Cluster-cluster aggregation controlled by the number of intercluster connections: kinetics of aggregation and cluster mass frequency

The aggregation of colloids in the presence of hydrodynamic forces was investigated, employing a numerical model that took into account the masses of the individual clusters and the number of intercluster connections established when two clusters stuck together. The number of possible connections was determined by analyzing all the possible nonoverlapping configurations of stuck clusters. This operation was done for a couple of clusters of various masses, taking into account the assembly of clusters of even and uneven masses. The formulation of the constraints established a certain hierarchy in the sticking on a basis compatible with the irregular fracture model of Horwatt and co-workers. As a result, the permanent sticking of large clusters required the formation of a large number of connections, whereas that of small clusters might be realized even with a small number of connections. Thus, the aggregation started with the features of the standard reaction-limited process and this cluster growth became progressively inhibited as a result of the prevailing effects of the connection constraints. The cluster-mass frequency showed the emergence at least of a second population whose bell-shaped mass distribution was superimposed on the monotonically decreasing distribution resulting from the reaction-limited aggregation process. The results of the numerical study were confronted with those previously obtained in the aggregation of hydrated polystyrene latex particles dispersed in 1 M sodium chloride solution. The two striking features--the aggregate growth kinetics and the mass distribution function--were common to the computer-generated clusters and the latex aggregates.     

Dielectric response of a concentrated colloidal suspension in a salt-free medium

In this paper the complex dielectric constant of a concentrated colloidal suspension in a salt-free medium is theoretically evaluated using a cell model approximation. To our knowledge this is the first cell model in the literature addressing the dielectric response of a salt-free concentrated suspension. For this reason, we extensively study the influence of all the parameters relevant for such a dielectric response: the particle surface charge, radius, and volume fraction, the counterion properties, and the frequency of the applied electric field (subgigahertz range). Our results display the so-called counterion condensation effect for high particle charge, previously described in the literature for the electrophoretic mobility, and also the relaxation processes occurring in a wide frequency range and their consequences on the complex electric dipole moment induced on the particles by the oscillating electric field. As we already pointed out in a recent paper regarding the dynamic electrophoretic mobility of a colloidal particle in a salt-free concentrated suspension, the competition between these relaxation processes is decisive for the dielectric response throughout the frequency range of interest. Finally, we examine the dielectric response of highly charged particles in more depth, because some singular electrokinetic behaviors of salt-free suspensions have been reported for such cases that have not been predicted for salt-containing suspensions.     

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     

Characterization of concentrated colloidal ceramics suspension: a new approach

The dispersion behavior of a concentrated ceramic suspension (Al(2)O(3)) has been investigated in terms of capillary suction time (CST) with varying solids concentration both in the absence as well as in the presence of dispersant (APC). The CST value is found to be the lowest at the pH(iep) whereas it increases as the pH is changed either to the acid side or alkaline side due to the repulsive forces acting among the neighboring particles keeping them in more dispersed state. It has been further observed that the CST value increases with increasing concentration of solids in the suspension. The dispersability of the suspension has been quantified in terms of dispersion ratio (DR). The higher the dispersion ratio of a particular system above unity, the better is the dispersability and vice versa. Further, quantification of dispersion stability by the CST technique is found to be useful and practical for optimization of different parameters concerning suspension stability. A correlation is found among the CST, zeta potential, colloidal stability, and maximum solids loading. It has been finally concluded that the CST method could be potentially employed as a quantitative and diagnostic technique for characterizing concentrated ceramic suspension.     

Sedimentation velocity and potential in a concentrated suspension of charged liquid drops

The sedimentation behavior of a concentrated suspension of charged liquid drops is analyzed theoretically at arbitrary surface potential and arbitrary double-layer thickness; that is, the effects of double-layer polarization and double-layer overlapping are taken into account. Kuwabara's unit cell model is employed to model the suspension system, and a pseudospectral method based on the Chebyshev polynomial is adopted to solve the governing electrokinetic equations numerically. Several interesting phenomena, which are of significant influence if the internal flow inside a liquid drop is taken into account, are observed. Key factors are examined such as the thickness of the electric double layer, the magnitude of the surface potential, the volume fraction of liquid drops, and the viscosity of the internal fluid. The results presented here add another dimension to the previous studies, which include concentrated suspensions of rigid particles and mercury drops under low zeta potential, with the consideration of the internal flow of liquid drops and double-layer polarization, characterized by its viscosity and the zeta potential respectively. It is found, among other things, that the smaller the viscosity of the internal fluid is, the higher the sedimentation velocity of liquid drops. The higher the zeta potential is, the larger the decrease in sedimentation velocity. In particular, the sedimentation velocity of an inviscid drop (gas bubble) is about three times higher than that of a rigid one. The decrease in sedimentation velocity resulting from the effect of double-layer polarization achieves about 50% if the zeta potential is sufficiently high.     

Cluster-cluster aggregation kinetics and primary particle growth of soot nanoparticles in flame by light scattering and numerical simulations

The agglomeration kinetics of growing soot generated in a diffusion atmospheric flame are here studied in situ by light scattering technique to infer cluster morphology and size (fractal dimension D(f) and radius of gyration R(g)). SEM analysis is used as a standard reference to obtain primary particle size D(P) at different residence times. The number N(P) of primary particles per aggregate and the number concentration n(A) of clusters are evaluated on the basis of the measured angular patterns of the scattered light intensity. The major finding is that the kinetics of the coagulation process that yields to the formation of chain-like aggregates by soot primary particles (size 10 to 40 nm) can be described with a constant coagulation kernel beta(c,exp)=2.37x10(-9) cm3/s (coagulation constant tau(c) approximately = 0.28 ms). This result is in nice accord with the Smoluchowski coagulation equation in the free molecular regime, and, vice versa, it is in contrast with previous studies conducted by invasive (ex situ) techniques, which claimed the evidence in flames of coagulation rates much larger than the kinetic theory predictions. Thereafter, a number of numerical simulations is implemented to compare with the experimental results on primary particle growth rate and on the process of aggregate reshaping that is observed by light scattering at later residence times. The restructuring process is conjectured to occur, for not well understood reasons, as a direct consequence of the atomic rearrangement in the solid phase carbon due to the prolonged residence time within the flame. Thus, on one side, it is shown that the numerical simulations of primary size history compare well with the values of primary size from SEM experiment with a growth rate constant of primary diameter about 1 nm/s. On the other side, the evolution of aggregate morphology is found to be predictable by the numerical simulations when the onset of a first-order "thermal" restructuring mechanism is assumed to occur in the flame at about 20 ms residence time leading to aggregates with an asymptotic fractal dimension D(f,infinity) approximately = 2.5.     

Stabilization of a concentrated suspension of calcium carbonate with cationic praestol

Russian Journal of Applied Chemistry - The sedimentation stability of a 60% suspension of calcium carbonate in the presence of various commercial samples of cationic Praestol was studied, using a...     

Molecular simulation of a concentrated aqueous KCl solution

A 1.0 M aqueous KCl solution was studied by molecular dynamics simulations at 293 K in order to study the influence of the ionic concentration on the hydration structure of the ions as well as the formation of ion clusters. The hydration structures of the ions are almost independent of the ionic concentration unless in respect to the perturbation that appears due to ionic clustering. Fractions equal to 31.9% of the anions and 37.8% of the cations are associated. Clusters constituted by two, three and four ions were detected. Their mean lifetimes are always affected by thermal effects, reorientational relaxation while the longest lifetimes are a consequence of ionic cloud relaxations. The pairs constituted by two anions or two cations are stabilized by water molecules belonging to the solvation shells of both ions. The neutral K⁺Cl⁻ pairs are formed under the influence of the electrostatic attraction that, however, is small due to the ionic radii of these ions. Consequently, this kind of pairs contains only 8.8% of the ions while the fraction of ions in the negative and positive pairs are equal to 29.2 and 39.3%, respectively, when the same ion can pertain to more than one pair.     

Primary electroviscous effect in a moderately concentrated suspension of charged spherical colloidal particles

On the basis of the standard theory of the primary electroviscous effect in a moderately concentrated suspension of charged spherical particles in an electrolyte solution presented by Ruiz-Reina et al. (Ruiz-Reina, E.; Carrique, F.; Rubio-Hernández, F. J.; Gómez-Merino, A. I.; García-Sánchez, P. J. Phys. Chem. B 2003, 107, 9528), which is applicable for the case where overlapping of the electrical double layers of adjacent particles can be neglected, the general expression for the effective viscosity or the primary electroviscous coefficient p of the suspension is derived. This expression is applicable for a suspension of spherical particles of radius a carrying arbitrary zeta potentials zeta at the particle volume fraction phi < or = 0.3 for the case of nonoverlapping double layers, that is, at kappaalpha > 10 (where kappa is the Debye-Hückel parameter). A simple approximate analytic expression for p applicable for particles with large kappaalpha and arbitrary zeta is presented. The obtained viscosity expression is a good approximation for moderately concentrated suspensions of the particle volume fraction phi < or = 0.3, where the relative error is negligible for kappaalpha > or =100 and even at kappaalpha = 50 the maximum error is approximately 20%. It is shown that a maximum of p, which appears when plotted as a function of the particle zeta potential, is due to the relaxation effect as in the case of the electrophoresis problem.     

Numerical and analytical studies of the electrical conductivity of a concentrated colloidal suspension

In the past few years, different models and analytical approximations have been developed facing the problem of the electrical conductivity of a concentrated colloidal suspension, according to the cell-model concept. Most of them make use of the Kuwabara cell model to account for hydrodynamic particle-particle interactions, but they differ in the choice of electrostatic boundary conditions at the outer surface of the cell. Most analytical and numerical studies have been developed using two different sets of boundary conditions of the Neumann or Dirichlet type for the electrical potential, ionic concentrations or electrochemical potentials at that outer surface. In this contribution, we study and compare numerical conductivity predictions with results obtained using different analytical formulas valid for arbitrary zeta potentials and thin double layers for each of the two common sets of boundary conditions referred to above. The conductivity will be analyzed as a function of particle volume fraction, phi, zeta potential, zeta, and electrokinetic radius, kappaa (kappa(-1) is the double layer thickness, and a is the radius of the particle). A comparison with some experimental conductivity results in the literature is also given. We demonstrate in this work that the two analytical conductivity formulas, which are mainly based on Neumann- and Dirichlet-type boundary conditions for the electrochemical potential, predict values of the conductivity very close to their corresponding numerical results for the same boundary conditions, whatever the suspension or solution parameters, under the assumption of thin double layers where these approximations are valid. Furthermore, both analytical conductivity equations fulfill the Maxwell limit for uncharged nonconductive spheres, which coincides with the limit kappaa --> infinity. However, some experimental data will show that the Neumann, either numerical or analytical, approach is unable to make predictions in agreement with experiments, unlike the Dirichlet approach which correctly predicts the experimental conductivity results. In consequence, a deeper study has been performed with numerical and analytical predictions based on Dirichlet-type boundary conditions.     

CFD simulation of floating particles suspension in a stirred tank

Computational fluid dynamics (CFD) simulations were performed to predict the floating particles suspension in a baffled tank stirred by a standard Rushton turbine. An Eulerian multiphase model and a standard k-ε turbulence model with mixture properties were used in the CFD simulation. The impeller rotation was solved using a moving reference frame method. Flow pattern, power number and solid holdup distribution were obtained and compared with the results in literature. The effects of operating condition on floating particles suspension characteristics were studied. It indicated that the influences of impeller speed and solid loading on particle suspension varied with particle sizes. For small particles, the impeller speed and solid loading have no obvious effects on solid holdup distribution and suspension quality. For large particles, particle suspension quality becomes better first, and then keeps almost unchanged with enhancing of the impeller speed. Suspension quality is better for higher solid loading of large particles. Within the scope of the present study, solid loading has no great effect on suspension quality. Suspension quality becomes worse with increasing of the particle size. Large particles are easy to accumulate in the centres of the liquid free surface and the upper circular loop, and the vicinity of the shaft.     

Transition from dilute to concentrated electrokinetic behavior in the dielectric spectra of a colloidal suspension

Dielectric spectroscopy is used to measure the complex permittivity of 200 and 100 nm diameter polystyrene latex suspended in potassium chloride (KCl) solutions over the frequency range 10(4)-10(7) Hz as a function of particle volume fraction (?) and ionic strength. Dilute suspension dielectric spectra are in excellent agreement with electrokinetic theory. A volume fraction dependence of the dielectric increment is observed for low electrolyte concentrations (0.01, 0.05, and 0.1 mM) above ? ≈ 0.02. This deviation from the dilute theory occurs at a critical frequency ω* that is a function of volume fraction, particle size, and ionic strength. The dielectric increment of suspensions at the highest salt concentration (1 mM) shows no volume fraction dependence up to ? = 0.09. Values of ω* are collapsed onto a master curve that accounts for the length and time scales of ion migration between neighboring particles. The measured conductivity increment is independent of volume fraction and agrees with theory after accounting for added counterions and nonspecific adsorption.     

Monte Carlo simulation of phase separation kinetics in a concentrated polymer solution

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Aging in a Laponite colloidal suspension: a Brownian dynamics simulation study

The authors report Brownian dynamics simulation of the out-of-equilibrium dynamics (aging) in a colloidal suspension composed of rigid charged disks, one possible model for Laponite, a synthetic clay deeply investigated in the last few years by means of various experimental techniques. At variance with previous numerical investigations, mainly focusing on static structure and equilibrium dynamics, the authors explore the out-of-equilibrium aging dynamics. They analyze the wave vector and waiting time dependence of the dynamics, focusing on the single-particle and collective density fluctuations (intermediate scattering functions), the mean-squared displacement, and the rotational dynamics. Their findings confirm the complexity of the out-of-equilibrium dynamical behavior of this class of colloidal suspensions and suggest that an arrested disordered state driven by a repulsive Yukawa potential, i.e., a Wigner glass, can be observed in this model.     

Sedimentation behavior of high-temperature concentrated colloidal suspension based on potassium cryolite

The paper describes the sedimentation behavior of concentrated high-temperature oxide-fluoride slurries with alumina particles volume fraction range 0.24?≤?φ?≤?0.32 at ～700 °C. The behavior is of interest due to perspectives of the non-Newtonian fluids usage in the future aluminium reduction technology. To characterize sedimentation behavior several techniques were used: density analysis, X-Ray diffraction, microphotography and electron scanning microscopy. Sample with ?63?µm dispersed phase as well as smelter-grade alumina which contains particles in a range of 10–150?µm has been examined. It has been found that particle settling occurs with the initial velocity 0.97·10^?5 m·s^?1 at φ?=?0.24 and gradually reduces reaching zero at φ close to 0.32 which was considered as a maximum packing fraction. MS^?1 sedimentation mode has been identified, the type of sedimentation was found to be changed from type 1 to type 3 in the sample with φ?=?0.24. The alumina partial density distribution in suspension as a function of time was determined. Alumina average motion velocity during sedimentation was calculated to be 154·10^?3?kg·m^?2·s^?1 at φ?=?0.24 in the top layer of the sample within the first 150?s of sedimentation. It had been reducing drastically before it reached zero after 300?s. An alumina flow was higher in the top layers. Some of the rheological properties (such as relaxation time, which increased from 7.2·10^?3 to 17.7·10^?3?s after the increase of φ from 0.24 to 0.28) has been determined.     

Computer simulation of selective aggregation in binary colloids

The morphology of clusters formed by selective aggregation of binary colloids is studied in a two-dimensional Monte Carlo simulation for a large range of number fractions (200:1, 100:1, 10:1, 2:1). We find remarkable similarity in morphology to those observed in experiments, from the formation of closed "micelles" to large branched clusters. Quantitative studies of the fractal dimension, kinetics, and cluster size distribution are also carried out and compared with diffusion-limited cluster aggregation and reaction-limited cluster aggregation models.     

表面活性剂在溶液中聚集形态的动力学模拟

用耗散颗粒动力学模拟方法(DPD)展示了表面活性剂分子在溶液中的聚集形态，用扩散程度表征了表面活性剂溶液中的自组装情况。结果发现：这种分子动力学模拟方法能够直观地得到表面活性剂的聚集形态；随着表面活性剂的浓度增加，聚集形态依次从球状胶束、棒状或虫状胶束，六角状相，向层状相变化。     

Modeling pulse apparatus for processing suspension with periodical unload of concentrated precipitate

The principle of work of a new apparatus for processing suspension with periodical unloading of concentrated precipitate is described. Mathematical model of the apparatus is created that allow calculating main technological parameters of the apparatus. The apparatus feature is application of potential energy accumulated by the compressed gas in the pulse chamber for the regeneration of the separating screen. The experiments with laboratory model of the apparatus allow to recommend this mathematical model for practical application.     

An empirical kinetic model for the gelation of a concentrated latex suspension in the presence of nonadsorbing polymer chains

An empirical model has been proposed to describe the kinetic aspect of the gelation process of a concentrated latex mixture in the presence of nonadsorbing polymer chains. It was found to allow the identification of two predominant effects, a viscosity effect and an excluded volume one effect that balance during gelation, and to predict the polymer volume fraction for which the transition between these two predominant effects occurs in the dilute polymer concentration range.