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.     

Deposition of particles under external forces in laminar flow through parallel-plate and cylindrical channels

A theoretical analysis of particle deposition kinetics onto walls of parallel-plate and cylindrical channels is presented. Rigorous transport equations are formulated by taking into account specific surface forces as well as external forces, e.g., gravity. By solving the transport equations numerically, the dimensionless mass transfer Sherwood number is determined as a function of various dimensionless parameters introduced such as Pe, Gr, Ad, and Dl, accounting for convection and diffusion, and for gravity, dispersion, and electrical double-layer interactions, respectively. The influence of attractive surface forces and gravity on the deposition kinetics is graphically presented and discussed. For large particles, i.e., about 1-μm diameter (Pe > 1), and for short distances from the point where deposition starts, a considerable increase in particle flux (up to an order of magnitude) is predicted over previous analytical values when strong attractive double-layer forces are present. For particles smaller than 0.1-μm diameter (Pe < 10^-4) our numerical results show that particle deposition rates may be successfully predicted by an analytical formula derived for particles of negligible size even in the presence of double-layer attractions (provided external forces are absent). Experimental results reported in the literature obtained under conditions of negligible gravity force are reinterpreted in terms of the present theory. A somewhat closer agreement with experimental data as compared to the analytical formula mentioned above is found in cases of strong double-layer attractions.     

Particle transfer to solid surfaces

Several theories for predicting deposition rates of flowing colloidal particles onto various collector surfaces are compared and discussed. Successful theories must include, besides hydrodynamic conditions in the vicinity of the collector and the energy of interaction between particles and the wall, a variety of other important factors affecting deposition such as particle detachment, aging of particle-collector bonds, masking, influence of the stability of the dispersion and surface heterogeneity and roughness.Several experimental procedures for measuring deposition rates are discussed and experimental data are compared with theoretical predictions. In the absence of energy barriers current theories predict deposition rates within 10–25% of their actual value. In their presence, discrepancies are usually much larger, mainly because theory neglects several of the above mentioned factors.Examples of dynamic simulation and Monte Carlo calculations suggest that these methods can incorporize the factors affecting deposition more readily than current theories.     

Deposition measurement of particulate matter in connection with corrosion studies

A new passive particle collector (inert surrogate surface) that collects particles from all directions has been developed. It was used to measure particle deposition at 35 test sites as part of a project that examined corrosion of materials in order that variation in particulate material could be used in development of dose–response functions in a modern multi-pollutant environment. The project, MULTI-ASSESS, was funded by the EU to examine the effects of air pollution on cultural heritage. Passive samplers were mounted rain-protected, and both in wind-protected and wind-exposed positions, to match the exposure of the samples for corrosion studies. The particle mass and its chemical content (nitrate, ammonium, sulfate, calcium, sodium, chloride, magnesium and potassium) were analysed. The loss of light reflectance on the surrogate surface was also measured. Very little ammonium and potassium was found, and one or more anions are missing in the ion balance. There were many strong correlations between the analysed species. The mass of analysed water-soluble ions was fairly constant at 24% of the total mass. The particle mass deposited to the samplers in the wind-protected position was about 25% of the particles deposited to an openly exposed sampler. The Cl⁻/Na⁺ ratios indicate a reaction between HNO₃ and NaCl. The deposited nitrate flux corresponds to the missing chloride. The Ca²⁺ deposition equals the deposition and the anion deficiency. The deposition most likely originates from SO₂ that has reacted with basic calcium-containing particles either before or after they were deposited. The particle depositions at the urban sites were much higher than in nearby rural sites. The deposited mass correlated surprisingly well with the PM₁₀ concentration, except at sites very close to traffic.     

The detachment of nylon particles from quartz plate by electro-osmotic flow

The direct application of electrokinetic phenomena to detergency was investigated. Experiments were carried out to remove particles from substrate by electro-osmosis. A model system which consisted of spherical nylon particles of 5m in mean diameter, a quartz plate, and wash liquid were used in analyzing the kinetic process of particle removal from substrate. When an electric field was applied to the system, electro-osmotic flow took place, and hence the particles were removed from the quartz surface. The -potentials of nylon particles and quartz plate were measured by electrophoresis. The rate constants of removal,, were obtained from the changes with time in the ratio of particle residue by applying the first-order reaction scheme. The value of increased with increasing electric field and with increasing concentration of surfactant. The total force of interaction between particle and plate was calculated on the basis of heterocoagulation theory of colloid stability.It was found from results thus obtained that the hydrodynamic force due to the electro-osmotic flow worked effectively as a mechanical force on the removal process and the adhesion force of particle to substrate reduced by adding surfactant.     

The Particle In-Flight Characteristics in Plasma Spraying Process Measured by Phase Doppler Anemometry (PDA)

Detailed measurements of particle in-flight characteristics have been carried out using a PDA system for benchmarking as well as to provide further information to aid the development of simulation models. The parameters studied included four conditions of primary gas flow rate and carrier gas flow rate. The particle velocities, diameters, and the corresponding volume flux at different locations were obtained. Due to the one port particle injection arrangement, it was noted that particles in general sprayed with an angle deviated from the nozzle axis Z_n, to the opposite side of the powder feeder port. The particles would also deviate from the spraying cone axis with a divergence angle (). The deviation and divergence angles were examined under different plasma spraying conditions. The measurement data rates at different cross-sectional planes were also obtained so as to compare the results derived from the volume flux measurement and the actual coating on a substrate at the equivalent standoff distance. It was found that the spraying area obtained from the measurement-data-rate increased with downstream distance and a linear relationship between spraying area and distance was also established. Comparing the integrated results, it was noted that the spraying areas derived from the measurement data rate were close to the actual spraying areas obtained from the coordinate measurement machine (CMM) results.     

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.     

Adhesion of nylon particles to a quartz plate in an aqueous solution and their removal by electro-osmosis

Particle removal by electro-osmotic flow was investigated by comparison with the removal by ordinary flow of water without electrokmetic effect. The relationship between adhesion and removal of particles in terms of force acting on the particle was also discussed. Experiments were carried out in an aqueous solution using nylon particles and a quartz plate. The adhesive force,F _T, for the particles which adhered to the quartz plate in secondary minima in the total potential energy of interaction versus separation distance curves was calculated. Particle removal experiments were carried out applying electro-osmotic and Poiseuille flows. The hydrodynamic force,F _d, which was required to remove particles from the plate was estimated using flow velocities. The effectiveness of electro-osmotic flow on particle removal was larger than that of Poiseuille flow. In the particle removal by electro-osmotic flow, the minimum of the ratioF _d/F _t for particle removal was found to be 50 and the ratio for removal efficiency of 0.5 was about 140.     

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.     

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.     

Well‐Defined SiO2@P(EtOx‐stat‐EI) Core–Shell Hybrid Nanoparticles via Sol‐Gel Processes

Positively charged nanoparticles (NPs) are very interesting for biomedical and pharmaceutical applications, such as nonviral gene delivery. Here, the synthesis of SiO₂ nanoparticles with a covalently grafted poly(2‐ethyl‐2‐oxazoline) (PEtOx) shell (SiO₂@PEtOx) is presented. PEtOx with a degree of polymerization of 20 and 38 is synthesized via microwave supported cationic ring‐opening polymerization and subsequently end‐functionalized with a triethoxysilyl linker for subsequent grafting to silica particles with hydrodynamic radii of 7, 31, and 152 nm. The resulting SiO₂@PEtOx particles are characterized by using dynamic light scattering (DLS), transmission electron microscopy (TEM, cryoTEM), and scanning electron microscopy (SEM) to determine changes in particle size. Thermal gravimetrical analysis is used to quantify the amount of polymer on the silica surface. Subsequent in situ transformation of SiO₂@PEtOx particles into SiO₂@P(EtOx‐stat‐EI) (poly(2‐ethyl‐2‐oxazoline‐stat‐ethylene imine) grafted silica particles) under acidic conditions inverts the surface charge from negative to positive according to ζ‐potential measurements. The P(EtOx‐stat‐EI) shell could be used for the deposition of Au NP afterward.

     

Relaxation of microparticles exposed to hydrodynamic forces in microfluidic conduits

The behavior of microparticles exposed to gravitational and lift forces and to the velocity gradient in flow velocity profile formed in microfluidic conduits is studied from the viewpoint of the transient period (the relaxation) between the moment at which a particle starts to be transported by the hydrodynamic flow and the time at which it reaches an equilibrium position, characterized by a balance of all active forces. The theoretical model allowing the calculation of the relaxation time is proposed. The numerical calculus based on the proposed model is compared with the experimental data obtained under different experimental conditions, namely, for different lengths of microfluidic channels, different average linear velocities of the carrier liquid, and different sizes and densities of the particles used in the study. The results are important for the optimization of microfluidic separation units such as microthermal field-flow fractionation channels in which the separation or manipulation of the microparticles of various origin, synthetic, natural, biological, etc., is performed under similar experimental conditions but by applying an additional thermodynamic force.

Adsorption and desorption of colloidal particles on glass in a parallel plate flow chamber—Influence of ionic strength and shear rate

The adsorption and desorption rates of 736 nm diameter polystyrene particles on glass were studiedin situ using a parallel plate flow chamber and automated image analysis. Adsorption and desorption rates were measured simultaneously during deposition, enabling the determination of initial deposition rates, blocked areas per particle, desorption rate coefficients, and the number of adhering particles in the stationary state. Deposition experiments were done from suspensions with different potassium nitrate concentrations (1, 10 and 50 mM) and at varying shear rates (15 to 200 s^–1). The initial deposition rate, the desorption rate, the blocked area per particle and the number of adhering particles in the stationary state showed major variations with the shear rate and the ionic strength of the suspension. At low ionic strength, the number of adhering particles showed an oscillatory behavior in time, presumably due to a varying interaction between particle and collector surface. Blocked areas, determined from deposition kinetics, ranged 705 to 2374 cross-sections at low ionic strength, and from 10 to 564 at high ionic strength and corresponded well with those estimated from local pair distribution functions which were obtained from an analysis of the spatial arrangement of the adhering particles.     

Particle adsorption and deposition: role of electrostatic interactions

This work demonstrates how electrostatic interactions, described in terms of the classical DLVO theory, influence colloid particle deposition phenomena at solid/liquid interfaces. Electrostatic interactions governing particle adsorption in both non-polar and polar media (screened interactions) are discussed. Exact and approximate methods for calculating the interaction energy of spherical and non-spherical (anisotropic) particles are presented, including the Derjaguin method. Phenomenological transport equations governing particle deposition under the linear regime are discussed with the limiting analytical expressions for calculating initial flux. Non-linear adsorption regimes appearing for higher coverage of adsorbed particles are analysed. Various theoretical approaches are exposed, aimed at calculating blocking effects appearing due to the presence of adsorbed particles. The significant role of coupling between bulk transport and surface blocking is demonstrated. Experimental data obtained under well-defined transport conditions, such as diffusion and forced convection (impinging-jet cells), are reviewed. Various experimental techniques for detecting particles at interfaces are discussed, such as reflectometry, ellipsometry, streaming potential, atomic force microscopy, electron and optical microscopy, etc. The influence of ionic strength and flow rate on the initial particle deposition rate (limiting flux) is presented. The essential role of electrostatic interactions in particle deposition on heterogeneous surfaces is demonstrated. Experimental data pertinent to the high-coverage adsorption regime are also presented, especially the dependence of the maximum coverage of particles and proteins on the ionic strength. The influence of lateral electrostatic interactions on the structure of particle monolayers is elucidated, and the links between colloid and molecular systems are pointed out.     

Formation and morphology of latex monolayers. Computer simulation studies

The results of computer simulations of monolayers created from monodisperse latex particles are presented and discussed. Layers are characterized by the normalized coverage,NC (the actual coverage of the surface related to its maximum possible coverage with particles), and by the average number of neighbors,ANN, calculated as the number of particles being in contact with a given one and averaged over all the particles on the surface. Variable parameters used in simulations include: the rate of particles deposition, the probability of lateral movements, the probability of desorption of particles adsorbed on the surface, the probability of covalent immobilization of adsorbed particles, and the on-sphere slip parameter, OSS (characterizing the scattering of a falling particle on the particles being already attached to the surface). Morphology of monolayers is qualitatively characterized by relations betweenANN andNC. It is shown that for all monolayers formed without adhesion (and without repulsion) between the particles adsorbed on the surface the dependence ofANN vs.NC is described by a characteristic master curve (regardless of the values of probabilities of desorption and lateral movements of particles). For the monolayers created including adhesive forces between the adsorbed particles the plots ofANN vs.NC lie above the master curve, while similar plots obtained for the layers made of particles showing various types of repulsive interactions are always placed below it. Thus, the dependencies ofANN vs.NC, derived from computer simulations, can be used for the determination of the character of the interparticle interactions in the real systems.     

Breakdown of colloid filtration theory: role of the secondary energy minimum and surface charge heterogeneities

The mechanisms and causes of deviation from the classical colloid filtration theory (CFT) in the presence of repulsive Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions were investigated. The deposition behavior of uniform polystyrene latex colloids in columns packed with spherical soda-lime glass beads was systematically examined over a broad range of physicochemical conditions, whereby both the fluid-phase effluent particle concentration and the profile of retained particles were measured. Experiments conducted with three different-sized particles in a simple (1:1) electrolyte solution reveal the controlling influence of secondary minimum deposition on the deviation from CFT. In a second series of experiments, sodium dodecyl sulfate (SDS) was added to the background electrolyte solution with the intent of masking near-neutrally charged regions of particle and collector surfaces. These results indicate that the addition of a small amount of anionic surfactant is sufficient to reduce the influence of certain surface charge inhomogeneities on the deviation from CFT. To verify the validity of CFT in the absence of surface charge heterogeneities, a third set of experiments was conducted using solutions of high pH to mask the influence of metal oxide impurities on glass bead surfaces. The results demonstrate that both secondary minimum deposition and surface charge heterogeneities contribute significantly to the deviation from CFT generally observed in colloid deposition studies. It is further shown that agreement with CFT is obtained even in the presence of an energy barrier (i.e., repulsive colloidal interactions), suggesting that it is not the general existence of repulsive conditions which causes deviation but rather the combined occurrence of "fast" and "slow" particle deposition.     

Adsorption of polyacrylic acid on hydrophobic and hydrophilic surfaces

In this paper the adsorption of polyacrylic acid (MW=5000) on the hydrophobic mercury surface and on the hydrophilic -Al₂O₃ surface at pH=3–4 in 0.55 M sodium chloride solution was investigated. Measurements of change of the double layer capacitance by phase selective a.c. voltammetry were used for determination of the adsorption of polyacrylic acid on the mercury electrode. The same method was used for the determination of the polyacrylic acid remaining in the solution after the adsorption on hydrophilic particles (-Al₂O₃ particles). The results obtained for adsorption of polyacrylic acid were compared to the results of the adsorption of humic substance of similar molecular weight under similar experimental conditions. The study has shown that polyacrylic acid in acidic solution is strongly adsorbed on the mercury surface, which is comparable to the adsorption of humic substance on the mercury surface. At the same time, the adsorption/deposition of polyacrylic acid on the -Al₂O₃ surface is weaker compared to humic acid, indicating at a smaller degree of interaction of polyacrylic acid with aluminium ions and with hydrophilic surface.     

Analysis of constant permeate flow filtration using dead-end hollow fiber membranes

Dead-end filtration of colloids using hollow fibers has been analysed theoretically and experimentally. A mathematical model for constant flux filtration using dead-end hollow fiber membranes has been developed by combining the Hagen–Poiseuille equation, the (standard) filtration equation, and cake filtration theory of Petsev et al. [D.N. Petsev, V.M. Starov, I.B. Ivanov, Concentrated dispersions of charged colloidal particles: sedimentation, ultrafiltration and diffusion, Colloid Surf. A: Physicochem. Eng. Aspects, 81 (1993) 65–81.] to describe the time dependence of the filtration behavior of hollow fiber membranes experiencing particle deposition on their surface. Instead of using traditional constitutive equations, the resistance of the cake layer formed by the deposited colloids has been directly correlated to the cake structure. This structure is determined by application of a force balance on a particle in the cake layer combined with the assumption that an electrostatically stable cake layer of mono-sized particles would be ordered in a regular packing geometry of minimum energy. The developed model has been used to identify the relationship between the filtration behavior of the hollow fiber membrane and the particle properties, fiber size, and imposed average flux. Filtration experiments using polystyrene latex particles of relatively narrow size distribution with a single dead-end hollow fiber membrane demonstrate good consistency between experimental results and model prediction. The developed model has been used to simulate the distribution of the cake resistance, transmembrane pressure, and flux along the hollow fiber membrane and used to assess the effect of fiber size, particle size, zeta potential, and the average imposed flux on the suction pressure-time profiles, flux, and cake resistance distributions. These results provide new insights into the filtration behavior of the hollow fiber membrane under constant flux conditions.     

The surface characterization of styrene-acrylamide copolymer latex particles and their deposition onto fibers

The surface characteristics of styrene-acrylamide (St-AAm) copolymer latex particles were investigated and their deposition onto polyamide (Nylon 6), polyester (polyethylene terephthalate) and polyacrylonitrile fibers was studied. Conductometric titrations and viscosity measurements of latex dispersions revealed the presence of a water-soluble polymer layer on the particle surface and the thickness of its polymer layer increased with increasing acrylamide fraction in a latex particle. The deposition rates of St-AAm copolymer latices onto Nylon 6 and polyester fibers increased with increasing acrylamide fraction and decreasing pH at a constant ionic strength. These deposition phenomena onto Nylon 6 and polyester fibers agreed qualitatively with prediction based on the electrokinetic data of the latices and the fibers. However, a participation of attractive interaction due to an increase in acrylamide fraction was also suggested.The deposition rate onto polyacrylonitrile fiber decreased with increasing acrylamide fraction in spite of a decrease in electrostatic repulsive interaction, and it was found that a specific large repulsive interaction acts between polyacrylonitrile fiber and St-AAm copolymer latex particles.This paper is part VIII in a series on Interfacial electrical studies on the deposition of polymer latexes onto fabrics and the removal of these deposited latexes. Part VII: Tamai H, Kimura I,Suaza T Coll Polym Sci 261: 661 (1983)     

Effect of Low-Temperature Treatment of Silver Hydrosol on Its Absorption Spectra

Absorption spectra of a stable silver hydrosol before and after low-temperature treatment were recorded and analyzed. An increased duration of this treatment leads to linear decrease in volume concentration of Ag particles having an absorption maximum _max = 412 nm and to the formation of a new fraction of larger particles. It was shown on the basis of calculation of spectra by the Mie theory and the theory of plasmon resonance absorption that the low-temperature treatment of hydrosol does not change the electron density of metal particles and the number of surface defects. The effect of low-temperature treatment is independent of sol concentration. The particle aggregation under low-temperature treatment conditions is favored by the preliminary adsorption of p-phenylenediamine derivative.