Interaction of micrometer-scale particles with nanotextured surfaces in shear flow

Dynamic particle adhesion from flow over collecting surfaces with nanoscale heterogeneity occurs in important natural systems and current technologies. Accurate modeling and prediction of the dynamics of particles interacting with such surfaces will facilitate their use in applications for sensing, separating, and sorting colloidal-scale objects. In this paper, the interaction of micrometer-scale particles with electrostatically heterogeneous surfaces is analyzed. The deposited polymeric patches that provide the charge heterogeneity in experiments are modeled as 11-nm disks randomly distributed on a planar surface. A novel technique based on surface discretization is introduced to facilitate computation of the colloidal interactions between a particle and the heterogeneous surface based on expressions for parallel plates. Combining these interactions with hydrodynamic forces and torques on a particle in a low Reynolds number shear flow allows particle dynamics to be computed for varying net surface coverage. Spatial fluctuations in the local surface density of the deposited patches are shown responsible for the dynamic adhesion phenomena observed experimentally, including particle capture on a net-repulsive surface.     

Micrometer scale adhesion on nanometer-scale patchy surfaces: adhesion rates, adhesion thresholds, and curvature-based selectivity

Using a model system based on electrostatics, we probe interactions between spherical particles (negative silica) and planar surfaces that present randomly placed discrete attractive regions, 10 nm in size, in a repulsive background (silica flats carrying cationic surface constructs). Experiments measure the adhesion rates of particles onto the patchy collecting surfaces from flowing dispersions, as a function of the surface loading of the attractive patches, for different particle sizes (0.5 and 1 mum diameter spheres) and different ionic strengths. Surfaces densely populated with patches, such that they present net electrostatic attractions to approaching particles, capture particles at the transport-limited (maximum) rate. Surfaces sparsely loaded with attractive patches (which present a repulsive mean field to approaching particles) are usually still adhesive, but the particle adhesion rate depends on particle size, ionic strength, and patch loading. Most significant is an adhesion threshold, a critical density of patches needed to capture particles. This threshold, which occurs at average patch spacings of 30 nm and larger and which can be tuned through ionic strength, comprises the ability of the patchy surfaces to selectively distinguish particles of different sizes or objects of different local curvature or roughness. The observation of such an adhesion threshold implicates spatial fluctuations in patch arrangement. In addition to experiments, this paper develops arguments for lengthscales that govern adhesion rate behavior, comparing particle geometry and fluctuation lengthscales, and then demonstrating qualitative consistency with the localized colloidal potentials involved.     

Particle capture via discrete binding elements: systematic variations in binding energy for randomly distributed nanoscale surface features

This work examines how the binding strength of surface-immobilized "stickers" (representative of receptors or, in nonbiological systems, chemical heterogeneities) influences the adhesion between surfaces that are otherwise repulsive. The study focuses on a series of surfaces designed with fixed average adhesive energy per unit area and demonstrates quantitatively how a redistribution of the adhesive functionality into progressively larger clusters (stronger stickers) increases the probability of adhesive events. The work employs an electrostatic model system: relatively uniform, negative 1 μm silica spheres flow gently over negative silica flats. The flats contain small amounts of randomly positioned nanoscale cationic patches. The silica-silica interaction is repulsive; however, the cationic patches (present at sufficiently low levels that the overall surface charge remains substantially negative) produce local attractions. In this study, the attractions are relatively weak so that multiple patches engage to capture flowing particles. Experiments reveal an adhesion signature characteristic of a renormalized random distribution when the sticker strength is increased at an overall fixed binding strength per unit area of surface. The form of the particle capture curves are in good quantitative agreement with a simple model that assumes only a fixed adhesion energy needed for particle capture. Aside from the quantitative details that provide a simple formalism for anticipating particle adhesion, this work demonstrates how increasing the heterogeneities in the surface functionality can cause a system to go from being nonadhesive to becoming strongly adhesive. Indeed, systems containing small amounts of discretized adhesive functionality are always more adhesive than systems in which the same functionality is distributed uniformly over the surface (the mean field scenario).     

Manipulation of micrometer-scale adhesion by tuning nanometer-scale surface features

This article demonstrates how the adhesion rates of micrometer-scale particles on a planar surface can be manipulated by nanometer-scale features on the latter. Here, approximately 500-nm-diameter spherical silica particles carrying a substantial and relatively uniform negative charge experienced competing attractions and repulsions as they approached and attempted to adhere to a negative planar silica surface carrying flat 11-nm-diameter patches of concentrated positive charge. The average spacing of these patches profoundly influenced the particle adhesion. For dense positive patch spacing on the planar collector, the particle adhesion was rapid, and the fundamental adhesion kinetics were masked by particle transport to the interface. For patch densities corresponding to a planar surface with net zero charge, particle adhesion was still rapid. Adhesion kinetics were observably reduced for patch spacings exceeding 20 nm and become slower with increased patch spacing. Ultimately, above a critical or threshold average patch spacing of 32 nm, no particle adhesion occurred. The presence of the threshold average patch spacing suggests that more than one positive surface patch was needed for particle capture under the particular conditions of this study. Furthermore, at the threshold, the length scales of the patch spacing and of the interactive surface area between the particle and the surface become similar: The concept of adhesion dominated by the matching of length scales is reminiscent of pattern recognition, even though the patch distribution on the collector is random in this work. Indeed, fluctuations play a critical role in these adhesion dynamics, hence the current behavior cannot be predicted by a mean field approach.     

Manipulating microparticles with single surface-immobilized nanoparticles

This experimental study explores the capture and manipulation of micrometer-scale particles by single surface-immobilized nanoparticles. The nanoparticles, approximately 10 nm in diameter, are cationic and therefore attract the micrometer-scale silica particles in an analyte suspension. The supporting surface on which the nanoparticles reside is negative (also silica) and repulsive toward approaching microparticles. In the limit where there are as few as 9 nanoparticles per square micrometer of collector, it becomes possible to capture and hold micrometer-scale silica particles with single nanoparticles. The strong nanoparticle-microparticle attractions, their nanometer-scale protrusion forward of the supporting surface, and their controlled density on the supporting surface facilitate microparticle-surface contact occurring through a single nanoelement. This behavior differs from most particle-particle, cell-cell, or particle (or cell)-surface interactions that involve multiple ligand-receptor bonds or much larger contact areas. Despite the limited contact of microparticles with surface-immobilized nanoparticles, microparticles resist shear forces of 9 pN or more but can be released through an increase in the ionic strength. The ability of nanoparticles to reversibly trap and hold much larger targets has implications in materials self-assembly, cell capture, and sorting applications, whereas the single point of contact affords precision in particle manipulation.     

Influence of adsorbed polymers on the removal of mineral particles from a planar surface

 Experimental results on the role of adsorbed polymers on the particle adhesion are presented. Both Brownian (silica particles) and non-Brownian (glass beads) particles were used. The particles were deposited onto the internal surface of a glass parallelepiped cell, and then submitted to increasing laminar flow rates. The pH and the ionic strength of the electrolytes were fixed. The adhesive force was related to the hydrodynamic force required to dislodge 50% of the initially attached beads. We found that high molecular weight PEO had little effect on the adhesion of small silica beads due to the low affinity of the polymer for silica or glass surfaces. On the contrary, PEO greatly enhanced the adhesion of bigger glass beads forced to deposit on the capillary surface because of gravity. The increase was all the more pronounced as the molecular weight of the polymer was high. The effect of high molecular weight cationic copolymers on the adhesion of silica particles was drastic. The maximal force (1500 pN) applied by the device could not enable any particle detachment even using polymers of low cationicity rate (5%), showing the efficiency of electrostatic attractions. When copolymers were adsorbed on both surfaces (particles and plane), the adhesive force exhibited a maximum at intermediate coverage of particles. This optimum was related to the optimum flocculation concentration classically observed in flocculation of suspensions by polymers. Received: 16 February 1996 Accepted: 10 September 1996     

Non-specific adhesion on biomaterial surfaces driven by small amounts of protein adsorption

This work explores how long-range non-specific interactions, resulting from small amounts of adsorbed fibrinogen, potentially influence bioadhesion. Such non-specific interactions between protein adsorbed on a biomaterial and approaching cells or bacteria may complement or even dominate ligand–receptor mating. This work considers situations where the biomaterial surface and the approaching model cells (micron-scale silica particles) exhibit strong electrostatic repulsion, as may be the case in diagnostics and lab-on-chip applications. We report that adsorbed fibrinogen levels near 0.5 mg/m² produce non-specific fouling. For underlying surfaces that are less fundamentally repulsive, smaller amounts of adsorbed fibrinogen would have a similar effect. Additionally, it was observed that particle adhesion engages sharply and only above a threshold loading of fibrinogen on the collector. Also, in the range of ionic strength, I, below about 0.05 M, increases in I reduce the fibrinogen needed for microparticle capture, due to screening of electrostatic repulsions. Surprisingly, however, ionic strengths of 0.15 M reduce fibrinogen adsorption altogether. This observation opposes expectations based on DLVO arguments, pointing to localized electrostatic attractions and hydration effects to drive silica–fibrinogen adhesion. These behaviors are benchmarked against microparticle binding on silica surfaces carrying small amounts of a polycation, to provide insight into the role of electrostatics in fibrinogen-driven non-specific adhesion.     

Dynamic adhesion behavior of micrometer-scale particles flowing over patchy surfaces with nanoscale electrostatic heterogeneity

The dynamic adhesion behavior of micrometer-scale silica particles is investigated numerically for a low Reynolds number shear flow over a planar collecting wall with randomly distributed electrostatic heterogeneity at the 10-nanometer scale. The hydrodynamic forces and torques on a particle are coupled to spatially varying colloidal interactions between the particle and wall. Contact and frictional forces are included in the force and torque balances to capture particle skipping, rolling, and arrest. These dynamic adhesion signatures are consistent with experimental results and are reminiscent of motion signatures observed in cell adhesion under flowing conditions, although for the synthetic system the particle–wall interactions are controlled by colloidal forces rather than physical bonds between cells and a functionalized surface. As the fraction of the surface (Θ) covered by the cationic patches is increased from zero, particle behavior sequentially transitions from no contact with the surface to skipping, rolling, and arrest, with the threshold patch density for adhesion (Θ_crit) always greater than zero and in quantitative agreement with experimental results. The ionic strength of the flowing solution determines the extent of the electrostatic interactions and can be used to tune selectively the dynamic adhesion behavior by modulating two competing effects. The extent of electrostatic interactions in the plane of the wall, or electrostatic zone of influence, governs the importance of spatial fluctuations in the cationic patch density and thus determines if flowing particles contact the wall. The distance these interactions extend into solution normal to the wall determines the strength of the particle–wall attraction, which governs the transition from skipping and rolling to arrest. The influence of Θ, particle size, Debye length, and shear rate is quantified through the construction of adhesion regime diagrams, which delineate the regions in parameter space that give rise to different dynamic adhesion signatures and illustrate selective adhesion based on particle size or curvature. The results of this study are suggestive of novel ways to control particle–wall interactions using randomly distributed surface heterogeneity.     

Targeted particulate adhesion to cellulose surfaces mediated by bifunctional fusion proteins

The adhesion of particles to surfaces is an integral element in many commercial and biological applications. In this article, we report on the direct measurements of protein-mediated deposition and binding of particles to model cellulose surfaces. This system involves a family of heterobifunctional fusion proteins that bind specifically to both a red dye and cellulose. Amine-coated particles were labeled with a red dye, and a fusion protein was attached to these particles at various number densities. The strength of adhesion of a single particle to a cellulose fiber was measured using micropipette manipulation as a function of the specificity of the protein and its surface density and contact time. The frequency and force of adhesion were seen to increase with contact time in fiber experiments. The dynamics of adhesion of the functionalized particles to cellulose-coated glass slides under controlled hydrodynamic flow was explored using a flow chamber for two scenarios: detachment of bound particles and attachment of particles in suspension as a function of the shear rate and surface density of protein. Highly specific adhesion was observed. The critical shear rate for particle detachment was an increasing function of cellulose binding domain (CBD) density on particle surface. A rapid irreversible attachment of particles to cellulose was observed under flow. Using a family of proteins that were divalent for binding either the red dye or cellulose, we found that particle detachment occurred because of the failure of the cellulose-CBD bond. A comparison of fiber binding and particle detachment results suggests that forces of adhesion of particles to cellulose of up to 2 nN can be obtained with this molecular system through multiple interactions. This study, along with the adhesion simulations currently under development, forms the basis of particulate design for specific adhesion applications.     

Resolving the coupled effects of hydrodynamics and DLVO forces on colloid attachment in porous media

Transport of colloidal particles in porous media is governed by the rate at which the colloids strike and stick to collector surfaces. Classic filtration theory has considered the influence of system hydrodynamics on determining the rate at which colloids strike collector surfaces, but has neglected the influence of hydrodynamic forces in the calculation of the collision efficiency. Computational simulations based on the sphere-in-cell model were conducted that considered the influence of hydrodynamic and Derjaguin-Landau-Verwey-Overbeek (DLVO) forces on colloid attachment to collectors of various shape and size. Our analysis indicated that hydrodynamic and DLVO forces and collector shape and size significantly influenced the colloid collision efficiency. Colloid attachment was only possible on regions of the collector where the torque from hydrodynamic shear acting on colloids adjacent to collector surfaces was less than the adhesive (DLVO) torque that resists detachment. The fraction of the collector surface area on which attachment was possible increased with solution ionic strength, collector size, and decreasing flow velocity. Simulations demonstrated that quantitative evaluation of colloid transport through porous media will require nontraditional approaches that account for hydrodynamic and DLVO forces as well as collector shape and size.     

Particle deposition onto Janus and patchy spherical collectors

An Eulerian model (convection-diffusion-migration equation) is presented to study colloid deposition behavior on Janus and patchy spherical collectors using Happel cell geometry. The model aims to capture the effect of the collector surface charge heterogeneity on the particle deposition rate. Two separate cases of surface charge distribution are presented. In the first case, the surface heterogeneity is modeled as half the collector favoring deposition and the other half hindering it (Janus collectors). For the second case, the surface heterogeneity is modeled as alternate stripes of attractive and repulsive regions on the collector (patchy collectors). The model also considers fluid flow approaching the collector at different angles in addition to the standard gravity assisted and gravity hindered flow conditions to analyze the effect of the collector orientation on the deposition. It was observed that particles tend to deposit at the edges of the favorable stripes and the extent of this preferential accumulation varies along the tangential position of the collector due to the nonuniform nature of the collector. The predicted deposition behavior is compared to the patchwise heterogeneity model. The study brings to fore how recent developments in synthesis of chemically heterogeneous particles and beads can be used for improved particle capture in porous media and for designing filter beds with enhanced life.     

A direct method for studying particle deposition onto solid surfaces

An experimental technique has been developed to study the deposition of colloidal particles under well controlled hydrodynamic conditions. The deposition process is observed under a microscope and recorded on video tape for further analysis. Fluid flow conditions in the experimental set-up were determined by numerical solution of the Navier-Stokes equations. Mass transfer equations were solved numerically (taking into account hydrodynamic, gravitational, electric double layer, and dispersion forces) for the stagnation point region. Also, some analytical solutions are presented. Deposition has been studied of 0.5m polystyrene latex particles on cover glass slides used as collectors. From an analysis of the shape of the coating density vs. time curves and independently from the distribution of the particles on collector surfaces, it was found that one particle is able to block an area of about 20 to 30 times its geometrical cross-section. The initial flux of particles to the collector for a given salt concentration was found to depend strongly on the method of cleaning the collector surface. In general the flux and the escape of particles to and from the collector surface are sensitive to the interaction energy at small separations. The direct method of observing particle deposition and detachment could lead to important insights into the nature of particle-wall interactions at near contact.On leave from Jagiellonian University, Cracow, Poland.     

Particle deposition onto micropatterned charge heterogeneous substrates: trajectory analysis

A trajectory analysis of particles near a micropatterned charged substrate under radial impinging jet flow conditions is presented to investigate the effect of surface charge heterogeneity on particle trajectory and deposition efficiency. The surface charge heterogeneity is modeled as concentric bands of specified width and pitch having positive and negative surface potentials. The flow distribution is obtained using finite element analysis of the governing Navier-Stokes equations. The particle trajectory analysis takes into consideration the hydrodynamic interactions, gravity, van der Waals and electrostatic double layer interactions. The presence of surface charge heterogeneity on the substrate gives rise to an oscillating particle trajectory near the collector surface due to repulsive and attractive forces. As a result of the coupled effects of hydrodynamic and colloidal forces, the particle trajectories and deposition efficiencies are increasingly affected by surface charge heterogeneity as one moves radially away from the stagnation point. The results indicate that it is possible to render collectors with up to 50% favorable surface fraction completely unfavorable by modifying the ratio of the radial to normal fluid velocity. Utilizing the real favorable area fraction of the collector, the patch model expression for calculating the deposition efficiency is modified for impinging jet flow geometry.     

Using flow to switch the valency of bacterial capture on engineered surfaces containing immobilized nanoparticles

Toward an understanding of nanoparticle-bacterial interactions and the development of sensors and other substrates for controlled bacterial adhesion, this article describes the influence of flow on the initial stages of bacterial capture (Staphylococcus aureus) on surfaces containing cationic nanoparticles. A PEG (poly(ethylene glycol)) brush on the surface around the nanoparticles sterically repels the bacteria. Variations in ionic strength tune the Debye length from 1 to 4 nm, increasing the strength and range of the nanoparticle attractions toward the bacteria. At relatively high ionic strengths (physiological conditions), bacterial capture requires several nanoparticle-bacterial contacts, termed "multivalent capture". At low ionic strength and gentle wall shear rates (on the order of 10 s(-1)), individual bacteria can be captured and held by single surface-immobilized nanoparticles. Increasing the flow rate to 50 s(-1) causes a shift from monovalent to divalent capture. A comparison of experimental capture efficiencies with statistically determined capture probabilities reveals the initial area of bacteria-surface interaction, here about 50 nm in diameter for a Debye length κ(-1) of 4 nm. Additionally, for κ(-1) = 4 nm, the net per nanoparticle binding energies are strong but highly shear-sensitive, as is the case for biological ligand-receptor interactions. Although these results have been obtained for a specific system, they represent a regime of behavior that could be achieved with different bacteria and different materials, presenting an opportunity for further tuning of selective interactions. These finding suggest the use of surface elements to manipulate individual bacteria and nonfouling designs with precise but finite bacterial interactions.     

A modeling approach to describe the adhesion of rough, asymmetric particles to surfaces

A combined theoretical and experimental study of the adhesion of alumina particles and polystyrene latex spheres to silicon dioxide surfaces was performed. A boundary element technique was used to model electrostatic interactions between micron-scale particles and planar surfaces when the particles and surfaces were in contact. This method allows quantitative evaluation of the effects of particle geometry and surface roughness on the electrostatic interaction. The electrostatic interactions are combined with a previously developed model for van der Waals forces in particle adhesion. The combined model accounts for the effects of particle and substrate geometry, surface roughness and asperity deformation on the adhesion force. Predictions from the combined model are compared with experimental measurements made with an atomic force microscope. Measurements are made in aqueous solutions of varying ionic strength and solution pH. While van der Waals forces are generally dominant when particles are in contact with surfaces, results obtained here indicate that electrostatic interactions contribute to the overall adhesion force in certain cases. Specifically, alumina particles with complex geometries were found to adhere to surfaces due to both electrostatic and van der Waals interactions, while polystyrene latex spheres were not affected by electrostatic forces when in contact with various surfaces.     

Friction of rodlike particles adsorbed to a planar surface in shear flow

A planar hard surface covered with elongated stiff rodlike particles in shear flow is considered in the low-Reynolds-number regime assuming low particle surface coverage. The particles are modeled as straight chains of spherical beads. Multipole expansion of the Stokes equations (the accurate HYDROMULTIPOLE algorithm) is applied to evaluate the hydrodynamic force exerted by the fluid on the rodlike particles, depending on their shape, i.e., on the number of beads and their orientation with respect to the wall and to the ambient shear flow.     

Numerical study on the adhesion and reentrainment of nondeformable particles on surfaces: the role of surface roughness and electrostatic forces

In this paper, the reentrainment of nanosized and microsized particles from rough walls under various electrostatic conditions and various hydrodynamic conditions (either in air or aqueous media) is numerically investigated. This issue arises in the general context of particulate fouling in industrial applications, which involves (among other phenomena) particle deposition and particle reentrainment. The deposition phenomenon has been studied previously and, in the present work, we focus our attention on resuspension. Once particles are deposited on a surface, the balance between hydrodynamic forces (which tend to move particles away from the surface) and adhesion forces (which maintain particles on the surface) can lead to particle removal. Adhesion forces are generally described using van der Waals attractive forces, but the limit of these models is that any dependence of adhesion forces on electrostatic forces (due to variations in pH or ionic strength) cannot be reproduced numerically. For this purpose, we develop a model of adhesion forces that is based on the DLVO (Derjaguin and Landau, Verwey and Overbeek) theory and which includes also the effect of surface roughness through the use of hemispherical asperities on the surface. We first highlight the effect of the curvature radius on adhesion forces. Then some numerical predictions of adhesion forces or adhesion energies are compared to experimental data. Finally, the overall effects of surface roughness and electrostatic forces are demonstrated with some applications of the complete reentrainment model in some simple test cases.     

Classical molecular dynamics study of [60]fullerene interactions with silica and polyester surfaces

This study examines the interaction of neutral and charged fullerenes with model silica and polyester surfaces. Molecular dynamics simulations at 298 K indicate that van der Waals forces are sufficiently strong in most cases to cause physisorption of the neutral fullerene particle onto the surfaces. The fullerenes are unable to penetrate the rigid silica surface but are generally able to at least partially infiltrate the flexible polymer surface by opening surface cavities. The introduction of charge to the fullerene generally leads to an increase in both the separation distance and Work of Separation with silica. However, the charged fullerenes generally exhibit significantly closer and stronger interactions with polyester films, with a distinct tendency to absorb into the "bulk" of the polymer. The separation distance and Work of Separation of C60 with each of the surfaces also depend greatly on the sign, magnitude, and localization of the charge on the particle. Cross-linking of the polyester can improve resistance to the neutral fullerene. Functionalization of the polyester surface (F and OH substituents) has been shown to prevent the C60 from approaching as close to the polyester surface. Fluorination leads to improved resistance to positively charged fullerenes, compared to the unmodified polyester. However, hydroxylation generally enables greater adhesion of charged fullerenes to the surface due to H-bonding and electrostatic attraction.     

Deposition of nanosized latex particles onto silica and cellulose surfaces studied by optical reflectometry

Deposition of positively charged nanosized latex particles onto planar silica and cellulose substrates was studied in monovalent electrolyte solutions at pH 9.5. The deposition was probed in situ with optical reflectometry in a stagnation point flow cell. The surface coverage can be estimated reliably with island film theory as well as with a homogeneous film model, as confirmed with atomic force microscopy (AFM). The deposition kinetics on the bare surface was of first order with respect to the particle concentration, whereby the deposition rate was close to the value expected for a perfect collector. The efficiency coefficient, which was defined as the ratio of the experimental and theoretical deposition rate constants, was in the range from 0.3 to 0.7. Subsequently, the surface saturated and a limiting maximum coverage was attained (i.e., blocking). These trends were in qualitative agreement with predictions of the random sequential absorption (RSA) model, where electrostatic interactions between the particles were included. It was observed, however, that the substrate strongly influenced the maximum coverage, which was substantially higher for silica than for cellulose. The major conclusion of this work was that the nature of the substrate played an important role in a saturated layer of deposited colloidal particles.