6, 1921−1931, DOI: 10.1039/ C9EN00306A. (30) Rasmuson, A.; Pazmino, E.; Assemi, S.; Johnson, W. P. Contribution of Nano- to Microscale Roughness to Heterogeneity: Closing the Gap between Unfavorable and Favorable Colloid Attachment Conditions. Environ. Sci. Technol. 2017, 51 (4), 2151− 2160. (31) Duffadar, R.; Kalasin, S.; Davis, J. M.; Santore, M. M. The Impact of Nanoscale Chemical Features on Micron-Scale Adhesion: Crossover from Heterogeneity-Dominated to Mean-Field Behavior. J. Colloid Interface Sci. 2009, 337 (2), 396−407. (32) Israelachvili, J. N. Solvation, Structural, and Hydration Forces. In Intermolecular and Surface Forces; Elsevier, 2011; pp 341−380. (33) Johnson, W. P.; Rasmuson, A.; Pazmiño, E.; Hilpert, M. Why Variant Colloid Transport Behaviors Emerge among Identical Individuals in Porous Media When Colloid-Surface Repulsion Exists. Environ. Sci. Technol. 2018, 52 (13), 7230−7239. (34) Ohshima, H. Electrophoresis of Soft Particles: Analytic Approximations. Electrophoresis 2006, 27 (3), 526−533. (35) Kern, W.; Puotinen, D. A. Cleaning Solutions Based on Hydrogen Peroxide for Use in Silicon Semiconductor Technology. RCA Rev. 1970, 31, 187−206. (36) Tong, M.; Johnson, W. P. Excess Colloid Retention in Porous Media as a Function of Colloid Size, Fluid Velocity, and Grain Angularity. Environ. Sci. Technol. 2006, 40 (24), 7725−7731. (37) Goldman, A. J.; Cox, R. G.; Brenner, H. Slow Viscous Motion of a Sphere Parallel to a Plane WallII Couette Flow. Chem. Eng. Sci. 1967, 22 (4), 653−660. (38) Masliyah, J. H.; Bhattacharjee, S. Deposition of Colloidal Particles. In Electrokinetic and Colloid Transport Phenomena; John Wiley & Sons, Inc.: Hoboken, NJ, 2005; pp 469−536. (39) Saffman, P. G. The Lift on a Small Sphere in a Slow Shear Flow. J. Fluid Mech. 1965, 22 (2), 385−400. (40) Yahiaoui, S.; Feuillebois, F. Lift on a Sphere Moving near a Wall in a Parabolic Flow. J. Fluid Mech. 2010, 662, 447−474. (41) Wood, J. A.; Rehmann, L. Geometric Effects on Non-DLVO Forces: Relevance for Nanosystems. Langmuir 2014, 30 (16), 4623− 4632. (42) Van Oss, C. J. Interfacial Forces in Aqueous Media; Taylor & Francis, 1994. (43) Van Oss, C. J. The Extended DLVO Theory. Interface Sci. Technol. 2008, 16, 31−48. (44) Hubbe, M. A. Theory of Detachment of Colloidal Particles from Flat Surfaces Exposed to Flow. Colloids Surf. 1984, 12 (C), 151− 178. (45) Johnson, K. L.; Kendall, K.; Roberts, A. D. Surface Energy and the Contact of Elastic Solids. Proc. R. Soc. London, Ser. A 1971, 324 (1558), 301−313. (46) Van Oss, C. J. Use of the Combined Lifshitz-van Der Waals and Lewis Acid-Base Approaches in Determining the Apolar and Polar Contributions to Surface and Interfacial Tensions and Free Energies. J. Adhes. Sci. Technol. 2002, 16 (6), 669−677. (47) Hoek, E. M. V.; Agarwal, G. K. Extended DLVO Interactions between Spherical Particles and Rough Surfaces. J. Colloid Interface Sci. 2006, 298 (1), 50−58. (48) Torkzaban, S.; Bradford, S. A. Critical Role of Surface Roughness on Colloid Retention and Release in Porous Media. Water Res. 2016, 88, 274−284. (49) Rasmuson, A.; VanNess, K.; Ron, C. A.; Johnson, W. P. Hydrodynamic versus surface interaction impacts of roughness in

closing the gap between favorable and unfavorable colloid transport conditions. Environ. Sci. Technol. 2019, 53 (5), 2450−2459. (50) Adamczyk, Z. Particle Transfer and Deposition from Flowing Colloid Suspensions. Colloids Surf. 1989, 35 (2), 283−308. (51) Shapiro, M.; Brenner, H.; Guell, D. C. Accumulation and Transport of Brownian Particles at Solid Surfaces: Aerosol and Hydrosol Deposition Processes. J. Colloid Interface Sci. 1990, 136 (2), 552−573.

9070

DOI: 10.1021/acs.langmuir.9b00911 Langmuir 2019, 35, 9061−9070