DLVO interaction energy between a sphere and a nano-patterned plate

Colloid interaction energies for physically and chemically heterogeneous porous media

The mean and variance of the colloid interaction energy (Φ*) as a function of separation distance (h) were calculated on physically and/or chemically heterogeneous solid surfaces at the representative elementary area (REA) scale. Nanoscale roughness was demonstrated to have a significant influence on the colloid interaction energy for different ionic strengths. Increasing the roughness height reduced the magnitude of the energy barrier (Φmax*) and the secondary minimum (Φ2min*). Conversely, increasing the fraction of the solid surface with roughness increased the magnitude of Φmax* and Φ2min*. Our results suggest that primary minimum interactions tend to occur in cases where only a portion of the solid surface was covered with roughness (i.e., isolated roughness pillars), but their depths were shallow as a result of Born repulsion. The secondary minimum was strongest on smooth surfaces. The variance in the interaction energy was also a strong function of roughness parameters and h. In particular, the variance tended to increase with the colloid size, the magnitude of Φ*, the height of the roughness, and especially the size (cross-sectional area) of the heterogeneity. Nonzero values of the variance for Φ2min* implied the presence of a tangential component of the adhesive force and a resisting torque that controls immobilization and release for colloids at this location. Heterogeneity reduced the magnitude of Φ* in comparison to the corresponding homogeneous situation. Physical heterogeneity had a greater influence on mean properties of Φ* than similar amounts of chemical heterogeneity, but the largest reduction occurred on surfaces with both physical and chemical heterogeneity. The variance in Φ* tended to be higher for a chemically heterogeneous solid.

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

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

Colloid adhesive parameters for chemically heterogeneous porous media

A simple modeling approach was developed to calculate colloid adhesive parameters for chemically heterogeneous porous media. The area of the zone of electrostatic influence between a colloid and solid-water interface (A(z)) was discretized into a number of equally sized grid cells to capture chemical heterogeneity within this region. These cells were divided into fractions having specific zeta potentials (e.g., negative or positive values). Mean colloid adhesive parameters such as the zeta potential, the minimum and maximum in the interaction energy, the colloid sticking efficiency (α), and the fraction of the solid surface area that contributes to colloid immobilization (S(f)) were calculated for possible charge realizations within A(z). The probability of a given charge realization in A(z) was calculated using a binomial mass distribution. Probability density functions (PDFs) for the colloid adhesive parameters on the heterogeneous surface were subsequently calculated at the representative elementary area (REA) scale for a porous medium. This approach was applied separately to the solid-water interface (SWI) and the colloid, or jointly to both the SWI and colloid. To validate the developed model, the mean and standard deviation of the interaction energy distribution on a chemically heterogeneous SWI were calculated and demonstrated to be consistent with published Monte Carlo simulation output using the computationally intensive grid surface integration technique. Our model results show that the PDFs of colloid adhesive parameters at the REA scale were sensitive to the size of the colloid and the heterogeneity, the charge and number of grid cells, and the ionic strength.

Site-specific retention of colloids at rough rock surfaces

The spatial deposition of polystyrene latex colloids (d = 1 μm) at rough mineral and rock surfaces was investigated quantitatively as a function of Eu(III) concentration. Granodiorite samples from Grimsel test site (GTS), Switzerland, were used as collector surfaces for sorption experiments. At a scan area of 300 × 300 μm(2), the surface roughness (rms roughness, Rq) range was 100-2000 nm, including roughness contribution from asperities of several tens of nanometers in height to the sample topography. Although, an increase in both roughness and [Eu(III)] resulted in enhanced colloid deposition on granodiorite surfaces, surface roughness governs colloid deposition mainly at low Eu(III) concentrations (≤5 × 10(-7) M). Highest deposition efficiency on granodiorite has been found at walls of intergranular pores at surface sections with roughness Rq = 500-2000 nm. An about 2 orders of magnitude lower colloid deposition has been observed at granodiorite sections with low surface roughness (Rq < 500 nm), such as large and smooth feldspar or quartz crystal surface sections as well as intragranular pores. The site-specific deposition of colloids at intergranular pores is induced by small scale protrusions (mean height = 0.5 ± 0.3 μm). These protrusions diminish locally the overall DLVO interaction energy at the interface. The protrusions prevent further rolling over the surface by increasing the hydrodynamic drag required for detachment. Moreover, colloid sorption is favored at surface sections with high density of small protrusions (density (D) = 2.6 ± 0.55 μm(-1), asperity diameter (φ) = 0.6 ± 0.2 μm, height (h) = 0.4 ± 0.1 μm) in contrast to surface sections with larger asperities and lower asperity density (D = 1.2 ± 0.6 μm(-1), φ = 1.4 ± 0.4 μm, h = 0.6 ± 0.2 μm). The study elucidates the importance to include surface roughness parameters into predictive colloid-borne contaminant migration calculations.

High density single-molecule-bead arrays for parallel single molecule force spectroscopy

The assembly of a highly parallel force spectroscopy tool requires careful placement of single-molecule targets on the substrate and the deliberate manipulation of a multitude of force probes. Since the probe must approach the target biomolecule for covalent attachment, while avoiding irreversible adhesion to the substrate, the use of polymer microspheres as force probes to create the tethered bead array poses a problem. Therefore, the interactions between the force probe and the surface must be repulsive at very short distances (<5 nm) and attractive at long distances. To achieve this balance, the chemistry of the substrate, force probe, and solution must be tailored to control the probe-surface interactions. In addition to an appropriately designed chemistry, it is necessary to control the surface density of the target molecule in order to ensure that only one molecule is interrogated by a single force probe. We used gold-thiol chemistry to control both the substrate's surface chemistry and the spacing of the studied molecules, through binding of the thiol-terminated DNA and an inert thiol forming a blocking layer. For our single molecule array, we modeled the forces between the probe and the substrate using DLVO theory and measured their magnitude and direction with colloidal probe microscopy. The practicality of each system was tested using a probe binding assay to evaluate the proportion of the beads remaining adhered to the surface after application of force. We have translated the results specific for our system to general guiding principles for preparation of tethered bead arrays and demonstrated the ability of this system to produce a high yield of active force spectroscopy probes in a microwell substrate. This study outlines the characteristics of the chemistry needed to create such a force spectroscopy array.

Deposition of latex colloids at rough mineral surfaces: an analogue study using nanopatterned surfaces

Deposition of latex colloids on a structured silicon surface was investigated. The surface with well-defined roughness and topography pattern served as an analogue for rough mineral surfaces with half-pores in the submicrometer size. The silicon topography consists of a regular pit pattern (pit diameter = 400 nm, pit spacing = 400 nm, pit depth = 100 nm). Effects of hydrodynamics and colloidal interactions in transport and deposition dynamics of a colloidal suspension were investigated in a parallel plate flow chamber. The experiments were conducted at pH ∼ 5.5 under both favorable and unfavorable adsorption conditions using carboxylate functionalized colloids to study the impact of surface topography on particle retention. Vertical scanning interferometry (VSI) was applied for both surface topography characterization and the quantification of colloidal retention over large fields of view. The influence of particle diameter variation (d = 0.3-2 μm) on retention of monodisperse as well as polydisperse suspensions was studied as a function of flow velocity. Despite electrostatically unfavorable conditions, at all flow velocities, an increased retention of colloids was observed at the rough surface compared to a smooth surface without surface pattern. The impact of surface roughness on retention was found to be more significant for smaller colloids (d = 0.3, 0.43 vs. 1, 2 μm). From smooth to rough surfaces, the deposition rate of 0.3 and 0.43 μm colloids increased by a factor of ∼2.7 compared to a factor of 1.2 or 1.8 for 1 and 2 μm colloids, respectively. For a substrate herein, with constant surface topography, the ratio between substrate roughness and radius of colloid, Rq/rc, determined the deposition efficiency. As Rq/rc increased, particle-substrate overall DLVO interaction energy decreased. Larger colloids (1 and 2 μm) beyond a critical velocity (7 × 10(-5) and 3 × 10(-6) m/s) (when drag force exceeds adhesion force) tend to detach from the surface irrespective of the impact of roughness. For polydisperse solutions, an increase in the polydispersity and flow velocity resulted in a reduction of colloid deposition efficiency due to the resulting enhanced double-layer repulsion. Quantification of surface topography variations of two endmembers of natural grain surfaces showed that half-pore depths and roughness of sedimentary quartz grains are mainly in the micrometer range. Grains with diagenetically formed quartz overgrowths, however, show surface roughness mainly in the submicrometer range. Thus, surface topography features applied in the here presented analogue study and resulting variation in particle retention can serve as quantitative analogue for particle reactions in diagenetically altered quartz sands and sandstones. The reported impact of particle polydispersity can have an important application for quantitative prediction of retention of varying types of minerals, such as different clay minerals in the environment under prevailing unfavorable conditions.

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

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

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

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

Angelo SK, González P, Keating CD, Fichthorn KA. Assembly of gold nanowires by sedimentation from suspension: Experiments and simulation

We investigated the ordering of gold nanowires that settled from aqueous suspension onto a glass substrate due to gravity. The nanowires, ca. 300 nm in cross-sectional diameter and ca. 2, 4, or 7 microns in length, were coated with 2-mercaptoethanesulfonic acid to provide electrostatic repulsion and prevent aggregation. The layer of nanowires in direct contact with the substrate was examined from below using optical microscopy and found to exhibit smectic-like ordering. The extent of smectic ordering depended on nanowire length with the shortest (2 μm) nanowires exhibiting the best ordering. To understand the assembly in this system, we used canonical Monte Carlo simulations to model the two-dimensional ordering of the nanowires on a substrate. We accounted for van der Waals and electrostatic interactions between the nanowires. The simulations reproduced the experimental trends and showed that roughness at the ends of the nanowires, which locally increased electrostatic repulsion, is critical to correctly predicting the experimentally observed smectic ordering.

Retention of latex colloids on calcite as a function of surface roughness and topography

Adhesion of colloidal particles to mineral and rock surfaces is important for environmental and technological processes. Surface topography variations of mineral and rock surfaces at the submicrometer scale may play a significant role in colloid retention in the environment. Here, we present colloid deposition data on calcite as a function of submicrometer surface roughness based on surface data over a field of view of several square millimeters, sufficient to trace the pattern of common inhomogeneities on mineral surfaces. A freshly cleaved calcite crystal was reacted to produce a well-defined etch pit density of approximately 3.4 +/- 1.2 to 8.3 +/- 1.6 [10(-3) microm(-2)] and etch pit depth ranging from approximately 4 to 50 nm. This surface was exposed at the point of zero charge (PZC) of calcite to a colloidal suspension. We used a bimodal particle size distribution of nonfunctionalized polystyrene latex spheres with average diameters of 499 and 903 nm. Vertical scanning interferometry (VSI) was applied to quantify calcite surface topography variations as well as the retention of latex colloids. For both particle sizes, the experiments showed a positive correlation between the surface roughness (Rq) and the number of adsorbed particles. Etch pits were preferred sites for colloidal deposition in contrast to surface steps. The majority of adsorbed particles were trapped at etch pit walls compared to etch pit bottoms. Increasing pit density (D) and depth (d) resulted in an increase of colloidal retention. Deposition of smaller particles exceeded that of the larger-sized fraction of the bimodal system investigated here. Our results show that colloidal deposition at rough mineral and rock surfaces is an important geochemical process. The results about surface roughness dependent particle adsorption will foster the understanding and predictability of colloidal retention for a multitude of natural and technical processes.

Is surface roughness a "scapegoat" or a primary factor when defining particle-substrate interactions?

Extended DLVO interaction potentials were determined for spherical particles approaching nanopatterned substrates using the numerical surface element integration (SEI) technique. In most cases, nanopatterned ("rough") surfaces produced smaller interaction potentials than chemically identical planar ("smooth") surfaces. For unfavorable scenarios, electrostatic double layer and acid-base potentials were reduced to a greater extent than van der Waals potentials, which made rough surfaces "more attractive" than smooth ones. Two influential surface morphological descriptors emerged: (1) the ratio of particle size to asperity size, a/r, and (2) the ratio of asperity separation to asperity size, p/r. As a/r increased, particle-substrate interaction energy decreased, while the opposite was true for p/r. The simple morphological descriptors gave rise to an analytical model based on the Derjaguin integration (DI) method that compared reasonably well with numerical SEI results, where the size and density of nanopatterned surface features dictated the magnitude of interaction potentials. In fact, changes in the size of nanopatterned surface features impacted the magnitudes of interaction potentials to the same extent as similar changes in the magnitudes of acid-base free energy and zeta potential, which begs the question, "is surface morphology a 'scapegoat' or a primary consideration when defining particle-substrate interactions?"