Interaction Of Colloidal Particles Research Articles

A class of difference schemes with flexible local approximation

Solutions of many physical problems have salient local features that are qualitatively known a priori (for example, singularities at point sources, edge and corners; boundary layers; derivative jumps at material interfaces; strong dipole field components near polarized spherical particles; cusps of electronic wavefunctions at the nuclei; electrostatic double layers around colloidal particles, etc.) The known methods capable of providing flexible local approximation of such features include the generalized finite element – partition of unity method, special variational-difference schemes in broken Sobolev spaces, and a few other specialized techniques. In the proposed new class of Flexible Local Approximation MEthods (FLAME), a desirable set of local approximating functions (such as cylindrical or spherical harmonics, plane waves, harmonic polynomials, etc.) defines a finite difference scheme on a chosen grid stencil. One motivation is to minimize the notorious ‘staircase’ effect at curved and slanted interface boundaries. However, the new approach has much broader applications. As illustrative examples, the paper presents arbitrarily high order 3-point schemes for the 1D Schrödinger equation and a 1D singular equation, schemes for electrostatic interactions of colloidal particles, electromagnetic wave propagation and scattering, plasmon resonances. Moreover, many classical finite difference schemes, including the Collatz “Mehrstellen” schemes, are direct particular cases of FLAME.

Clustering of aerosol particles in isotropic turbulence

It has been recognized that particle inertia throws dense particles out of regions of high vorticity and leads to an accumulation of particles in the straining-flow regions of a turbulent flow field. However, recent direct numerical simulations (DNS) indicate that the tendency to cluster is evident even at particle separations smaller than the size of the smallest eddy. Indeed, the particle radial distribution function (RDF), an important measure of clustering, increases as an inverse power of the interparticle separation for separations much smaller than the Kolmogorov length scale. Motivated by this observation, we have developed an analytical theory to predict the RDF in a turbulent flow for particles with a small, but non-zero Stokes number. Here, the Stokes number (. Predictions of the analytical theory are compared with two types of numerical simulation: (i) particle pairs interacting in a local linear flow whose velocity varies according to a stochastic velocity gradient model; (ii) particles interacting in a flow field obtained from DNS of isotropic turbulence. The agreement with both types of simulation is very good. The theory also predicts the RDF for unlike particle pairs (particle pairs with different Stokes numbers). In this case, a second diffusion process occurs owing to the difference in the response of the pair to local fluid accelerations. The acceleration diffusivity is independent of the pair separation distance; thus, the RDF of particles with even slightly different viscous relaxation times undergoes a transition from the power law behaviour at large separations to a constant value at sufficiently small separations. The radial separation corresponding to the transition between these two behaviours is predicted to be proportional to the difference between the Stokes numbers of the two particles. Once again, the agreement between the theory and simulations is found to be very good. Clustering of particles enhances their rate of coagulation or coalescence. The theory and linear flow simulations are used to obtain predictions for the rate of coagulation of particles in the absence of hydrodynamic and colloidal particle interactions.

Depletion interactions of non-spherical colloidal particles in polymer solutions

We consider anisotropic colloidal particles immersed in a solution of long, flexible, andnon-adsorbing polymers. For the dumbbell shapes of recently synthesized particlesconsisting of two intersecting spheres, and for lens-shaped particles with spherical surfaces,we calculate the isotropic and anisotropic interaction parameters that determine theimmersion free energy and the orientation-dependent depletion interaction betweenparticles that are induced by the polymers. Exact results are obtained for ideal (randomwalk) polymer chains.

Chemical control of colloidal fouling of reverse osmosis systems

Fouling of membranes by colloidal organic and inorganic particles continues to be documented as the most common and challenging obstacle in attaining stable continuous operation of reverse osmosis (RO) and ultrafiltration (UF) systems. Much current research is being conducted on physical parameters to mitigate such fouling. The focus has been on membrane synthesis and element design; microfiltration and ultrafiltration pretreatment; electromagnetic devices; correlation with physical factors such as Silt Density Index, zeta potential and critical flux; technique of direct observation of fouling process through a membrane; and classification of macromolecular organics for correlation with fouling characteristics. We report initial successes with chemical control of colloidal fouling. Through screening with a large number of observable coagulations of natural colloids, we have developed a group of proprietary anticoagulants and dispersants that would, at less than 10 ppm dosage to the RO feedwater, control various classes of colloidal foulants. Case studies of the control of humic matter, elemental sulfur and colloidal silicate in problematic RO systems that became stabilized are briefly presented. We conclude that a great need and potential exists in economically controlling the myriads of fouling interactions of colloidal particles during concentration within the brine channels of RO membrane elements. Low dosages of antifoulants can in many cases obviate the need for installation and maintenance of pretreatment unit or operations designed to remove such colloidal foulants from the process stream.

Equilibrium cluster formation in concentrated protein solutions and colloids

Controlling interparticle interactions, aggregation and cluster formation is of central importance in a number of areas, ranging from cluster formation in various disease processes to protein crystallography and the production of photonic crystals. Recent developments in the description of the interaction of colloidal particles with short-range attractive potentials have led to interesting findings including metastable liquid-liquid phase separation and the formation of dynamically arrested states (such as the existence of attractive and repulsive glasses, and transient gels). The emerging glass paradigm has been successfully applied to complex soft-matter systems, such as colloid-polymer systems and concentrated protein solutions. However, intriguing problems like the frequent occurrence of cluster phases remain. Here we report small-angle scattering and confocal microscopy investigations of two model systems: protein solutions and colloid-polymer mixtures. We demonstrate that in both systems, a combination of short-range attraction and long-range repulsion results in the formation of small equilibrium clusters. We discuss the relevance of this finding for nucleation processes during protein crystallization, protein or DNA self-assembly and the previously observed formation of cluster and gel phases in colloidal suspensions.

The foam analogy: from phases to elasticity

By mapping the interactions of colloidal particles onto the problem of minimizing areas, the physics of foams can be used to understand the phase diagrams of both charged and fuzzy colloids. We extend this analogy to study the elastic properties of such colloidal crystals and consider the face-centered cubic, body-centered cubic and A15 lattices. We discuss two types of soft interparticle potentials corresponding to charged and fuzzy colloids, respectively, and we analyze the dependence of the elastic constants on density as well as on the parameters of the potential. We show that the bulk moduli of the three lattices are generally quite similar, and that the shear moduli of the two non-close-packed lattices are considerably smaller than in the face-centered cubic lattice. We find that in charged colloids, the elastic constants are the largest at a finite screening length, and we discuss a shear instability of the A15 lattice.

Effect of Membrane Surface Roughness on Colloid−Membrane DLVO Interactions

Recent experimental investigations suggest that interaction of colloidal particles with polymeric membrane surfaces is influenced by membrane surface morphology (roughness). To better understand the consequences of surface roughness on colloid deposition and fouling, it is imperative that models for predicting the Derjaguin−Landau−Verwey−Overbeek (DLVO) interaction energy between colloidal particles and rough membrane surfaces be developed. We present a technique of reconstructing the mathematical topology of polymeric membrane surfaces using statistical parameters derived from atomic force microscopy roughness analyses. The surface element integration technique is used to calculate the DLVO interactions between spherical colloidal particles and the simulated (reconstructed) membrane surfaces. Predictions show that the repulsive interaction energy barrier between a colloidal particle and a rough membrane is lower than the corresponding barrier for a smooth membrane. The reduction in the energy barrier is ...

Measuring a colloidal particle's interaction with a flat surface under nonequilibrium conditions. Total internal reflection microscopy with absolute position information.

A new and general approach is proposed to analyze the dynamics of a colloidal particle interacting with a nearby wall. This analysis can be used to determine the acting forces even when the system is non-stationary. As an illustration, we use total internal reflection microscopy to investigate the forces acting on a polystyrene sulfate latex particle as it is receding from a charged glass surface.

Colloidal behaviour in a confined cylindrical cell

The interactions of colloidal particles in a confined cylindrical cell have been investigated using a combination of video microscopy, real-time digital imaging and still micrographs. Confinement of colloidal latex particles of diameter 4.5 μm in cylindrical glass capillaries of diameter 25 μm resulted in their alignment along the centre of the cell with a clear particle-free zone along the wall. This tendency was observed over a range of ionic strengths from deionised water to 0.1 M NaCl, but was greatest at low concentrations of electrolyte. The dimensions of the particle-free zone were orders of magnitude greater than the Debye lengths of the solutions. Particles of diameter 3.0 μm also exhibited alignment, but not 1.2 μm particles, indicating that there is a fine balance between the forces promoting alignment and kinetic effects. The particles along the centre of the capillary formed dynamic chains in which an average of ∼3 particles were in contact at any time. The rate of movement of the particles increased with decreasing salt content. These observations are consistent with asymmetries in electrostatic or hydrodynamic interactions induced by the cell wall, or possibly by a combination of such effects.

Effects of Flow on Measurements of Interactions in Colloidal Suspensions

A hydrodynamic mechanism of interactions of colloidal particles is considered. The mechanism is based on the assumption of tiny background flows in the experimental cells during measurements by Grier et al. Both trivial (shear flow) and nontrivial (force propagation through viscous fluid) effects are taken into account for two colloidal particles near a wall bounding the solvent. Expressions for the radial (attractive or repulsive) forces and the polar torques are obtained. Quantitative estimates of the flow needed to produce the observed strength of attractive force are given; other necessary conditions are also considered. The following conclusion is made: the mechanism suggested most likely is not responsible for the attractive interactions observed in the experiments of Grier et al.; however, it may be applicable in other experimental realizations and should be kept in mind while conducting colloidal measurements of high sensitivity. Several distinctive features of the interactions due to this mechanism are identified.

Overcoming the phage replication threshold: a mathematical model with implications for phage therapy.

Prior observations of phage-host systems in vitro have led to the conclusion that susceptible host cell populations must reach a critical density before phage replication can occur. Such a replication threshold density would have broad implications for the therapeutic use of phage. In this report, we demonstrate experimentally that no such replication threshold exists and explain the previous data used to support the existence of the threshold in terms of a classical model of the kinetics of colloidal particle interactions in solution. This result leads us to conclude that the frequently used measure of multiplicity of infection (MOI), computed as the ratio of the number of phage to the number of cells, is generally inappropriate for situations in which cell concentrations are less than 10(7)/ml. In its place, we propose an alternative measure, MOI(actual), that takes into account the cell concentration and adsorption time. Properties of this function are elucidated that explain the demonstrated usefulness of MOI at high cell densities, as well as some unexpected consequences at low concentrations. In addition, the concept of MOI(actual) allows us to write simple formulas for computing practical quantities, such as the number of phage sufficient to infect 99.99% of host cells at arbitrary concentrations.

Mechanical properties and microstructure of bioactive ORMOSILs containing silica particles

We synthesized organically modified silicate (ORMOSILs) gels with colloidal silica (CS) (AEROSIL®) starting from polydimethylsiloxane (PDMS), tetraethoxysilane (TEOS) and calcium nitrate (Ca(NO 3) 2·4H 2O) through sol–gel processing. Dynamic mechanical analysis indicated that relative height of the tan δ peak at about −100 °C increased with an increase in the relative content of the inorganic components. This peak growth was accounted for by the relative increase in PDMS–colloidal silica particle interactions. The colloidal silica could control the mechanical behavior of the hybrids. The gel of a specific composition could deposit apatite within 3 days of soaking in the simulated body fluid (SBF), since it included many calcium ions on the surface.

Symmetry breaking and interaction of colloidal particles in nematic liquid crystals.

We propose a general approach to the description of the long-ranged elastic interaction in the nematic colloids, based on the symmetry breaking of the director field. The type of the far-field interaction between particles immersed in a nematic host is determined by the way the symmetry is broken in the near-field region around the colloidal particle. This is caused both by the particle's shape and the anchoring at the surface. If the director field near the particle has a set of three symmetry planes, the far-field interaction falls off as d(-5) with d being the distance between particles. If one symmetry plane is absent, a dipolar moment perpendicular to it is allowed and yields dipole-dipole interactions, which decays as d(-3). If both the horizontal and vertical mirror symmetries are broken (it is equivalent to the case when the nonzero torque moment is applied to the particle by the nematic liquid crystal), the particles are shown to attract each other following the Coulomb law. We propose a simple method for the experimental observation of this Coulomb attraction. The behavior of colloid particles in curved director fields is analyzed. Quadrupolar particles with planar anchoring are shown to be attracted toward the regions with high splay deformations, while quadrupoles with homeotropic anchoring are depleted from such regions. When there are many colloidal particles in the nematic solvent, the distortions of the director from all of them are overlapped and lead to the exponential screening in the elastic pair interaction potential. This is a many-body interaction effect. This screening is essential in the real dense colloid systems, such as ferronematics--suspensions of magnetic cylindrical grains in the nematic liquid crystal. External magnetic field induces an elastic Yukawa attraction between them. We apply this attraction to the explanation of the cellular texture in magnetically doped liquid crystals.

Strong and Weak Interactions of Colloidal Particles with High Surface Potentials

A simple method for calculating the interaction force and energy per unit area between two dissimilar plates with high potentials at constant surface potential presented. Using Derjaguin's method and the improved Derjaguin' method, the expressions of the interaction free energy between two dissimilar spheres with high surface potentials are derived. These formulae may be divided into two groups: those for the strong interaction and those for the weak interaction. The juncture of strong and weak interactions is at κh=4 for dissimilar plates and at κh=2.8 for spheres The relative error is largest at this point, about 10%.

Approximate Expressions for Strong Interaction of Colloidal Particles with High Surface Potential

Approximate Expressions for Strong Interaction of Colloidal Particles with High Surface Potential

Colloidal Interaction at the Air–Liquid Interface

In this paper, we propose a model to analyze the stability of colloidal particles at the air–liquid interface. The proposed model for the colloidal particle interaction considers DLVO interactions and capillary, hydrophobic, and dipolar interactions between the particles. Typical values from the literature were assigned to most parameters included in the model. Numerical computation revealed the most important parameter in determining the total interaction is the density of dipoles at the external surface of the particles. We have found significant differences for the pair potential between hydrophobic and hydrophilic particles. Hydrophobic particles must aggregate in a principal minimum of the interaction potential curve while hydrophilic particles aggregate in a secondary minimum.

Role of Co-Ion Specificity and Dissolved Atmospheric Gas in Colloid Interaction

Co-ions, dissolved atmospheric gas, and buffers are shown to play an apparently remarkable role in colloidal particle interactions. The effects are exhibited in flocculation studies on suspensions of charged solid paraffin particles. The effects cannot be explained by present theories of colloid science. In the standard theory, co-ions, electrolyte ions of the same charge as a colloid particle, ought to exhibit little or no qualitative variation in their effects on the stability of suspensions. Dissolved gas has been assumed to have no role, and buffers have always been thought to influence interactions via pH alone. In this work, reasons that theory is inadequate are advanced.

Indirect interaction of colloidal particles adsorbed on smectic films.

Colloidal particles like peptides and proteins adsorbed on a stack of lipid bilayers cause elastic deformations which disturb the smectic order. Two adsorbed particles attract each other due to the superposition of their deformation fields. The effective pair potential attributed to this substrate-mediated force decays exponentially with the particle distance. The range of this potential coincides with the decay length of elastic deformations, and is found to be proportional to the square root of the stack thickness. If the stack is sufficiently thick, the substrate-mediated interaction is estimated to be strong enough to overcome the entropic barrier and enforce aggregation or even crystallization of the adsorbate.

Perspective on "The effect of shape on the interaction of colloidal particles"

Perspective on "The effect of shape on the interaction of colloidal particles"

Molecular interaction of disk-shaped colloidal particles

On the basis of relations of Lifshitz macroscopic theory of molecular forces, valid in case of the flat body interaction, and Deryaguin transition as well, making it possible to take account of a curvature of the separation surfaces of phases, an expression for the attraction force of the same size clay particles has been obtained. The particles have a shape of very oblate ellipsoids of revolution and, in the process of motion, are arranged with respect to each other so that their axes remain parallel. Analysis of the relationships obtained shows that the normal component of the attraction force is a monotonically decreasing function of the distance between the particles. The tangential component of that force changes with a change of the distance unmonotonically: at first, it increases from zero (at coaxial arrangement of the particles) to some maximum and then decreases tending to zero in the limit.