Autostratification in drying colloidal dispersions: experimental investigations

In films cast from a colloidal dispersion comprising two particle sizes, we experimentally examine the distribution of particles normal to the substrate. The particle concentrations at various positions in the film are determined through atomic force microscopy and NMR profiling. The results are compared to a previously derived diffusional model. Evidence for diffusional driven stratification is found, but the importance of other flows is also highlighted. The conditions that enhance particle stratification are found to be a colloidally stable dispersion, low initial volume fractions, a low concentration of the stratifying particle, and for the Peclet numbers of the two components to straddle unity.     

Auto-stratification in drying colloidal dispersions: a diffusive model

The mechanism by which the particles in a drying film come into close packing during solvent evaporation has an important role to play in the final film morphology. During drying the particles can develop non-uniform concentrations across the vertical height of the film, depending on their diffusion rate. By applying the principles of classical diffusion mechanics to a hard sphere system, a theory for this novel method of stratification during drying of a two component film has been derived. The model is dependent on the particle Peclet numbers and when one is above unity and the other below, maximum stratification is observed.     

Electroviscous sphere-wall interactions

A theoretical analysis is presented to determine the forces of interaction between an electrically charged spherical particle and a charged plane wall when the particle translates parallel to the wall and rotates around its axis in a symmetric electrolyte solution at rest. The electroviscous effects, arising from the coupling between the electrical and hydrodynamic equations, are determined as a solution of three partial differential equations, derived from Cox's general theory [R.G. Cox, J. Fluid Mech. 338 (1997) 1], for electroviscous ion concentration, electroviscous potential and electroviscous flow field. It is a priori assumed that the double layer thickness surrounding each charged surfaces is much smaller than the particle size. Using the matched asymptotic expansion technique, the electroviscous forces experienced by the sphere are explicitly determined analytically for small particle-wall distances, but low and intermediate Peclet numbers.     

Perfusive flow and intraparticle distribution of a neutral analyte in capillary electrochromatography

The relevance and magnitude of an electroosmotic perfusion mechanism in electrochromatography is analyzed. To systemize our studies we first considered the transport of an electroneutral and nonadsorbing tracer. Based on the refractive index matching in a microfluidic setup containing fixed spherical porous particles, we conducted a quantitative analysis in real time of the spatio-temporal distribution of fluorescent tracer molecules during their uptake by (and a release from) single particles using confocal laser scanning microscopy. Even under conditions of a significant electrical double layer overlap the intraparticle electroosmotic flow produces due to its unidirectional nature and in striking contrast to the symmetric (spherical) distributions typical for purely diffusive transport strongly asymmetric concentration profiles inside spherical particles as the locally charged pore liquid begins to respond to the externally applied electrical field. The profiles retain an axisymmetric nature, i.e., rotational symmetry with respect to the field direction. Results of our measurements could be successfully interpreted and further analyzed by a compact mathematical model. Intraparticle Peclet numbers of up to 150 have been realized and found to significantly enhance the mass transport on particle scale towards the convection-dominated regime when compared to a conventional (diffusion-limited) kinetics.     

Effects of particle size on near-wall depletion in mono-dispersed colloidal suspensions

In this work we investigate the change in particle concentration near a solid boundary for colloidal dispersions in pressure driven flow, commonly referred to as wall depletion. In particular we determine the effect of Peclet number on the strength and spatial extent of the depleted layer. The change in concentration near the solid boundary is measured with attenuated total reflection infrared (ATR-IR) spectroscopy described previously (P.J.A. Hartman Kok et al., J. Rheol. 46 (2002) 481). The method is capable of measuring the concentration of particles at distances ranging from 0.2 to 1.0 mum from the boundary. The suspensions investigated consisted of mono-dispersed polystyrene particles in water. Particles of four different sizes were used, with radius, a, of 30, 54, 105, and 197 nm. (The ratio H/a was in the range 2500-17,000 with H being the height of the flow cell.) This enabled us to measure the wall depletion effect over a wide range of Peclet numbers, ranging from 0.01 to 45. We found that wall depletion was not significant for Peclet numbers smaller than unity. Estimates of the wall slip layer thickness obtained from rheological experiments were consistent with the results obtained by ATR-IR spectroscopy.     

Stability in Colloidal Mixtures Containing Particles with a Large Disparity in Size

An experimental approach, based on turbidity measurements, is proposed for studies of the stability in colloidal mixtures containing particles with large disparity in size. The main advantage of this approach is that it permits investigations even under conditions of comparable particle number concentrations of the two colloidal populations. Binary mixtures containing a poly(vinyl acetate) (PVAc) latex and a Ludox AS-40 silica sol were investigated. The silica particles were much smaller than the latex ones. The experimental stability factors were compared with the theoretical values computed on the basis of the Kihira-Ryde-Matijevic model (J. Chem. Soc., Faraday Trans. 88(16), 2379 (1992)) for interaction between spherical particles with unevenly distributed surface charges. All the experimental results support the idea that, even when both sols are negatively charged, the small silica particles are adsorbed onto the latex surface. Under these conditions, the heteroaggregates, which are composed of PVAc cores surrounded with silica particles, can be modeled as PVAc particles having "modified" surface characteristics (i.e., average Stern potential and varying extents of the surface charge segregation). Copyright 2001 Academic Press.     

Ultrafast electrokinetics

The influence of a high electric field applied on both fluid flow and particle velocities is quantified at large Peclet numbers. The experiments involved simultaneous particle image velocimetry and flow rate measurements. These are conducted in polydimethylsiloxane channels with spherical nonconducting polystyrene particles and DI water as the background flow. The high electric field tests produced up to three orders of magnitude higher electrokinetic velocities than any previous reports. The maximum electroosmotic velocity and electrophoretic velocity measured were 3.55 and 2.3 m/s. Electrophoretic velocities are measured over the range of 100 V/cm < E < 250 000 V/cm. The results are separated according to the different nonlinear theoretical models, including low and high Peclet numbers, and weak and strong concentration polarization. They show good agreement with the models. Such fast velocities could be used for flow separation, mixing, transport, control, and manipulation of suspended particles as well as microthrust generation among other applications.     

The metastable states of foam films containing electrically charged micelles or particles: experiment and quantitative interpretation

The stepwise thinning (stratification) of liquid films containing electrically charged colloidal particles (in our case - surfactant micelles) is investigated. Most of the results are applicable also to films from nanoparticle suspensions. The aim is to achieve agreement between theory and experiment, and to better understand the physical reasons for this phenomenon. To test different theoretical approaches, we obtained experimental data for free foam films from micellar solutions of three ionic surfactants. The theoretical problem is reduced to the interpretation of the experimental concentration dependencies of the step height and of the final film thickness. The surface charges of films and micelles are calculated by means of the charge-regulation model, with a counterion-binding (Stern) constant determined from the fit of surface tension isotherms. The applicability of three models was tested: the Poisson-Boltzmann (PB) model; the jellium-approximation (JA), and the cell model (CM). The best agreement theory/experiment was obtained with the JA model without using any adjustable parameters. Two theoretical approaches are considered. First, in the energy approach the step height is identified with the effective diameter of the charged micelles, which represents an integral of the electrostatic-repulsion energy calculated by the JA model. Second, in the osmotic approach the step height is equal to the inverse cubic root of micelle number density in the bulk of solution. Both approaches are in good agreement with the experiment if the suspension of charged particles (micelles) represents a jellium, i.e. if the particle concentration is uniform despite the field of the electric double layers. The results lead to a convenient method for determining the aggregation number of ionic surfactant micelles from the experimental heights of the steps.     

Coupled Influence of Colloidal and Hydrodynamic Interactions on the RSA Dynamic Blocking Function for Particle Deposition onto Packed Spherical Collectors

The influence of electrostatic double-layer and hydrodynamic interactions on random sequential adsorption (RSA) of colloidal particles onto packed spherical collectors was investigated using inverse analysis of colloid breakthrough data obtained from well-controlled particle deposition experiments. Deposition experiments were carried out using monodisperse aqueous suspensions of positively charged latex colloids and packed columns of negatively charged uniform glass beads for different combinations of ionic strength, particle size, and approach velocity. From the experimental particle breakthrough data, the initial particle deposition rates and the virial coefficients of the dynamic blocking function based on RSA mechanics were determined. The magnitudes of the virial coefficients were observed to increase from the hard sphere values with increasing flow rates and decreasing ionic strengths of the background electrolyte. Particle size also plays a significant role in governing the deposition dynamics. The deviation from the hard sphere RSA behavior becomes more prominent for larger particles. Copyright 2000 Academic Press.     

Diffusiophoresis in a concentrated suspension of colloidal spheres in nonelectrolyte gradients

The diffusiophoretic motion of a homogeneous suspension of identical spherical particles is considered under conditions of small Reynolds and Peclet numbers. The effects of interaction of the individual particles are taken into explicit account by employing a unit cell model which is known to provide good predictions for the sedimentation of monodisperse suspensions of spherical particles. The appropriate equations of conservation of mass and momentum are solved for each cell, in which a spherical particle is envisaged to be surrounded by a concentric shell of suspending fluid, and the diffusiophoretic velocity of the particle is calculated for various cases. Analytical expressions of this mean particle velocity are obtained in closed form as functions of the volume fraction of the particles. Comparisons between the ensemble-averaged diffusiophoretic velocity of a test particle in a dilute suspension and our cell-model results are made. Received: 30 June 1999 Accepted: 8 December 1999     

Interpretation of conservative forces from Stokesian dynamic simulations of interfacial and confined colloids

This paper presents Stokesian dynamics simulations of experiments involving one or two charged colloids near either a single charged wall or confined between parallel charged walls. Equilibrium particle-particle and particle-wall interactions are interpreted from dynamic particle trajectories in simulations involving (1) a single particle levitated above a wall, (2) two particles below a wall, and (3) two particles confined between two parallel walls. By specifying only repulsive electrostatic Derjaguin-Landau-Verwey-Overbeek (DLVO) potentials and including multibody hydrodynamics, we successfully recover expected potentials in some cases, while anomalous attraction is observed in other cases. Attraction inferred in the latter simulations displays quantitative agreement with literature measurements when particle dynamics are interpreted using reported analyses. Because anomalous attraction is reproduced in simulations using only electrostatic repulsive DLVO potentials, our results reveal the one-dimensional analyses to be invalid for configurations that are inherently multidimensional via multibody hydrodynamics. Parameters related to experimental sampling of particle dynamics are also found to be critical for obtaining accurate potentials. We explain the anomalous attraction in each experiment using effective potentials, which can be employed in an a priori fashion to assist the confident design of future experiments involving interfacial and confined colloids. Ultimately, our findings reveal the importance of dimensionality and multibody hydrodynamics for understanding nonequilibrium dynamics of colloids near surfaces.     

A model for surfactant distribution in latex coatings

The presence of surfactants in dried latex films can adversely affect the adhesive, water-resistant, and gloss properties, so investigating the surfactant distribution in latex coatings is of prime industrial relevance. Here we present a model that predicts the distribution of surfactant in a latex coating during the solvent evaporation stage. The conservation equation for surfactant during solvent evaporation is solved in the limit of infinite particle Peclet numbers, a dimensionless quantity giving the measure of relative magnitudes of evaporative to diffusive fluxes. A parametric analysis using the model reveals that the surfactant adsorption isotherm is the determining physical parameter. The model always predicts surfactant excesses at the top surface and either excess or depletion at the bottom surface depending on the isotherm. Uniform distributions are predicted for low surfactant Peclet numbers. Attenuated total reflection Fourier transform infrared spectroscopic probes on film surfaces conform to the behavior predicted by the model.     

Modeling the velocity field of the electroosmotic flow in charged capillaries and in capillary columns packed with charged particles: interstitial and intraparticle velocities in capillary electrochromatography systems

Mass transfer systems based on electrokinetic phenomena (i.e., capillary electrochromatography (CEC)) have shown practical potential in becoming powerful separation methods for the biotechnology and pharmaceutical industries. A mathematical model has been constructed and solved to describe quantitatively the profiles of the electrostatic potential, pressure, and velocity of the electroosmotic flow (EOF) in charged cylindrical capillaries and in capillary columns packed with charged particles. The results obtained from model simulations (i) provide significant physical insight and understanding with regard to the velocity profile of the EOF in capillary columns packed with charged porous particles which represent systems employed in CEC, (ii) provide the physical explanation for the experimental results which indicate that the velocity of the EOF in capillary columns packed with charged porous particles is a very weak function (it is almost independent) of the diameter of the particles, and (iii) indicate that the intraparticle velocity, nu(p,i), of the EOF can be greater than zero. The intraparticle Peclet number, Pe(int rap), for lysozyme was found to be greater than unity and this intraparticle convective mass transfer mechanism could contribute significantly, if the appropriate chemistry is employed in the mobile liquid phase and in the charged porous particles, in (a) decreasing the intraparticle mass transfer resistance, (b) decreasing the dispersive mass transfer effects, and (c) increasing the intraparticle mass transfer rates so that high column efficiency and resolution can be obtained. Furthermore, the results from model simulations indicate that for a given operationally permissible value of the applied electric potential difference per unit length, Ex, high values for the average velocity of the EOF can be obtained if (1) the zeta potential, zeta(p), at the surface of the particles packed in the column has a large negative magnitude, (2) the value of the viscosity, mu, of the mobile liquid phase is low, (3) the magnitude of the dielectric constant, epsilon, of the mobile liquid phase is reasonably large, and (4) the combination of the values of the concentration, C(infinity), of the electrolyte and of the dielectric constant, epsilon, provide a thin double layer. The theoretical results for the velocity of the EOF obtained from the solution of the model presented in this work were compared with the experimental values of the velocity of the EOF obtained from a fused-silica column packed with charged porous silica C8 particles. Systems with four different particle diameters and three different concentrations of the electrolyte were considered, and the magnitude of the electric field was varied widely. The agreement between theory and experiment was found to be good.     

Effect of water chemistry and aging on iron-mica interaction forces: implications for iron particle transport

The transport of particles through groundwater systems is governed by a complex interplay of mechanical and chemical forces that are ultimately responsible for binding to geological substrates. To understand these forces in the context of zero valent iron particles used in the remediation of groundwater, atomic force microscopy (AFM)-based force spectroscopy was employed to characterize the interactions between AFM tips modified with either carbonyl iron particles (CIP) or electrodeposited Fe as a function of counterion valency, temperature, particle morphology, and age. The measured interaction forces were always attractive for both fresh and aged CIP and electrodeposited iron, except in 100 mM NaCl, as a consequence of electrostatic attraction between the negatively charged mica and positively charged iron. In 100 mM NaCl, repulsive hydration forces appeared to dominate. Good agreement was found between the experimental data and predictions based on the extended DLVO (XDLVO) theory. The effect of aging on iron particle composition and morphology was assessed by X-ray photoelectron spectroscopy (XPS), scanning electron microscopy (SEM), and energy dispersive spectroscopy (EDS) revealing that the aged particles comprising a zero valent iron core passivated by a mixture of iron oxides and hydroxides. Force spectroscopy showed that aging caused variations in the adhesive force due to the changes in particle morphology and contact area.     

Particle zips: vertical emulsion films with particle monolayers at their surfaces

Vertical emulsion films with particle monolayers at their surfaces have been studied by direct microscope observations. The effects of particle wettability and surface coverage on the structure and stability of water films in octane and octane films in water have been investigated. Monodisperse silica particles (3 microm in diameter) hydrophobized to different extents have been used. It is found that the structure and stability of emulsion films strongly depend on the film type (water-in-oil or oil-in-water), the particle contact angle, the interactions between particles from the same and the opposite monolayer, and the monolayer density. Stable films are observed only when the particle wettability fulfills the condition for stable particle bridges--in agreement with the concept that hydrophilic particles can give stable oil-in-water emulsions, whereas hydrophobic ones give water-in-oil emulsions. In the case of water films with dilute disordered monolayers at their surfaces, the hydrophilic particles are expelled from the film center toward its periphery, giving a dimple surrounded by a ring of particles bridging the film surfaces. In contrast, the thinning of octane films with dilute ordered monolayers at their surfaces finally leads to the spontaneous formation of a dense crystalline monolayer of hydrophobic particles bridging both surfaces at the center of the film. The behaviors of water and octane films with dense close-packed particle monolayers at their surfaces are very similar. In both cases, a transition from bilayer to bridging monolayer is observed at rather low capillary pressures. The implications of the above finding for particle stabilized emulsions are discussed.     

The effect of gas slip on pressure drop and deposition of submicron particles in model granular filters

The Stokes flow field and aerosol particle deposition from flows in model filters, i.e., separate layers of granules with square and hexagonal structures, have been calculated taking into account the effect of gas slip at granule surface. Approximating formulas have been derived for granule drag forces to a flow. The efficiencies of diffusion collection of particles have been calculated in a wide range of Peclet numbers with allowance for a finite particle size and the existence of a Knudsen boundary layer, the layer thickness being comparable with the particle sizes. The applicability of the cell model to the calculation of granular filters has been discussed.     

Polyion-induced aggregation of lipidic-coated solid polystyrene spheres: the many facets of complex formation in low-density colloidal suspensions

We have investigated the formation of a cluster phase in low-density colloidal systems formed by charged solid charged particles stuck together by an oppositely charged polyion. In analogy with what we have previously observed in the case of soft charged particles, also in this case the same basic phenomenology occurs, consisting of the presence of the two well-known characteristic phenomena of this class of colloids, that is, reentrant condensation and charge inversion. With the aim of comparing the cluster formation in both soft and solid charged particles, we have, in previous works, employed cationic liposomes (soft particles, lipidic vesicles built up by dioleoyltrimethylammonium propane [DOTAP] lipid) and, in the present work, polystyrene particles (solid particles) covered by the same lipidic bilayer as the one of the soft particles, so that the two classes of particles share electrostatic interactions of the same nature. These charged particle clusters, where the single aggregating particles maintain their integrity without undergoing a structural rearrangement, join to a class of different aggregated structures (lamellar or inverse hexagonal phases) observed as well in the polyion-induced aggregation of oppositely charged mesoscopic particles, in particular, lipidic vesicles. Our results show that the formation of relatively large, equilibrium clusters of particles which maintain their integrity, stuck together by a polyion which acts as an electrostatic glue, is one of the many facets of the complex phenomenology underlying the interactions of charged particles with oppositely charged objects.     

Deposition of nanoparticles in filters composed of permeable porous fibers

The diffusion deposition of nanoparticles is studied from a flow at low Reynolds numbers in model filters composed of permeable circular porous fibers. The field of particle concentration is calculated and the capture coefficient is determined for a cell, as well as the isolated row of parallel fibers within a wide range of Peclet numbers (Pe) depending on the fiber permeability. It is shown that at Pe > 1, the diffusion capture coefficient η increases with permeability, while at Pe → ∞, it tends toward the limiting value, which is equal to the gas flow rate through the porous fiber. The capture coefficients calculated from a cell model and for a row of fibers are almost equal to each other. The diffusion deposition of aerosol particles in the highest penetration range is calculated with an allowance for their finite sizes and it is shown that the radii of most penetrable particles decrease with an increase in fiber permeability.     

Electroviscous cylinder-wall interactions

A theoretical analysis is presented to determine the forces of interaction between an electrically charged cylindrical particle and a charged plane boundary wall when the particle translates parallel to the wall and rotates around its axis in a symmetric electrolyte solution at rest. The electroviscous effects, arising from the coupling between the electrical and hydrodynamic equations, are determined as a solution of three partial differential equations, derived from R.G. Cox's general theory [J. Fluid Mech. 338 (1997) 1], for electroviscous ion concentration, electroviscous potential, and electroviscous flow field. It is assumed a priori that the double layer thickness surrounding each charged surface is much smaller than the length scale of the problem. Using the matched asymptotic expansion technique, the electroviscous forces experienced by the cylinder are explicitly determined analytically for small particle-wall distances for low and intermediate Peclet numbers. It is found that the tangential force usually increases the drag above the purely hydrodynamic drag, although for certain conditions the drag can be reduced. Similarly the normal force is usually repulsive, i.e., it is an electrokinetic lift force, but under certain conditions the normal force can be attractive.     

Simulation study of charged nanoparticles confined in a rectangular tube with discrete wall charges

The development of novel nanomaterials has been a subject of intense interest in recent years. An interesting structure among these materials is the so-called "pea pods" (i.e., nanoparticles confined in nanotubes). To facilitate the development and commercialization of these materials, it is important that we have an in-depth understanding of their behavior. The study of confined charged particles is particularly challenging because of the long-ranged nature of electrostatic interaction, and both interparticle and particle-confinement interactions are likely to play a role in determining the system behavior. The primary objective of this study is to develop a better understanding of the behavior of charged nanoparticles in a charged tubular confinement using Monte Carlo simulation, with particular focus on the effect of electrostatic interactions on the structure of the particles. Simulation results have shown that (i) the structuring of confined particles is associated with the asymmetry of the long-ranged interaction and (ii) factors such as confinement geometry and particle charge and size asymmetry can be manipulated to produce different particle structures. The present study represents the first step in an attempt to gain further insight into the behavior of confined nanosystems, with the ultimate objective of exploiting these characteristics, particularly the interactions between the confined particles and their external environment, in developing novel nanomaterials.