Reversible coagulation of colloidal suspension in shallow potential wells: Direct numerical simulation

Brownian dynamics computer simulations of aggregation in 2D colloidal suspensions are discussed. The simulations are based on the Langevin equations, pairwise interaction between colloidal particles and take into account Brownian, hydrodynamic and colloidal forces. The chosen mathematical model enables to predict the correct values of diffusion coefficient of freely moving particle, the mean value of kinetic energy for each particle in ensemble of interacting colloidal particles and residence times of colloidal particles inside the potential wells of different depths. The simulations allow monitoring formation and breakage of clusters in a suspension as well as time dependence of the mean cluster size. The article is published in the original.     

Prediction of Brownian particle deposition in porous media using the constricted tube model

The deposition of colloidal particles onto the collector surfaces of porous media is investigated using the Brownian dynamics simulation method. The pore structure in a filter bed was characterized by the constricted tube model. The effects of various shapes of the total interaction energy curves of DLVO theory and the effects of different particle diameters on the collection efficiencies of particles are examined. The simulation results show that the particle collection efficiency is strongly dependent on the geometry of the tube and on the shape of the total interaction energy curve. In a comparison with the available experimental measurements of the filter coefficient, it is found that the present model can give a smaller discrepancy than that of the convective diffusion model in the unfavorable deposition region.     

Simulations of the PDF functions for dilute colloidal suspensions of molecular particles flowing in mesopores with rough surface boundaries

Simulations have been carried out to analyze the dynamics of dilute colloidal suspensions of macromolecular particles in solutions flowing in pores, subject to hydrodynamic forces, Brownian motion and stochastic collisions at rough pore boundaries in a two-dimensional spatial frame. A theoretical model is developed and intensively analyzed for the treatment of the mechanical restitution of the particles due to dynamic collisions at these boundaries. In particular we are able to calculate the Probability distribution functions for the spatial positions and the orientations of rod-like particles inside the pores. The results are presented for different widths of pore channels referenced to the size of a rod-like particle. These simulations are general in the sense that they are developed for confining and open pore channels, rough at the nano scale. The simulations also permit calculating the nematic order parameters for colloidal suspensions; the model calculation is applied for dilute colloidal suspensions of carbon nano-tubes in an aqueous single-stranded DNA solution flowing inside pores. Our calculated nematic order results for dilute suspensions of particles of known lengths flowing inside porous systems should indicate, when coupled to birefringence and dichroism experimental results, the possibility to estimate the pore widths for these systems.     

Dielectrophoretic levitation in the presence of shear flow: implications for colloidal fouling of filtration membranes

The ability of dielectrophoretic (DEP) forces created using a microelectrode array to levitate particles in a colloidal suspension is studied experimentally and theoretically. The experimental system employs microfabricated electrode arrays on a glass substrate to apply repulsive DEP forces on polystyrene latex particles suspended in an aqueous medium. A numerical model based on the convection-diffusion-migration equation is presented to calculate the concentration distribution of colloidal particles in shear flow under the influence of a repulsive DEP force field. The results obtained from the numerical simulations are compared against trajectory analysis results and experimental data. The results indicate that by incorporating ac electric field-induced DEP forces in a shear flow, particle accumulation and deposition on the flow channel surfaces can be significantly reduced or even completely averted. The mathematical model is then used to indicate how the deposition behavior is modified in the presence of a permeable substrate, representative of tangential flow membrane filtration operations. The results indicate that the repulsive dielectrophoretic (DEP) forces imparted to the particles suspended in the feed can be employed to mitigate membrane fouling in a cross-flow filtration process.     

Effect of particle size distribution on the collection efficiency of Brownian particles

The main purpose of the present paper is to investigate the effect of the normal Gaussian size distribution on the deposition of Brownian particles onto a spherical collector, by applying the Brownian dynamic simulation method and the Kuwabara flow field model with different types of DLVO interaction energy curves and the shadow effect. The simulation results show that the collection efficiency of Brownian particles always increases with a wider particle size distribution region. The same increased tendencies are also observed for the case of increasing Reynolds number and for the case of increasing the particle size to the collector size ratio. When compared to the available experimental data, the present simulation method fits well with the experimental data when the specific deposit per collector is not large.     

Theoretical analysis of factors affecting the formation and stability of multilayered colloidal dispersions

A mathematical analysis of the major factors influencing the formation and stability of colloidal dispersions containing spherical particles surrounded by multilayered polymeric interfacial membranes formed by the layer-by-layer electrostatic deposition technique is carried out. The mathematical model assumes that (i) the colloidal dispersion initially consists of a mixture of electrically charged monodisperse spherical particles and oppositely charged polymer molecules, (ii) the adsorption of polymer molecules to the particle surfaces is diffusion-limited, and (iii) the dominant particle-particle collision mechanism is Brownian motion. This approach was used to produce stability maps that highlight conditions under which bridging flocculation, multilayer formation, or depletion flocculation occurs. The stability maps are derived from calculations of the critical polymer concentrations required to (i) saturate the particle surfaces (C(Sat)), (ii) ensure that polymer adsorption is faster than particle collisions (C(Ads)), and (iii) promote depletion flocculation (C(Dep)). In addition, the influence of interfacial properties on the stability of multilayer colloidal dispersions was assessed by calculating the colloidal interactions between the coated particles (i.e., van der Waals, electrostatic, steric, and depletion). These calculations indicated that the major factors are the interfacial charge and composition rather than the interfacial thickness. This article provides useful insights into the factors affecting the formation of stable multilayer colloidal dispersions.     

Dynamics of interacting Brownian particles

A memory function formulation has been used for the dynamics of interacting Brownian particles in colloidal systems and polymer dispersions. By introducing approximations at the level of the force correlation function, the theoretical scattering functions agree well with the experimental photon correlation spectroscopy data.     

Rheological properties and particle behaviors of a nondilute colloidal dispersion composed of ferromagnetic spherocylinder particles subjected to a simple shear flow: analysis by means of mean-field approximation for the two typical external magnetic field directions

We have analyzed the orientational distributions and rheological properties of a nondilute colloidal dispersion composed of ferromagnetic spherocylinder particles subjected to a simple shear flow. In order to understand the effects of the magnetic interactions between the particles, we have applied the mean-field theory to a nondilute colloidal dispersion for the two typical external magnetic field directions, that is, the direction parallel to the shear flow and the direction parallel to the angular velocity vector of the shear flow. The main results are summarized as follows. The particle-particle interactions suppress the Brownian motion of the particles and, therefore, make the particles incline toward the same direction. For the magnetic direction parallel to the shear flow, the influence of the particle-particle interactions makes the peak of the orientational distribution sharper and higher. The viscosity generally increases as the interactions between particles become stronger in the case where the effects of the shear flow and magnetic field are relatively small. For the magnetic direction parallel to the angular velocity vector of the shear flow, the influence of the particle-particle interactions on the orientational distribution appears significantly, when the influences of the shear flow and magnetic field are not so strong that the particles can be aligned sufficiently to form stable chainlike clusters in a certain direction.     

Patterned assembly of colloidal particles by confined dewetting lithography

We report the assembly of colloidal particles into confined arrangements and patterns on various cleaned and chemically modified solid substrates using a method which we term "confined dewetting lithography" or CDL for short. The experimental setup for CDL is a simple deposition cell where an aqueous suspension of colloidal particles (e.g., polystyrene spheres) is placed between a floating deposition template (i.e., metal microgrid) and the solid substrate. The voids of the deposition template serve as an array of micrometer-sized reservoirs where several hydrodynamic processes are confined. These processes include water evaporation, meniscus formation, convective flow, rupturing, dewetting, and capillary-bridge formation. We discuss the optimal conditions where the CDL has a high efficiency to deposit intricate patterns of colloidal particles using polystyrene spheres (PS; 4.5, 2.0, 1.7, 0.11, 0.064 microm diameter) and square and hexagonal deposition templates as model systems. We find that the optimization conditions of the CDL method, when using submicrometer, sulfate-functionalized PS particles, are primarily dependent on minimizing attractive particle-substrate interactions. The CDL methodology described herein presents a relatively simple and rapid method to assemble virtually any geometric pattern, including more complex patterns assembled using PS particles with different diameters, from aqueous suspensions by choosing suitable conditions and materials.     

Structure and rheological behavior of highly charged colloidal particles in a cylindrical pore I. Effect of pore size

In this work we performed nonequilibrium Brownian dynamics (NEBD) computer simulations of highly charged colloidal particles in diluted suspension under a parabolic flow in cylindrical pores. The influence of charged and neutral cylindrical pores on the structure and rheology of suspensions is analyzed. A shear-induced disorder-order-disorder-like transition was monitored for low shear rates and small pore diameters. We calculate the concentration profiles, axial distribution functions, and axial-angular pair correlation functions to determine the structural properties at steady state for a constant shear flow for different pore sizes and flow strengths. Similar behavior has been observed in a planar narrow channel in the case of charged interacting colloidal particles (M.A. Valdez, O. Manero, J. Colloid Interface Sci. 190 (1997) 81). The mobility of the particles in the radial direction decreases rapidly with the flow and becomes practically frozen. The flow exhibits non-Newtonian shear thinning behavior due to interparticle interactions and particle-wall interaction; the apparent viscosity is lower as the pore diameter decreases, giving rise to an apparent slip in the colloidal suspension. The calculated slip velocity was higher than that obtained in a rectangular slit under shear flow.     

Cathodic electrodeposition of ceramic and organoceramic materials. Fundamental aspects

Electrodeposition of ceramic materials can be performed by electrophoretic (EPD) or electrolytic (ELD) deposition. Electrophoretic deposition is achieved via motion of charged particles towards an electrode under an applied electric field. Electrolytic deposition produces colloidal particles in cathodic reactions for subsequent deposition. Various electrochemical strategies and deposition mechanisms have been developed for electrodeposition of ceramic and organoceramic films, and are discussed in the present article. Electrode-position of ceramic and organoceramic materials includes mass transport, accumulation of particles near the electrode and their coagulation to form a cathodic deposit. Various types of interparticle forces that govern colloidal stability in the absence and presence of processing additives are discussed. Novel theoretical contributions towards an interpretation of particle coagulation near the electrode surface are reviewed. Background information is given on the methods of particle charging, stabilization of colloids in aqueous and non-aqueous media, electrophoretic mobility of ceramic particles and polyelectrolytes, and electrode reactions. This review also covers recent developments in the electrodeposition of ceramic and organoceramic materials.     

Interactions between colloidal particles in simple shear flow

Recent progress in experimental and theoretical developments dealing with colloidal. interactions between two spheres in shear flow is reviewed. A systematic comparison is made between spheres suspended in simple electrolyte and in cationic polyelectrolye solutions. Microrheological observations, performed with the traveling microtube, make an in-depth investigation possible of the colloidal forces and the mechanisms of polymer bridge formation. Reasons are discussed for the often-observed aging of colloidal aggregates. Finally, coagulation rates are presented for systems with weak and strong Brownian motion. It is shown that the often-used assumption of additivity of the ortho- and perikinetic coagulation rates is incorrect.     

Effective medium approximation and deposition of colloidal particles in fibrous and granular media

Laminar flow of fluids through fibrous and granular media and deposition of colloidal particles from a liquid suspension are two fundamental phenomena encountered in many industrial applications. An Effective Medium Approximation (EMA) is used to determine the fluid flow permeability and particle capture efficiency of random arrays of cylindrical and spherical collectors. The EMA assumes a model system in which a packing element (a single fiber in the fibrous medium and a single sphere in the granular medium) is surrounded by a fluid envelope and an effective-medium beyond the envelope. It integrates the important features of both the cell models and Brinkman's model. The Stokes equation and Brinkman equation are solved for the fluid envelope and effective medium regions, respectively, to obtain the permeability and close-to-surface velocity field around the collectors. The convective diffusion equation is then solved to determine the particle deposition rate. The analytical expressions for the permeability and particle deposition rate are derived for all possible cases of random packing of uniform and non-uniform cylinders and spheres. Effects of various system properties and operating conditions on deposition of colloidal particles are investigated. The physical or chemical conditions include the properties which affect the magnitude of double layer interaction: the electrolyte concentration and surface potentials, and the property which affects the van der Waals interaction: the Hamaker constant. It was found that the effects of the above properties is much more significant when the surface interactions play more important roles in the particle deposition process, or when the height of the total interaction energy barrier is higher than 5 kBT. Particle deposition becomes virtually impossible when the height of the repulsive energy barrier increases beyond 20 kBT.     

Long-time self-diffusion of charged colloidal particles: electrokinetic and hydrodynamic interaction effects

The authors analyze the long-time self-diffusion of charge-stabilized colloidal macroions in nondilute suspensions using a mode-coupling scheme developed for multicomponent suspensions of interacting Brownian spheres. In this scheme, all ionic species, including counterions and electrolyte ions, are treated on an equal footing as charged hard spheres undergoing overdamped Brownian motion. Hydrodynamic interactions between all ions are accounted for on the far-field level. We show that the influence on the colloidal long-time self-diffusion coefficient arising from the relaxation of the microionic atmosphere surrounding the colloids, the so-called electrolyte friction effect, is usually insignificant in comparison with the friction contributions arising from direct and hydrodynamic interactions between the colloidal particles. This finding is true even for small colloid concentrations unless the mobility difference between colloidal particles and microions is not large. Furthermore, we observe an interesting nonmonotonic density dependence of the colloidal long-time self-diffusion coefficient in suspensions with low amount of added salt. We show that this unusual density dependence is due to colloid-colloid hydrodynamic interactions.     

Application of the network model for studying the delivery of colloidal drugs

From the viewpoint of colloidal transport phenomena, the individual drug particle’s movement through the tumor is studied by using the square network model. The effects of drug concentration, arterial pressure, and interstitial pressure of the tumor on the concentration breakthrough moment of drug particles are investigated by using the Brownian dynamics simulation method. From the simulation results, we find that the present network model and the Brownian dynamics simulation method can successfully analysis the therapeutic ranges achieved by the drug particles in the tumor at different magnitudes of the drug concentration, the inlet blood velocity, the arterial pressures, and the interstitial pressures of the tumor. Because of the high interstitial fluid pressure, the drug particles can only reach the peripheral region and cannot penetrate inside the target tumor efficiently, and the decreased interstitial fluid pressure will lead more drug particles to penetrate inside the tumor.     

胶体晶体自组装排列进展

自组装排列胶体晶体是发展光子晶体等亚微米周期有序结构及新型光电子器件十分重要的环节.高电荷密度单分散胶体球在较弱的离子强度和稀浓度下会自发排列形成紧密堆积的周期性结构(ccp),常常是面心立方(fcc),科学家们以此为基础发展了多种结晶化胶体粒子的方法,包括重力场沉积、电泳沉积、胶体外延技术、垂直沉积、流通池、物理束缚排列及其他的许多方法.目前排列的胶体粒子基本为球形,材料也多为SiO2、PS、PMMA,此外一些复合粒子,主要为核壳粒子的排列这里也稍作介绍,这些方法及其变通的使用可以形成类蛋白石及反蛋白石结构,最终实现光子带隙及其它多种用途。     

Aggregate structure and coagulation kinetics in a concentrated dispersion of interacting colloidal particles

A real-time Brownian dynamics simulation of irreversible coagulation in a concentrated dispersion of interacting colloidal particles is presented. Aggregate structure in two dimensions is sensitive to colloidal forces on a length scale of a few particle radii, but not otherwise. Colloidal forces and aggregate diffusion coefficients are rate-limiting at short and long times, respectively.     

Dispersion of magnetic susceptibility and the microstructure of magnetic fluid

The microstructure of magnetic fluid produced on the basis of kerosene with oleic acid as a stabilizer is studied experimentally. An analytical procedure based on the known dependence of the time of Brownian relaxation of the magnetic moment of the colloidal particle on its size and the expansion of a low-frequency spectrum of dynamic susceptibility into the series of Debye functions is used. Magnetic susceptibility is measured at frequencies from 10 Hz to 100 kHz and temperatures from 225 to 360 K for colloidal solutions with the volume fraction of magnetite from 0.08 to 0.17. The clusters with uncompensated magnetic moments and sizes varying from 50 to 70 nm that are three-or fourfold larger than the mean diameter of a single colloidal particle are found. It is revealed that characteristic sizes of clusters are virtually independent of temperature and concentration of colloidal particles. The contribution of clusters to the equilibrium susceptibility of magnetic fluid grows exponentially with decreasing temperature, being manyfold larger at low temperatures than that of single particles. The obtained temperature dependence of equilibrium susceptibility is compared with that predicted from current theoretical models.     

Colloidal dynamics: influence of diffusion, inertia and colloidal forces on cluster formation

Computer simulations of colloidal suspensions are discussed. The simulations are based on the Langevin equations, pairwise interaction between colloidal particles and take into account Brownian, hydrodynamic and colloidal forces. Comparison of two models, one taking into account inertial term in Langevin equation and another based on diffusional approximation proposed in [D.L. Ermak, J.A. McCammon, J. Chem. Phys. 69 (1978) 1352], has shown that both models enable the prediction of the correct values of the diffusion coefficient and residence time of particle in a doublet and are therefore suitable to study the dynamics of formation and breakage of clusters in colloidal suspensions. It is shown that the appropriate selection of the time step and taking into account inertia of particles provides also the correct value of the average kinetic energy of each particle during the simulations, what allows to use the model based on full Langevin equations as a reference model to verify the validity of the numerical scheme for simulation using diffusion approximation.     

Alignment of particles in sheared viscoelastic fluids

We investigate the shear-induced structure formation of colloidal particles dissolved in non-Newtonian fluids by means of computer simulations. The two investigated visco-elastic fluids are a semi-dilute polymer solution and a worm-like micellar solution. Both shear-thinning fluids contain long flexible chains whose entanglements appear and disappear continually as a result of Brownian motion and the applied shear flow. To reach sufficiently large time and length scales in three-dimensional simulations with up to 96 spherical colloids, we employ the responsive particle dynamics simulation method of modeling each chain as a single soft Brownian particle with slowly evolving inter-particle degrees of freedom accounting for the entanglements. Parameters in the model are chosen such that the simulated rheological properties of the fluids, i.e., the storage and loss moduli and the shear viscosities, are in reasonable agreement with experimental values. Spherical colloids dispersed in both quiescent fluids mix homogeneously. Under shear flow, however, the colloids in the micellar solution align to form strings in the flow direction, whereas the colloids in the polymer solution remain randomly distributed. These observations agree with recent experimental studies of colloids in the bulk of these two liquids.