Dynamics and sedimentation velocity in charge-stabilized colloidal suspensions

Summary Charge-stabilized suspensions are characterized by the strong electrostatic interactions between the particles so that rather dilute systems may exhibit strong correlation resulting in a well-developed short-range order. This microstructure, quantitatively described by the pair distribution functiong(r), is rather different from that of (uncharged) hard spheres. It is shown how this difference affects the ?hydrodynamic function?H(k), which appears in the expression for the first cumulant Γ(k)=k ² D _eff(k)=k ² H(k)/S(k) of the dynamic autocorrelation function. Without hydrodynamic interaction,H(k)=D ⁰, which is the free-diffusion coefficient. Using pairwise additive hydrodynamic interaction and the lowest-order many-body theory of hydrodynamic interaction, it is found thatH(k) can deviate considerably fromD ⁰ even for systems of volume fractions ϕ as low as 10⁻³. These effects are more pronounced for collective diffusion than for self-diffusion. SinceH(k=0) is closely related to the sedimentation velocity, we have studied this quantity as a function of volume fraction. It is found that (H(0)/D ⁰) −1 scales asφ ^1/3 at low ϕ in salt-free suspensions. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Physics of particulate flows: From sand avalanche to active suspensions in plants

Flows of granular media in air or in a liquid have been a research field for physicists for several decades. Sometimes solid, sometimes liquid, these particulate materials exhibit peculiar behaviors, which have motivated many studies at the frontiers between nonlinear physics, soft matter physics and fluid mechanics. This paper presents a summary of the recent advances in the field, with a focus on the development of continuous approaches, which make it possible to treat granular media as a complex fluid and to develop a granular hydrodynamics. We also discuss how the better understanding of granular flows we have today may help to address more complex materials, such as colloidal suspensions or some biological systems.     

Collective purchase behavior toward retail price changes

By analyzing a huge amount of point-of-sale data collected from Japanese supermarkets, we find power law relationships between price and sales numbers. The estimated values of the exponents of these power laws depend on the category of products; however, they are independent of the stores, thereby implying the existence of universal human purchase behavior. The rate of sales numbers around these power laws are generally approximated by log-normal distributions implying that there are hidden random parameters, which might proportionally affect the purchase activity.     

Dynamics in dense suspensions of charge-stabilized colloidal particles

The dynamic behavior of charge-stabilized colloidal particles in suspension was studied by photon correlation spectroscopy with coherent X-rays (XPCS). The short-time diffusion coefficient, D(Q) , was measured for volume concentrations φ ⩽ 0.18 and compared to the free particle diffusion constant D₀ and the static structure factor S(Q) . The data show that indirect, hydrodynamic interactions are relevant for the system and hydrodynamic functions were derived. The results are in striking contrast to the predictions of the PA (pairwise-additive approximation) model, but show features typical for a hard-sphere system. The observed mobility is however considerably smaller than the one of a respective hard-sphere system. The hydrodynamic functions can be modelled quantitatively if one allows for an increased effective viscosity relative to the hard-sphere case.     

Transport and crystallization of colloidal particles in a thin nematic cell

In a thin planar nematic cell, the application of an AC electric field induces a macroscopic transport of micrometer-sized colloidal particles along the nematic director. We have analyzed the dependence of particle velocities on the electric-field amplitude and frequency and found that it decreases exponentially with increasing frequency. Using specially designed electrodes we have observed that colloidal particles could be pumped and accelerated across the field-no-field interface, and measured the structural force and the corresponding potential, which is of the order of 10000 k_BT for 4μm particles. We demonstrate that spatially periodic close-packed crystalline colloidal structures can be obtained, which are thermodinamically metastable for many days after turning off the electric field and slowly decay into linear chains. Above the nematic-isotropic phase transition, such crystalline structures are non-stable and decay in few minutes.     

Measuring colloidal forces with the magnetic chaining technique

In 1994 Leal Calderon et al. (Phys. Rev. Lett. 72, 2959 (1994)) introduced the magnetic chaining technique to directly probe the force-distance profile between colloidal particles. In this paper, we revisit this approach in two ways. First, we describe a new experimental design which allows us to utilize sample volumes as low as a few microliters, involving femtomoles of surface active macromolecules. Secondly, we extensively describe the characterization and preparation of the magnetic colloids, and we give a quantitative evaluation of performance and resolution of the technique in terms of force and interparticle separation.     

Transport coefficients and mechanical response in hard-disk colloidal suspensions

We investigate the transport properties and mechanical response of glassy hard disks using nonlinear Langevin equation theory.We derive expressions for the elastic shear modulus and viscosity in two dimensions on the basis of thermalactivated barrier-hopping dynamics and mechanically accelerated motion.Dense hard disks exhibit phenomena such as softening elasticity,shear-thinning of viscosity,and yielding upon deformation,which are qualitatively similar to dense hard-sphere colloidal suspensions in three dimensions.These phenomena can be ascribed to stress-induced "landscape tilting".Quantitative comparisons of these phenomena between hard disks and hard spheres are presented.Interestingly,we find that the density dependence of yield stress in hard disks is much more significant than in hard spheres.Our work provides a foundation for further generalizing the nonlinear Langevin equation theory to address slow dynamics and rheological behavior in binary or polydisperse mixtures of hard or soft disks.     

Collective diffusion in a lattice gas automaton

We report on non-mean-field and ring-kinetic-theory calculations of both the momentum autocorrelation function and the collective diffusion coefficient in a diffusive lattice gas automaton. For both quantities the ring approximation is calculated exactly. A saddle point method yields a leadingt ^–2 and a subleadingt ^–5/2 long-time tail in the momentum autocorrelation function. The ring kinetic corrections to the mean field value of the diffusion coefficient are in good agreement with computer simulations.     

Collective modes in a one-dimensional nonuniform fluid model

A one-dimensional fluid with short-range repulsive interaction and one period of cosinusoidal attraction in a periodic container is transformed to a two-mode format. The system has both high-temperature single-phase regions and lowtemperature two-phase regions with a very broad spatial interface that can be stabilized by a weak external field. The case of vanishing external field brings out properties of the mode amplitude dependence which one expects to extend to more complex systems.     

Collective flows in high-energy heavy-ion collisions at AGS and SPS energies

Proton collective flows in heavy-ion collisions from AGS ((2–11) A GeV) to SPS ((40,158) A GeV) energies are investigated in a nonequilibrium transport model with nuclear mean-field (MF). Sideward (p _x), directedv ₁, and ellipticv ₂ flows are systematically studied with different assumptions on the nuclear equation of state (EoS). We find that momentum dependence in the nuclear MF is important for understanding the proton collective flows at AGS and SPS energies. Calculated results with momentum-dependent MF qualitatively reproduce the experimental data of proton sideward, directed, and elliptic flows in an incident energy range of (2–158) A GeV This talk is based on ref. [1]     

Structure and fragmentation in colloidal artificial molecules and nuclei

Motivated by recent experiments on colloidal systems with competing attractive and repulsive interactions, we simulate a two-dimensional system of colloids with competing interactions that can undergo fragmentation. In the absence of any other confining potential, the colloids can form stable clusters depending on the strength of the short range attractive term. By suddenly changing the strength of one of the interaction terms we find a rich variety of fragmentation behavior which is affected by the existence of “magic” cluster numbers. Such soft matter systems can be used to construct artificial nuclei.     

A statistical-mechanical theory of self-diffusion in colloidal suspensions — application to colloidal glass transitions

A statistical-mechanical theory of self-diffusion in colloidal suspensions is presented. A renormalized linear Langevin equation is derived from a nonlinear Langevin equation by employing the Tokuyama–Mori projection operator method. The friction constant is thus shown to be renormalized by the many-body correlation effects due to not only the direct interactions between particles, but also due to the hydrodynamic interactions between particles. The equations for the mean-square displacement and the non-Gaussian parameter are then derived. The present theory is applied to colloidal glass transitions to discuss the crossover phenomena in the dynamics of a single particle from a short-time self-diffusion process to a long-time self-diffusion process via a β (caging) stage. The effects of the renormalized friction coefficient on self-diffusion are thus explored with the aid of the analyses of the experimental data and the simulation results by the mean-field theory proposed by the present author. It is thus shown that the relaxation time of the renormalized memory function is given by the β-relaxation time. It is also shown that the non-Gaussian parameter is very small, even near the glass transition, because of the existence of the short-time self-diffusion coefficient caused by the hydrodynamic interactions.     

Nonequilibrium Brownian dynamics simulations of shear thinning in concentrated colloidal suspensions

The effect of interparticle forces on shear thinning in concentrated aqueous and nonaqueous colloidal suspensions was studied using nonequilibrium Brownian dynamics. Hydrodynamic interactions among particles were neglected. Systems of 108 particles were studied at volume fractions of 0.2 and 0.4. For the nonaqueous systems, shear thinning could be correlated with the gradual breakup of small flocs present because of the weak, attractive secondary minimum in the interparticle potential. At the highest shear rate for=0.4, the particles were organized into a hexagonally packed array of strings. For the strongly repulsive aqueous systems, the viscosity appeared to be a discontinuous function of the shear rate. For=0.4, this discontinuity coincided with a transition from a disordered state to a lamellar structure for the suspension.     

Effects of unsymmetrical geometric confinements on depletion interactions in colloidal suspensions

The depletion interactions between two large-spheres immersed in a fluid of small spheres under unsymmetrical geometrical confinement are studied through the acceptance ratio method. The numerical results show that no matter whether the volume fraction is large or small, both the depletion potential and depletion force are affected by the presence of the two plates; the closer the two large spheres are to the plate, the larger the effects of the unsymmetrical confinements.     

Collective modes in the generator coordinate method

Using the harmonic version of the generator coordinate method, and Skyrme interaction, the frequencies of the isoscalar breathing and quadrupole modes are related to the relevant incompressibility coefficients. The possibility of extending this to spin modes is also examined. It is found that a spin incompressibility coefficient is negative for a particular set of Skyrme parameter for⁴He. Other sets produce low positive values and these in turn could imply a relatively low lyingS=2,T=1 state. The replacement of the three-body term by the density-dependent one, suggested by Chang provides a cure for this pathology.     

Cluster formation in binary charge-stabilized colloidal suspensions confined to a two-dimensional plane

Hypernetted chain (HNC) integral equation theory has been used to study the structural features of binary charged stabilized colloidal suspensions confined to a two-dimensional plane. The particles interact via purely repulsive Yukawa intermolecular potential, the inverse screening length scaled by the average distance between strongly interacting components of the mixture (dimensionless screening parameter) being 1, 3 and 5. Results of HNC theory for one-component systems are found to be in very good agreement with that of simulation, in the parameter range of our study. Binary Yukawa systems with dimensionless screening parameters 1 and 3 are found to exhibit diffuse clusters of the weakly interacting particles, marked by the emergence of a cluster peak in the corresponding partial structure factor curves. No cluster peak is found in the system with the screening parameter 5. For the entire range of mixture parameters, the strongly interacting particles remain homogeneously distributed.     

Collective motion of microspheres in suspensions observed by phase-mode dynamic ultrasound scattering technique

Compared with a nano-sized particle, dynamics of a micron-sized particle in a liquid is often associated with sedimentation (or floating) due to its relatively large mass. The motion of more than two particles is dominated by the hydrodynamic interactions, which are known to persist over a fairly long range, e.g., several millimeters, in suspensions. The particle size may be obtained from the dynamic ultrasound scattering (DSS) technique by the analysis of velocity fluctuations, whose origin is believed to take root in the particle-number fluctuations among temporally formed domains involving collective motion of particles with a certain cut-off length. In this study, such collective particle motion in highly turbid solutions was visualized by means of the phase-mode DSS technique with a single element transducer. Quantitative agreement between the velocity fluctuations obtained by the phase- and conventional amplitude-mode analyses was confirmed, followed by examination of the concentration and the particle size dependences on the dynamic structures induced by the long-ranged interactions. It was found that the phase mode-DSS was a promising method to evaluate the time-dependent structures of the micro-particles in highly turbid suspensions.     

A new way to apply ultrasound in cross-flow ultrafiltration: Application to colloidal suspensions

A new coupling of ultrasound device with membrane process has been developed in order to enhance cross-flow ultrafiltration of colloidal suspensions usually involved in several industrial applications included bio and agro industries, water and sludge treatment. In order to reduce mass transfer resistances induced by fouling and concentration polarization, which both are main limitations in membrane separation process continuous ultrasound is applied with the help of a vibrating blade (20 kHz) located in the feed channel all over the membrane surface (8 mm between membrane surface and the blade). Hydrodynamic aspects were also taking into account by the control of the rectangular geometry of the feed channel.Three colloidal suspensions with different kinds of colloidal interaction (attractive, repulsive) were chosen to evaluate the effect of their physico-chemical properties on the filtration.For a 90 W power (20.5 W cm⁻²) and a continuous flow rate, permeation fluxes are increased for each studied colloidal suspension, without damaging the membrane. The results show that the flux increase depends on the initial structural properties of filtered dispersion in terms of colloidal interaction and spatial organizations.For instance, a Montmorillonite Wyoming–Na clay suspension was filtered at 1.5 × 10⁵ Pa transmembrane pressure. Its permeation flux is increased by a factor 7.1, from 13.6 L m⁻² h⁻¹ without ultrasound to 97 L m⁻² h⁻¹ with ultrasound.