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The Contribution of Nano- to Micro-scale Roughness to Heterogeneity: Closing the Gap between Unfavorable and Favorable Colloid Attachment Conditions Anna Rasmuson, Eddy Pazmino, Shoeleh Assemi, and William P. Johnson Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.6b05911 • Publication Date (Web): 30 Jan 2017 Downloaded from http://pubs.acs.org on February 5, 2017
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The Contribution of Nano- to Micro-scale Roughness to Heterogeneity:
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Closing the Gap between
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Unfavorable and Favorable Colloid Attachment Conditions
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Anna Rasmuson1, Eddy Pazmino2, Shoeleh Assemi3, William P. Johnson1,*
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Department of Geology and Geophysics, University of Utah,
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Salt Lake City, Utah 84112, United States 2
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Department of Extractive Metallurgy, Escuela Politécnica Nacional, Quito, Ecuador 3
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Department of Metallurgical Engineering, University of Utah, Salt Lake City, Utah 84112, United States
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*
Corresponding author. Email:
[email protected]; Tel: (801)585-5033; Fax: (801)5817065.Engineering, University of Utah, Salt Lake City, Utah 84112, United States 1
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Abstract
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Surface roughness has been reported to both increase as well as decrease colloid retention. In
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order to better understand the boundaries within which roughness operates, attachment of a
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range of colloid sizes to glass with three levels of roughness was examined under both
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favorable (energy barrier absent) and unfavorable (energy barrier present) conditions in an
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impinging jet system. Smooth glass was found to provide the upper and lower bounds for
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attachment under favorable and unfavorable conditions, respectively. Surface roughness
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decreased, or even eliminated, the gap between favorable and unfavorable attachment, and
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did so by two mechanisms: 1) under favorable conditions attachment decreased via increased
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hydrodynamic slip length and reduced attraction ; 2) under unfavorable conditions attachment
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increased via reduced colloid-collector repulsion (reduced radius of curvature) and increased
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attraction (multiple points of contact, and possibly increased surface charge heterogeneity).
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Absence of a gap where these forces most strongly operate for smaller (< 200 nm) and larger (>
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2 µm) colloids was observed and discussed. These observations elucidate the role of roughness
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in colloid attachment under both favorable and unfavorable conditions.
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Introduction
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Significant progress has been made in understanding the nature of nanoscale heterogeneity
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responsible for colloid attachment to bulk repulsive surfaces. 1-4 Colloid-collector repulsion in
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the environment often arises from like-charged colloids and collectors wherein counter-ions
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that shield surface charge are “squeezed” between two approaching surfaces.5,6 This repulsion
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is reduced or eliminated by zones of charge opposite to the colloid/collector surfaces that
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create local zones of attraction.2,4,7,8 Because the magnitude of repulsion between like-charged
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colloids and collectors scales directly with their radii of curvature, low radii of curvature of
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nanoscale asperities (roughness) also locally diminish or eliminate repulsion between like-
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charged surfaces.1,3,9 Therefore, both nanoscale charge heterogeneity and roughness may
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counteract repulsion between like-charged surfaces.
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Experimentally roughness has been shown to increase,10-13 as well as decrease14-16 attachment.
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This apparent discrepancy may result from different influences of roughness under favorable
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(energy barrier absent) versus unfavorable (energy barrier present) conditions. Limited studies
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were conducted under favorable conditions15,17,19 under which the influence of roughness was:
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1) non-monotonic15 showing a minimum collector efficiency (η = # colloids attached per #
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colloids introduced) for intermediate roughness (~200 nm root mean square roughness); and 2)
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monotonic, with η decreasing19 or increasing17 as roughness increased.
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To understand the seemingly contradictory effects of roughness on particle attachment, its
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influence needs to be understood via the following mechanisms: 1) interception of the surface,
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and 2) arrest on the surface (attachment).20 Colloid interception of the surface via fluid drag
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(fluid streamlines) is enhanced by particle settling and diffusion as encapsulated in colloid
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filtration theory (CFT).21 Additionally, roughness may diminish interception when the near-
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surface colloid velocities are increased by the slip layer which is the zone of fluid shear that
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exists between asperities 22,23 (Figure 1). Roughness may enhance interception18 via local
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protrusion of the surface into the pore domain, and by decreasing hydrodynamic drag in
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regions between these asperities.2
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Colloid arrest is governed by the balance of mobilizing and arresting torques, emanating
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primarily from fluid drag and colloid-collector interaction forces, respectively. 4,21,26,27,31
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Roughness influences arresting torque in several ways: 1) By decreasing the magnitude of
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colloid-collector interactions3,9,13,24,25 such that net repulsion (unfavorable conditions) and net
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attraction (favorable conditions) are decreased since electric double layer (EDL) and van der
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Waals (VdW) interactions scale to the local radius of curvature of the interacting surfaces;3,19 2)
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By increasing colloid-collector contact area by establishing multiple points of contact and
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thereby increasing the arresting torque; 3) By potentially creating additional lever arms
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associated with contact,27 thereby increasing the arresting torque.
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The above review demonstrates that roughness has contrasting influences on attachment
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under unfavorable versus favorable conditions. Experiments performed under these contrasting
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conditions should help to elucidate these effects of roughness. For this reason, we examined
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attachment under favorable versus unfavorable conditions for variably rough surfaces.
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Attachment was examined in pore-scale experiments (impinging jet) where the mode of
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attachment was directly observed, and motion was tracked in a single focal plane. In contrast,
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column scale observations do not elucidate the specific modes of attachment, which include
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immobilization on open surface, wedging in grain-to-grain contacts, and retention without
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attachment,288 nor do porous media experiments (even direct observation micromodels) allow
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motion tracking over significant distances because the curved surfaces cross focal planes.
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Direct observation of attachment on the planar surface therefore allows elucidation of the
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influence of the hydrodynamic slip layer on near-surface colloid velocities and colloid
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attachment. The planar surface also eliminates topological complications such as ripening via
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funneling of colloids into aggregates in grain-to-grain contacts.29 Notably, the experiments of
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Torkzaban and Bradford19 examined colloid retention in smooth versus rough porous media
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under high IS conditions where favorable colloid-colloid interaction promote ripening. Such
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interactions may confound elucidating the influence of roughness on observed colloid release
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via ionic strength (IS) reduction, since colloid-colloid interactions also respond to IS reduction.
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The impinging jet system represents only divergent flow at the forward flow stagnation zone,
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and does not capture Happel sphere-in-cell flow convergence at the rear-flow stagnation zone21
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representative of porous media. However, by capturing attachment on the open collector
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surface, the impinging jet allows calibration of the discrete heterogeneity responsible for
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attachment4,8 and detachment30 under unfavorable conditions. Upon calibrating the
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contribution of roughness, the resulting representative heterogeneity can be incorporated into
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other existing collector geometries, such as the Happel sphere-in-cell and Hemisphere-in-cell
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models.31
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To ascertain the contribution of roughness, attachment of colloids ranging in diameter from 20
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nm to 4.4 µm was examined on surfaces with root mean square (RMS) roughness ranging from
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≤1 nm to 546 nm. This range of asperity/colloid size ratios spans from 1E-5 to 5 (Figure 1),
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where the largest colloid size (4.4 µm) represents a practical upper limit for stably-suspended
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non-buoyant colloids in groundwater. The smallest colloid size (20 nm) represents what was
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possible to resolve optically in our experiments. This colloid size and the largest asperities (546
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nm RMS) define the largest asperity/colloid size ratio examined here (~5). Above this
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asperity/colloid size ratio it is reasonable to expect that flow field geometry will be
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characterized by additional forward and rear flow stagnation zones where impingement and
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retention may occur as demonstrated in porous media micromodels (e.g., Ausset and Keller32).
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Because this becomes an issue of resolving a modified flow field (fluid streamlines) rather than
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the specific influence of roughness on colloid-surface interactions and hydrodynamic slip, we
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therefore consider larger asperity/colloid size ratios (e.g., > 5) as complex porous media for
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which the path toward improved prediction is development of corresponding flow fields that
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represent the associated forward and rear flow stagnation zones.
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In summary, our goal was to determine the range over which roughness operates (short of
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creating new impingement surfaces) by defining upper and lower boundaries of attachment
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which we posit correspond to smooth surfaces under favorable (upper bound attachment) and
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unfavorable (lower bound attachment) conditions. An additional objective was to understand
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the influence of roughness not only on attachment but also on detachment.
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Methods
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Collector Surfaces
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Microscope soda lime glass slides and coverslips (Fisher Scientific, Inc.) were used as the
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impinging surface in the cell, the coverslips were used for smaller colloids that required higher
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magnification for optical resolution. Three levels of roughness were developed for the glass
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surfaces by examining them as: 1) untreated; 2) after NaOH-treatment (5 N for 80 min at 90ºC);
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and 3) after trace metal grade hydrofluoric acid (HF) treatment (27.6 N for 12 hours at 21ºC).
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Each treatment was followed by extensive rinsing with MilliQ until the rinse solution pH was
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6.5. The HF treated surface was then heated in air at 250ºC for 2 hours to remove any residual
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surface impurities. All surfaces were cleaned prior to experiments via the SC-1 procedure. The
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treatment methods that were used to produce roughness may also introduce defects and
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uncoordinated atoms on asperities that can increase charge heterogeneity.34 However, it is
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reasonable to expect that if roughness and charge heterogeneity co-vary on chemically-etched
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mineral surfaces in the laboratory, then they also co-vary in aquifer media that has undergone
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natural chemical and mechanical weathering. Our observations are keyed to roughness, since
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charge heterogeneity is inferred, whereas roughness is measurable.
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Roughness was measured with an atomic force microscope (model N9451A Agilent
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Technologies; Santa Clara, CA) following SC-1 cleaning using contact mode in air with silicon
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nitride probes (type DNP-S10; Bruker Nano, Inc.) with a nominal spring constant of 0.12 N/m.
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Roughness was evaluated using SPIP software (Image Metrology; Hørsholm Denmark), and was
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measured as the root mean square height (Figure 2). The minimum scan size for each surface
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was determined by measuring the RMS roughness over a large area (~50 µm) and then
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sampling ten random small scan areas (5 µm) within that larger area. If the average RMS
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roughness of the small scans approximated that of the larger area, the smaller area was
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accepted and the process was repeated. A minimum of five random locations taken randomly
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across the observation area of the jet (~500 µm) were used to obtain average values and
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standard deviations of roughness parameters including: average roughness, root mean square
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(RMS) roughness, max valley depth, and max peak height. Three dimensional images were
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generated using Gwyddion software (Czech Metrology Institute, Brno, Czech Republic). The
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average wavelengths (peak to peak distances) of primary (larger scale) and secondary (small-
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scale) asperities were measured from five representative profiles (Supplementary Information
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Figure SI-1) for each surface using the ISO 4287-1997 written standard (ISO; Geneva
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Switzerland).
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Microsphere Suspensions
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Carboxylate-modified polystyrene latex (CML) fluorescent (λex = 505, λem = 515 nm)
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microspheres of six sizes (0.02, 0.1, 0.25, 1.1, 2.0 (Molecular Probes, Inc., Eugene, OR), and 4.4
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(Polysciences, Washington, PA) μm diameter) were used in the experiments. Colloid
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suspensions were prepared from stock in relevant solution with concentrations ranging from 5
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× 106 to 2 × 107 microspheres per milliliter. The microsphere suspension concentration was
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determined via vacuum filtration of colloid solution (volume adjusted to ensure >20 CML per
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view area) on 0.05 or 0.1 μm polycarbonate filters (Millipore) followed by averaging counts of
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25 random observation areas using wide-field fluorescence for colloid illumination and scaling
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this average to the area of deposition on the filter. Suspension ionic strength (IS) was adjusted
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using NaCl. Unfavorable solutions (IS 6 mM) were buffered with 2.2 mM MOPS (3-(N-
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morpholino) propanesulfonic acid, 4-morpholinepropanesulfonic acid; Sigma-Aldrich Corp.)
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with pH set to 8.0 using NaOH (0.5 M). Favorable solutions were set to pH 2.0 using HCL (1.3 M)
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and IS 50 mM. Dissolution of the collector surface was not a concern at these pH values as the
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solubility of amorphous silica is stable and very low at pH values below pH 9.35
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The Péclet (Pe) and Reynolds (Re) numbers for each colloid size under the relevant fluid
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velocities are included in the Supplementary Information (Supplementary Information, Table SI-
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1). Pe numbers all exceed 50,000, corresponding to advection–dominated conditions, and Re
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numbers range from 1.73 to 5.94, corresponding to laminar creeping flow conditions.
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The CML electrophoretic mobility (EPM) was measured in suspensions using ζ-potential
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analyzer (Mobiuζ, Wyatt Technology Corp., Santa Barbara, CA). CML ζ-potentials were
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calculated from EPM via the Smoluchowski equation for large colloids (i.e. ≥ 100 nm diameter),
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and the Huckel approximation when the colloid diameter was smaller than the Debye length
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(i.e. colloids < 100 nm diameter36 (Supplementary Information Table SI-2). The glass slide EPM
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was measured in the filtrate ( 0.95) was
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required to quantify η. This initial slope of deposition (across the area of observation, Aobs) was
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used to calculate the collector efficiency (η) via the following equation:
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ߟ=
ቀ
#ೌೌ ቁ ಲ
ቀ
#ೕ ቁ ಲ
ೀಳೄ
ಶ
=
#ೌೌ
(1)
ೀ ொ
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where CO is the injected concentration of colloids and Q is the flow rate of the fluid that enters
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the cell (across the area of the jet, Ajet). The product COQ is equal to the number of particles
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injected per unit time across Ajet. This expression was developed specifically for the impinging
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jet geometry,4 therefore comparison of results with porous media is qualitative. However, note
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that the conversion of attachment to η as opposed to flux does not change the relative values
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since the influence of concentration and velocity is equivalent for η (efficiency) and flux (e.g.,
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dimensionless parameters such as the Sherwood number).
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Near-surface velocities were determined by tracking particle displacement at the near-surface
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as a function of time from the images captured using constant streaming (time intervals were
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less than 1 second between images). Velocities were averaged for 0.25, 1.1 and 2.0 µm colloids
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for a minimum of 10 particles. Near-surface colloids were distinguished from bulk colloids using
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TIRF-M (i.e. over the ≤ 1 nm and 38 nm RMS glass surfaces). For the 546 nm RMS surface, a
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threshold velocity of ~400 µm/min was selected to distinguish particles in the bulk solution.
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Near-surface velocities were determined under favorable conditions in order to eliminate
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interactions with the secondary minimum. 13 ACS Paragon Plus Environment
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Favorable Simulations
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A Lagrangian particle trajectory model developed for the smooth impinging jet system was used
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to predict η under favorable conditions.4 The model accounts for fluid drag, hydrodynamic
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retardation, gravity, diffusion, colloid−surface interaction forces, and virtual mass. A more
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detailed description of the force and torque balances including fluid drag, hydrodynamic
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retardation, gravity, diffusion, steric forces, and virtual mass is described in previous
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publications. 4,29,31 Favorable conditions were set by assigning measured colloid and collector ζ
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potentials for the pH 2 50 mM conditions (Supplementary Information, Table SI-2) in the model
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input.
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The complete experimental matrix corresponding to the range of collector surfaces (3), colloid
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sizes (6), fluid velocities (2), IS (2), and pH (2) yielded 72 experiments without replicates and 144
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experiments with complete replication. In order to produce a tractable set of experiments and
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simulations, some experimental conditions were not run when the observed trends could be
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discerned from bracketing experiments, whereas in other cases it was not possible to optically
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resolve colloids under certain conditions. For example, particles ≤ 100 nm were not examined
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on the 546 nm RMS surface due to inability to distinguish faint particles from light scattering.
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Approximately 75 experiments (including replicates) were conducted. Replicates were
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performed for all experiments conducted on the untreated and NaOH treated slides under the
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1.7E-3 ms-1 velocity condition. The complete experimental matrix with replicates indicated is
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shown the Supplementary Information (Supplementary Information Table SI-3).
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Results
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Roughness
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Roughness parameters measured using AFM (Figure 2) are summarized in Supplementary
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Information (Supplementary Information Table SI-4), where untreated, NaOH-treated, and HF-
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treated glass slides and coverslips showed progressively increasing roughness. The glass slides
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and coverslips showed similar RMS values for a given treatment. Three levels of roughness
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were generated on glass slides and coverslips: a) ≤ 1 nm RMS roughness (untreated); b) 38 nm
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RMS roughness (NaOH-treated); and c) 546 nm RMS roughness (HF-treated). The maximum
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valley depths and peak heights were approximately a factor of five times the RMS roughness for
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the untreated and NaOH-treated silica, and approximately a factor of three times the RMS for
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the HF-treated silica. The primary (large scale) wavelengths were approximately equal to the
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RMS roughness, suggesting that the asperities were evenly spaced. The untreated glass surface
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did not exhibit secondary roughness. The secondary wavelengths were similar for both NaOH-
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treated and HF-treated surfaces (~ 3.5 nm), which indicates that secondary roughness did not
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change as overall roughness increased, and that roughness appears to follow a fractal
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relationship.
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The maximum collector (impinging surface) asperity size was on the order of size of the largest
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colloids, whereas the smallest collector asperity size was
