Collision efficiencies of diffusing spherical particles: hydrodynamic,van der waals and electrostatic forces

A practical limitation of the application of Smoluchowski's classical estimate for the collisions probability of two diffusing spherical particles in Brownian motion is the non-consideration of interparticle forcves. For suspended particles in water such forces can arise from the disturbance the particle causes in the fluid (hydrodynamic forces), from the cloud of ions which surround an electrically charged particle (double layer forces) or they can be of molecular origin (van der Waals forces). In this paper corrections to Smoluckhowski's collision probability are computed when such forces operate Scoluchowski's collision probability are computed when such forces operate between two approaching particles of various sizes. Results for several values of the van der Waals energy of attraction and the ionic strength of the electrolyte are presented in a way convenient for particle collision modeling.     

Influence of the Type of Contact between Particles Joined by a Liquid Bridge on the Capillary Cohesive Forces

The influence of the particle dimensions and type of interparticle contact on the magnitude of the capillary forces between the powder particles is studied on the basis of a model describing a capillary interaction of two particles joined by a liquid bridge. Various contact types were implemented using combinations of different particle shapes: spherical, conical, or plane. The meniscus of the bridge is described using a circular approximation; experimental results confirm that its use is justified. A method is developed for calculating the capillary forces and the amount of the liquid in the bridge with allowance for various parameters of the powder. The calculated results show that the dimensions of the particles and the type of their contact significantly affect the magnitude of the capillary forces.     

Directed assembly and rupture mechanics of colloidal aggregates

The macroscopic rheological behavior of colloidal gels arises from the micromechanical properties of the gel backbone, which are governed by nanoscale particle interactions. These colloidal interactions have been commonly understood in terms of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Recent work has shown, however, that nonidealities, such as surface roughness and charge nonuniformity, may cause the particle interactions to significantly deviate from DLVO predictions at near-contact separations. Here we present novel techniques for directing the assembly of colloidal aggregates that mimic the gel backbone, based on optical micromanipulation of multiple particles using laser tweezers. This also provides an in situ method for measuring near-contact interactions via single-bond rupture forces. We find that PMMA particles aggregated in the presence of nonorganic salts exhibit interparticle bond strengths more than 10 times greater than those predicted by DLVO theory. However, good agreement is found with DLVO predictions when the anionic surfactant sodium dodecyl sulfate (SDS) is used as the flocculant.     

Recent developments in the measurement of interparticle forces

In the last twenty years there has been an explosion of experimental work devoted to determining the forces between colloidal particles. There have been considerable experimental and theoretical advances. In this review we shall concentrate on the experimental aspects. Currently there is no technique which directly measures the interaction between two individual particles as a function of their separation. Particle - particle forces can only be inferred. In this paper we review the experimental procedures which have been used to determine the nature and range of interparticle forces in this indirect way. The many different experimental techniques which have been developed are outlined and typical data presented. The relative merits and demerits of each technique is discussed and the way forward to measuring particle - particle interactions directly is proposed.     

Control of particle assisted wetting by an external magnetic field

It is shown that repulsive particles can assist wetting of a water surface by an organic liquid even at a particle density substantially less than a close packed monolayer. By applying external fields, one can change the interparticle interactions from net attractive to net repulsive and thus induce a transition from nonwetting to wetting conditions. This was achieved by applying superparamagnetic polystyrene particles together with a polymerizable organic liquid (trimethylolpropane trimethacrylate) to a water surface in the middle of a solenoid. Passing a current through the solenoid created a magnetic field perpendicular to the interface that polarized the particles and induced repulsive dipole-dipole forces. Without the field, lenses of the organic liquid that included aggregates of particles floating on the water surface were observed. In the presence of the field, the organic liquid and the particles were evenly distributed across the surface. The interparticle distance increases proportional to the square root of the area per particle and is close to the value expected for hexagonal order.     

Velocity domain and volume fraction distribution of heavy microparticles in low reynolds number flow in microchannel

In this paper, a two-dimensional Stokes flow having particle size distribution ranging from 10 to 50 µm in a rectangular channel is simulated numerically with focus on the hydrodynamic forces. The results show that due to the disparity between the density of the fluid and particles, velocity domain of particles deviates from the fluid velocity domain and this phenomenon occurs significantly for the larger particles. Also, with the increase of Reynolds number, the volume fraction of dispersed phase near the bottom wall of the channel increases either. Compared to similar studies, this investigation employs numerical simulation of microparticulate flow and interparticle hydrodynamic forces with emphasis on the dispersed phase volume fraction in order to present the microchannel flow properties.     

Dynamic self-assembly in ensembles of camphor boats

Millimeter-sized gel particles loaded with camphor and floating at the interface between water and air generate convective flows around them. These flows give rise to repulsive interparticle interactions, and mediate dynamic self-assembly of nonequilibrium particle formations. When the numbers of particles, N, are small, particle motions are uncorrelated. When, however, N exceeds a threshold value, particles organize into ordered lattices. The nature of hydrodynamic forces underlying these effects and the dynamics of the self-assembling system are modeled numerically using Navier-Stokes equations as well as analytically using scaling arguments.     

Aggregation Stability of Aqueous Dispersions of Microcrystalline Cellulose: pH Dependence

The aggregation stability of aqueous dispersions of microcrystalline cellulose (MCC) was studied by the flow ultramicroscopy in a wide range of pH (1–11). The calculations of the molecular and ion-electrostatic components of the interparticle interaction energy, which were performed according to the DLVO theory with and without allowance for the particle conductivity, demonstrated that, in most cases, the loss of the aggregation stability can not be explained without taking into account the concept of additional attraction forces between the MCC particles. It was assumed that such forces could be attributed to the dipole–dipole interactions or hydrogen bonding between hydrated particles.     

Low Reynolds Number Interactions between Colloidal Particles near the Entrance to a Cylindrical Pore

The interaction between stable colloidal particles arriving at a pore entrance was studied using a numerical method for the case where the particle size is smaller than but of the same order as the pore size. The numerical method was adapted from a front-tracking technique developed for studying incompressible, multifluid flow by S. O. Unverdi and G. Tryggvason (J. Comp. Phys. 100, 25, 1992). The method is based on the finite difference solution of Navier-Stokes equation on a stationary, structured, Cartesian grid and the explicit representation of the particle-liquid interface using an unstructured grid that moves through the stationary grid. The simulations are in two dimensions, considering both deformable and nondeformable particles, and include interparticle colloidal interactions. The interparticle and particle-pore hydrodynamic interactions, which are very difficult to determine using existing analytical and semi-numerical, semi-analytical techniques in microhydrodynamics, are naturally accounted for in our numerical method and need not be explicity determined. Two- and three-particle motion toward a pore has been considered in our simulations. The simulations demonstrate how the competition between hydrodynamic forces and colloidal forces acting on particles dictate their flow behavior near the pore entrance. The predicted dependence of the particle flow behavior on the flow velocity and the ratio of pore size to particle size are qualitatively consistent with the experimental observations of V. Ramachandran and H. S. Fogler (J. Fluid Mech. 385, 129, 1999). Copyright 2000 Academic Press.     

Aggregation and gelation kinetics of fumed silica-ethanol suspensions

The kinetics of aggregation and gelation of fumed silica suspended in ethanol were investigated as a function of volume fraction. At low particle concentrations, gelation is well described by aggregation into a primary minimum arising from hydrogen bonding and dispersion forces. The gelation is extremely slow due to an energetic barrier (approximately 25 kT) in the interparticle potential associated with solvation forces. The solvation forces also contribute to the formation of a secondary minimum in the interparticle potential. The depth of this minimum (approximately 3 kT) is sufficient that, at a critical particle concentration, long-range diffusion is arrested due to the short-range attractions and the cooperative nature of particle interactions, as described by mode coupling theory. The presence of the secondary minimum is also observed in the microstructure of the gels studied using X-ray scattering. These observations reinforce the importance of understanding the role of solvent-particle interactions in manipulating suspension properties.     

Formation and drying of colloidal crystals using nanosized silica particles

Much interest has been generated in the fabrication of colloidal crystals from suspensions because of the promise of photonic band gap applications. However, since the case of small, nonsedimenting colloidal particles indeed remains rather rarely treated, spherical silica particles with diameters varying from 75 down to 20 nm have been used in the present work to fabricate colloidal crystals by drying the suspending liquid. Typical events that take place during the drying process of a particulate film, such as cracking, compaction and penetration of air into a porous network, have been evaluated using existing theories, and the maximum stress in the drying film could be approximated. Investigation on the dry film structure by scanning electron microscopy showed the arrangement of particles in a close-packed system. To interpret the formation of such crystals, the amplitudes of the interparticle and capillary forces have been estimated from existing models. The repulsive interparticle forces allow the particles to remain stable and thus rearrange up to fairly high particle concentration. These modeling results showed the dominance of the capillary contribution at the end of the drying process. Nitrogen adsorption/desorption measurements gave very coherent results regarding both pore volume and pore size of the dry particulate films when compared to the expected ordered packing arrangements.     

Hard structured particles: suspension synthesis, characterization, and compressibility

Hard interactions are developed on three grades of fumed silica by eliminating interparticle forces and sterically stabilizing the particles by attaching an organic coating to the surface of the particles, suspending them in an index-matching solvent and screening the electrostatics. These hard-structured particles are studied to understand the effects of the particle's microstructure on suspension properties without the influence of interparticle forces other than volume exclusion, Brownian, and hydrodynamic interactions. Light and X-ray scattering studies of low-volume-fraction suspensions suggest that the fumed silicas consist of primary particle of radius of gyration R(g1) approximately equals 16 nm and aggregate size R(g2) approximately 50 nm and mass fractal dimension D(f) approximately equals 2.2. Osmotic compressibilities of these suspensions are measured as a function of particle concentration exploring the packing mechanism of fumed silica. While there is minimal detectable change in the primary particle size, R(g2) varies by approximately 15%, providing insight into how suspension properties are related to particle size. As expected of hard particles with the same microstructure, the concentration dependence on the osmotic pressure superimposes with volume fraction of solids. The comparison of fumed-silica-suspension measurements to the known behavior of hard-sphere suspensions demonstrates the effects of particle geometry on suspension properties with indications of interpenetration of the fumed silica due to their open geometry.     

Lattice Boltzmann simulation of particles agglomeration and rheology in a particulate flow

The dynamics and rheology of particles in a Newtonian fluid subjected to shear are simulated using Lattice Boltzmann Method. A computationally-efficient Smoothed Profile Method is used to resolve fluid-solid interactions, and the Lennard-Jones inter-particle potential is implemented to account for inter-particle forces. The use of a bi-periodic computational domain with Lees-Edward boundary conditions allows simulation for systems consisting of a large number of particles under shear. The method is validated for single and dual particle problems and an analysis is performed for multi-particle problems under a range of shear rates and particle fractions. The introduction of particle-particle interactions, which are physically important in many engineering processes, is found to have a considerable impact on the dynamics, agglomeration and rheology. The total stress exhibits high unsteadiness primarily due to the solid component contribution, at higher particle fractions. The simulations underscore the complex interplay between shear, interparticle forces and agglomeration and the complex dependencies of the rheological properties.     

Determination of cluster composition in heteroaggregation of binary particle systems by flow cytometry

Cluster composition in aggregation processes of multiple particle species can be dynamically determined by flow cytometry if particle populations are fluorescently labeled. By flow cytometric single particle analysis, aggregates can be characterized according to the exact amount of constituent particles, allowing the detailed and separate quantification of homo- and heteroaggregation. This contribution demonstrates the application of flow cytometry for the experimental detection of heteroaggregation in a binary particle mixture of oppositely charged polystyrene (PS) particles and Rhodamine-B labeled melamine-formaldehyde (MF-RhB) particles. Experiments with different particle concentration, temperature, mixing mode, ionic strength and particle mixing ratio are presented. Aggregation kinetics are enhanced with increasing particle concentration and temperature as well as by increased shear of mixing. These results represent well-known behavior published in previous investigations and validate the performance of flow cytometry for probing heteroaggregation processes. Physical insight with a novel level of detail is gained by the quantification of de- and restabilization phenomena. At low ionic strength, "raspberry"-type aggregates with PS cores are formed by primary heteroaggregation. At moderate particle number ratios, these aggregates are electrostatically destabilized and form more complex aggregates in a secondary heteroaggregation process. At high particle number ratios (> or =50:1), the raspberry-type aggregates are electrostatically restabilized and secondary heteroaggregation is prevented. The dynamic change of aggregate charge was verified by zeta-potential measurements. The elevation of salt concentration over several orders of magnitude retards aggregation dynamics, since attractive interparticle forces are diminished by an electrostatic double layer. This indicates that heteroaggregation induced by attractive interparticle forces is faster than aggregation due to random Brownian motion. Destabilization at high ionic strength is facilitated by charged ions and no longer by MF-RhB coverage. This results in a species independent one step aggregation process.     

Modification of Surface Forces by Metal Ion Adsorption

Abstract

Sorption of ions may lead to variations in interparticle forces and, thus, changes in the stability of colloidal particles. Chemical interactions between metal ions and colloidal particles modify the molecular structure of the surface, the surface charge, and the electrical potential between colloidal particles. These modifications to the surface and to the electrical double layer due to metal ion sorption are reflected in the interaction force between a particle and another surface, which is measured in this study by atomic force microscopy (AFM). Specifically, AFM is used to investigate the sorption of copper ions from aqueous solutions by silica particles. The influence of metal ion concentration and solution ionic strength on surface forces is studied under transient conditions. Results show that as the metal ion concentration is decreased, charge reversal occurs and a longer period of time is required for the system to reach equilibrium. The ionic strength has no significant effect on sorption kinetics. Furthermore, neither metal concentration nor ionic strength exhibits any effect on sorption equilibria, indicating that for the experimental conditions used in this study, the surface sites of the silica particle are fully occupied by copper ions.     

Optical manipulation and characterisation of aerosol particles using a single-beam gradient force optical trap

The application of optical tweezers (a single-beam gradient force optical trap) to the manipulation and characterisation of aerosol particles is discussed in this tutorial review. Optical tweezers allow not only the indefinite control over a single droplet, but control over arrays of particles. Typical particle sizes span the 1-10 microm diameter range. When coupled with spectroscopic techniques for probing evolving particle size (with nanometre accuracy), composition, phase and mixing state, detailed investigations of the thermodynamic properties of aerosol, the kinetics of particle transformation, and the nature of interparticle forces and coagulation can be undertaken.     

Study on temperature response in raspberry-form gels of poly (N,N-diethylacrylamide)

Slow swelling and shrinking rates are a significant challenge for some applications of temperature-sensitive hydrogels. This study reports raspberry-form poly N,N-diethylacrylamide (DEAA) gel particles, which are aggregates of single spherical gel particles. The raspberry-form gel particles show improved temperature-response rates especially for swelling. This improvement in the response rate is attributed to two key factors: the free space between the individual gel particles that make up the aggregated gel particle, and the constraints from the contact points between the individual gel particles. During the swelling process, the polymer chain networks can diffuse at the faster rate characteristic of the individual gel particles constructing the raspberry-form gel, and consequently the response rate of the overall raspberry-form gels can be accelerated. During the shrinking process, the constraints from the contact points between the individual gels dominate the polymer chain diffusion and the shrinking rate because of non-zero shear modulus. The shrinking behavior was affected not by the individual particle size, but rather the apparent gel size and shape.     

On the elastic and swelling behaviour of swollen poly(vinyl alcohol) networks filled with anisometric colloidal iron(III) hydroxide sol particles

A new method of preparing filled networks has been developed. Well-characterized, colloidal iron(III) hydroxide particles are incorporated into chemically cross-linked poly(vinyl alcohol) gels. Evidence for the random distribution of individual particles is provided by transmission electron microscopy. A filler-induced gel collapse was observed when the strength of repulsion forces between filler particles is decreased by the screening of Coulombic interactions with electrolytes.     

Toughening of polycarbonate by core‐shell latex particles: Influence of particle size and spatial distribution on brittle‐ductile transition

The impact toughness of polycarbonate modified with acrylic core‐shell latex particles was investigated. Addition of impact modifiers with size ranging from 115.7 to 231.4 nm can result in maximum impact strength. Equations for spatial distribution of modified particles were proposed to associate the interparticle distance with particle size and modifier volume fraction in terms of two possible morphologies, given by T = d[0.91/(φ)^1/3 ? 1] or T = d[0.88/(φ)^1/3 ? 1]. The influence of particle size on brittle‐ductile transition was also studied. The results indicated that critical interparticle distance was not a definitive value and had a narrow region. Moreover, there existed a linear relationship between critical interparticle distance and modifier size, that is, critical interparticle distance would enlarge with the increasing of core‐shell particle size. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1970–1977, 2010     

Strong magnetic field effects on solid-liquid and particle-particle interactions during the processing of a conducting liquid containing non-conducting particles

The behavior of micrometer-sized weak magnetic insulating particles migrating in a conductive liquid metal is of broad interest during strong magnetic field processing of materials. In the present paper, we develop a numerical method to investigate the solid-liquid and particle-particle interactions by using a computational fluid dynamics (CFDs) modeling. By applying a strong magnetic field, for example, 10 Tesla, the drag forces of a single spherical particle can be increased up to around 15% at a creeping flow limit. However, magnetic field effects are reduced when the Reynolds number becomes higher. For two identical particles migrating along their centerline in a conductive liquid, both the drag forces and the magnetic interaction will be influenced. Factors such as interparticle distance, Reynolds number and magnetic flux density are investigated. Shielding effects are found from the leading particle, which will subsequently induce a hydrodynamic interaction between two particles. Strong magnetic fields however do not appear to have a significant influence on the shielding effects. In addition, the magnetic interaction forces of magnetic dipole-dipole interaction and induced magneto-hydrodynamic interaction are considered. It can be found that the induced magneto-hydrodynamic interaction force highly depends on the flow field and magnetic flux density. Therefore, the interaction between insulating particles can be controlled by applying a strong magnetic field and modifying the flow field. The present research provides a better understanding of the magnetic field induced interaction during liquid metal processing, and a method of non-metallic particles manipulation for metal/ceramic based materials preparation may be proposed.