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.     

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.     

Effect of electrostatic, hydrodynamic, and Brownian forces on particle trajectories and sieving in normal flow filtration

Particle deposition and fouling are critical factors governing the performance of microfiltration and ultrafiltration systems. Particle trajectories were evaluated by numerical integration of the Langevin equation, accounting for the combined effects of electrostatic repulsion, enhanced hydrodynamic drag, and Brownian diffusion. In the absence of Brownian forces, particles are unable to enter the membrane pores unless the drag associated with the filtration velocity can overcome the electrostatic repulsion. Brownian forces significantly alter this behavior, allowing some particles to enter the pore even at low filtration velocities. The average particle transmission, evaluated from the probability of having a particle enter the pore, increases with increasing filtration velocity due to the greater hydrodynamic drag force on the particle. These results provide important insights into particle behavior in membrane systems.     

Hydrodynamic crossover in dynamic microparticle adhesion on surfaces of controlled nanoscale heterogeneity

This note documents the crossover from a regime where shear flow hinders microparticle adhesion on collecting surfaces to that where increased flow aids particle capture. Flow generally works against adhesion and successfully hinders particle capture when the net physicochemical attractions between the particles and collector are weak compared with hydrodynamic forces on the particle. Conversely, with strong attractions between particles and collector, flow aids particle capture by increasing the mass transport of particles to the interfacial region. Here, local hydrodynamics still generally oppose adhesion but are insufficient to pull particles off of the surface. Thus, flow actually increases the particle capture rate through the increased transport to the surface. These behaviors are demonstrated using 1 mum silica spheres flowing over electrostatically heterogeneous (length scales near 10 nm) collecting surfaces at shear rates from 22 to 795 s(-1). The net surface charge on the collector is varied systematically from strongly negative (pure silica) to strongly positive (a saturated polycationic overlayer), demonstrating the interplay between physicochemical and hydrodynamic contributions. These results clearly apply to situations where heterogeneous particle-surface interactions are electrostatic in nature; however, qualitatively similar behavior was previously reported for the effect receptor density on bacterial adhesion.     

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.     

Influence of surface topography on the interactions between nanostructured hydrophobic surfaces

Nanostructured particle coated surfaces, with hydrophobized particles arranged in close to hexagonal order and of specific diameters ranging from 30 nm up to 800 nm, were prepared by Langmuir-Blodgett deposition followed by silanization. These surfaces have been used to study interactions between hydrophobic surfaces and a hydrophobic probe using the AFM colloidal probe technique. The different particle coated surfaces exhibit similar water contact angles, independent of particle size, which facilitates studies of how the roughness length scale affects capillary forces (previously often referred to as "hydrophobic interactions") in aqueous solutions. For surfaces with smaller particles (diameter < 200 nm), an increase in roughness length scale is accompanied by a decrease in adhesion force and bubble rupture distance. It is suggested that this is caused by energy barriers that prevent the motion of the three-phase (vapor/liquid/solid) line over the surface features, which counteracts capillary growth. Some of the measured force curves display extremely long-range interaction behavior with rupture distances of several micrometers and capillary growth with an increase in volume during retraction. This is thought to be a consequence of nanobubbles resting on top of the surface features and an influx of air from the crevices between the particles on the surface.     

Influence of very small bubbles on particle/bubble heterocoagulation

Very small bubbles which partially coat the surface of particles influence whether or not heterocoagulation between a particle and a bubble occurs. The electrostatic and van der Waals forces of interaction between particles and bubbles were calculated as a function of electrolyte concentration, particle size, and the size and distributions of these very small bubbles present on the particle surface. The height of the surface force barrier was compared with the hydrodynamic pressing force under conditions of flotation. The presence of these very small bubbles has a profound effect on the interaction between particles and bubbles and, in particular, strongly decreases the critical particle radius for heterocoagulation.     

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.     

Comparison of the adhesion forces in single and double-layer coatings on the MEMS surfaces by JKR and DMT models

In many medical and industrial applications, some strategies are needed to control the adhesion forces between the materials, because surface forces can activate or hinder the function of the device. All actual surfaces present some levels of roughness and the contact between two surfaces is transferred by the asperities on the surfaces. The force of the adhesion, which depends on the operating situations, can be influenced by the contact region. The aim of the present study is to predict the adhesion force in MEMS surfaces using the JKR and DMT models. The surfaces of the coating material in this research consisted of the single-layer coating of Gold and Silver, and the double-layer coating of TiO₂/Gold and TiO₂/Silver on the silicon (100) substrates. The depositing was done by the thermal evaporation method. The results showed that the double-layer coating developed by the new deposition method helped the reduction of the adhesion forces between the probe tip and the specimen surface. The predicted adhesion forces between the probe and the specimens with DMT and JKR models were compared with the experimental results. For all specimens, the simulated data by applying the JKR theory were in a good agreement with the adhesion force experimental values.     

Dielectrophoresis of nanoparticles

A numerical scheme based on the distributed Lagrange multiplier method (DLM) is used to study the motion of nano-sized particles of dielectric suspensions subjected to uniform and nonuniform electric fields. Particles are subjected to both electrostatic and hydrodynamic forces, as well as Brownian motion. The results of the simulations presented in this paper show that uniform electric fields the evolution of the particle structures depends on the ratio of electrostatic particle-particle interactions and Brownian forces. When this ratio is of the order of 100 or greater, particles form stable chains and columns, whereas when it is of the order of 10 or smaller the particle distribution is random. For the nonuniform electric field cases considered in this paper, the relative magnitude of Brownian forces is in the range such that it does not influence the eventual collection of particles by dielectrophoresis and the particular locations where the particles are collected. However, Brownian motion is observed to influence the transient particle trajectories. The deviation of the particle trajectories compared to those determined by the electrostatic and hydrodynamic forces alone is characterized by the ratio of Brownian and dielectrophoretic forces.     

Electrostatic double-layer interaction between spherical particles inside a rough capillary

Predictions of electrostatic double-layer interaction forces between two similarly charged spherical colloidal particles inside an infinitely long "rough" capillary are presented. A simple model of a rough cylindrical surface is proposed, which assumes the capillary wall to be a periodic function of axial position. The periodic roughness of the wall is characterized by the wavelength and amplitude of the undulations. The electrostatic double-layer interaction force between two spherical particles located axially inside this rough capillary is determined by solving the nonlinear Poisson-Boltzmann equation employing finite element analysis. The effect of surface roughness of the cylindrical enclosure on the interaction force between two particles is extensively studied on the basis of this model. The simulations are carried out for dimensionless amplitudes (amplitude/particle radii) ranging from 0.05 to 0.15 and scaled wavelengths (wavelength/particle radii) ranging from 0.4 to 4.0. The interaction force between the particles is significantly modified by the proximity of the rough capillary wall. Generally, the interaction force for rough capillaries oscillates around the corresponding interaction force in a smooth capillary depending on the magnitudes of the scaled amplitude and wavelength of the roughness. The influence of roughness on the electrostatic interactions becomes more pronounced when the surface potential of the cylinder wall is different from the sphere surface potentials. When the cylinder and the particle surfaces have large potential differences, the axial force experienced by a particle is dominated by the capillary roughness. There are dramatic oscillations of the force, which alternately becomes repulsive and attractive as the particle moves from the crest to the trough of the rough capillary wall. These results suggest that manipulation of colloidal particles in narrow microchannels may be subject to significant force variations owing to the roughness inherent in microfabricated channels etched on metal films.     

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.     

Experimental humidity dependency of small particle adhesion on silica and titania

The humidity present in ambient atmosphere affects the adhesion of small particles by causing capillary bridge formation between the particle and the surface. Even in moderate relative humidities this, usually attractive, force can have a significant effect on adhesion behaviour of micro and sub-micro particles. We have directly measured the pull-off forces of initially adhered oxide particles on oxide surfaces with atomic force microscope in controlled atmosphere with adjustable humidity. We demonstrate the effect of the surface roughness resulting in two different regions of capillary formation and the particle shape having a strong effect on the humidity dependency of adhesion. The experimental results are explained by theoretical framework.     

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.     

Microflotation Suppression and Enhancement Caused by Particle/Bubble Electrostatic Interaction

The processes of attachment and detachment of small or medium-sized particles to relatively large bubbles during microflotation are considered in terms of the heterocoagulation theory. Calculations are made for the conditions that the surface potentials are of similar sign and constant, that one of the surface potentials is small, that hydrophobic attraction is absent, and that there are no surface deformations. Under these conditions bubble-particle aggregates may form as a result of an electrostatic attraction which exceeds the repulsive van der Waals force at intermediate distances. Next to electrostatic and van der Waals forces, hydrodynamic and gravitational forces are considered. These forces may overcome the electrostatic repulsion at large distances and promote particle bubble attachment. Strong electrostatic attraction at small distances, arising at a large difference of the surface potentials of the bubble and the particle and of low electrolyte concentrations, can prevent subsequent detachment by hydrodynamic and gravitational forces. With increasing electrolyte concentration the electrostatic barrier increases and the attractive electrostatic force diminishes. As a result, a critical electrolyte concentration for microflotation exists. Above this concentration attachment may still occur but it is followed by detachment. At lower electrolyte concentrations the electrostatic attractive force prevents the detachment. The dependence of the critical electrolyte concentration on the values of the bubble and particle potentials and the Hamaker constant is calculated. The critical concentration does not depend on particle or bubble size if the absolute values of the total detachment force and the total pressing force coincide, which is the case for Stokes and potential flow. For every electrolyte concentration lower than the critical value there are two critical particle sizes that limit the flotation possibility. For small particle sizes attachment is impossible because the pressing force is smaller than the electrostatic barrier. For large particle sizes detachment cannot be prevented because the detachment force exceeds the maximum electrostatic attraction. A microflotation domain of intermediate particle sizes exists in which irreversible heterocoagulation occurs. Copyright 2001 Academic Press.     

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.     

Effect of roughness on particle adhesion in aqueous solutions: a study of Saccharomyces cerevisiae and a silica particle

An atomic force microscope (AFM) has been used to quantify the adhesion of living cells Saccharomyces cerevisiae on three different silica surfaces with defined roughness. The effects of support roughness on the adhesion forces of a smooth silica particle were studied in addition. A living single cell was immobilized at the apex of a tipless AFM cantilever using a key-lock mechanism. Adhesion was quantified from the force-distance data measured on a smooth silica substrate and two substrates coated with hydrophilic monodisperse silica particles with 110 and 240 nm in diameter to study the effect of roughness on particle adhesion. The AFM technique gives unique insight into the primary colonization event of biofilm formation. The new knowledge helps substantially to design surface coatings relevant for biotechnology, medicine and dentistry.     

Changes in the interaction characteristics of polyelectrolyte complex covered silica surfaces

The adsorption of polyelectrolyte complexes, PEC, made from the cationic poly (diallyldimethylammonium) chloride (PDADMAC) and the anionic maleic acid-co-propene copolymer (MA-P) on a Si-wafer surface has been studied. The application of highly diluted colloidally dispersed PEC solutions led to the deposition of single PEC particles onto the surface of the Si-wafer. The interaction forces of the heterogeneously covered surface were monitored by direct force measurements with an atomic force microscope (AFM) in the force volume mode. On the surface of a single PEC particle drastic changes in the interaction forces were found in comparison with the unmodified Si-wafer: in all force vs. distance curves a strong increase of the adhesion was measured that can be attributed to the formation of electrostatic bonds between the negatively charged Si₃N₄-tip and the cationic excess charge of the PEC. Additionally, the behavior during approach of both surfaces has been distinct: at pH 6.1 we see a long range electrostatic attraction between the tip and the PEC particle. The attraction becomes even stronger at pH 4.1, because of an increased positive net charge. Generally, a heterogeneous surface with a wide variety of interaction features can be created by the adsorption of PEC particles.     

Adhesion as an interplay between particle size and surface roughness

Surface roughness plays an important role in the adhesion of small particles. In this paper we have investigated adhesion as a geometrical effect taking into account both the particle size and the size of the surface features. Adhesion is studied using blunt model particles on surfaces up to 10 nm root-mean-square (RMS) roughness. Measurements with particles both smaller and larger than surface features are presented. Results indicate different behavior in these areas. Adhesion of particles smaller than or similar in size to the asperities depend mainly on the size and shape of the asperities and only weakly on the size of the particle. For large particles also the particle size has a significant effect on the adhesion. A new model, which takes the relative size of particles and asperities into account, is also derived and compared to the experimental data. The proposed model predicts adhesion well over a wide range of particle/asperity length scales.