Influence of hydrodynamics on many-particle diffusion in 2D colloidal suspensions

We study many-particle diffusion in 2D colloidal suspensions with full hydrodynamic interactions through a novel mesoscopic simulation technique. We focus on the behaviour of the effective scaled tracer and collective-diffusion coefficients and , respectively, where D₀ is the single-particle diffusion coefficient, as a function of the density of the colloids . At low Schmidt numbers , we find that hydrodynamics has essentially no effect on the behaviour of . At larger Sc, seems to be enhanced at all densities, although the differences compared to the case without hydrodynamics are rather minor. The collective-diffusion coefficient, on the other hand, is much more strongly coupled to hydrodynamical conservation laws and is distinctly different from the purely dissipative case without hydrodynamic interactions.Received: 20 October 2003, Published online: 23 March 2004PACS: 68.35.Fx Diffusion; interface formation - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 82.20.Wt Physical chemistry and chemical physics: Computational modeling; simulation     

Depletion-induced structure and dynamics in bimodal colloidal suspensions

Combined small angle x-ray scattering and x-ray photon correlation spectroscopy studies of moderately concentrated bimodal hard-sphere colloidal suspensions in the fluid phase show that depletion-induced demixing introduces spatially heterogeneous dynamics with two distinct time scales. The adhesive nature, as well as the mobility, of the large particles is determined by the level of interaction within the monomodal domains. This interaction is driven by osmotic forces, which are governed by the relative concentration of the constituents.     

Shear-induced migration in colloidal suspensions

Using Brownian dynamics simulations, we perform a systematic investigation of the shear-induced migration of colloidal particles subject to Poiseuille flow in both cylindrical and planar geometry. We find that adding an attractive component to the interparticle interaction enhances the migration effect, consistent with recent simulation studies of platelet suspensions. Monodisperse, bidisperse and polydisperse systems are studied over a range of shear-rates, considering both steady-states and the transient dynamics arising from the onset of flow. For bidisperse and polydisperse systems, size segregation is observed.     

Short-time dynamics in quasi-two-dimensional colloidal suspensions

The short-time dynamic properties of colloidal particles in quasi-two-dimensional geometries are studied by digital video microscopy. We demonstrate experimentally that the effective-two-dimensional physical quantities such as the dynamic structure factor, the hydrodynamic function, and the hydrodynamic diffusion coefficients are related in exactly the same manner as their three-dimensional counterparts.     

Collective behavior in out-of-equilibrium colloidal suspensions

Colloidal suspensions, heterogeneous fluids containing solid microscopic particles, play an important role in our everyday life, from food and pharmaceutical industries to medicine and nanotechnology. Colloidal suspensions can be divided in two major classes: equilibrium, and active, i.e. maintained out of thermodynamic equilibrium by external electric or magnetic fields, light, chemical reactions, or hydrodynamic shear flow. While the properties of equilibrium colloidal suspensions are fairly well understood, out-of-equilibrium colloids pose a formidable challenge and the research is in its early exploratory stage. The possibility of dynamic self-assembly, a natural tendency of simple building blocks to organize into complex functional architectures, is one of the most remarkable properties of out-of-equilibrium colloids. Examples range from tunable, self-healing colloidal crystals and membranes to self-assembled microswimmers and robots. In contrast to their equilibrium counterparts, out-of-equilibrium colloidal suspensions may exhibit novel material properties, e.g. reduced viscosity, enhanced self-diffusivity, etc. This work reviews recent developments in the field of self-assembly and collective behavior of out-of-equilibrium colloids, with the focus on the fundamental physical mechanisms.     

Convection in colloidal suspensions with particle-concentration-dependent viscosity

The onset of thermal convection in a horizontal layer of a colloidal suspension is investigated in terms of a continuum model for binary-fluid mixtures where the viscosity depends on the local concentration of colloidal particles. With an increasing difference between the viscosity at the warmer and the colder boundary the threshold of convection is reduced in the range of positive values of the separation ratio y psi with the onset of stationary convection as well as in the range of negative values of y psi with an oscillatory Hopf bifurcation. Additionally the convection rolls are shifted downwards with respect to the center of the horizontal layer for stationary convection (y psi > 0 and upwards for the Hopf bifurcation (y psi < 0 .     

Dynamics of polymers in flowing colloidal suspensions

Using hydrodynamic simulations we examine the behavior of single polymers in a confined colloidal suspension under flow. We study the conformations of both, collapsed and noncollapsed polymers. Our results show that the presence of the colloids has a pronounced effect on the unfolding and refolding cycles of collapsed polymers, but does not have a large effect for noncollapsed polymers. Further inspection of the conformations reveals that the strong flow around the colloids and the direct physical compressions exerted on a globular polymer diffusing in between colloidal shear bands largely facilitate the initiation and unraveling of the globular chains. These results are important for rheological studies of (bio)polymer-(bio)colloid mixtures.     

Sedimentation of nanoparticles in nanoscale colloidal suspensions

A theoretical model is developed to study the sedimentation characteristics of nanoscale colloidal suspensions (nanofluids). The influences of various deterministic and stochastic forcing parameters in the transport characteristics of the suspended nanoparticles are investigated by employing a Langevin formalism of particle transport. The role of collective particle interaction phenomena in the sedimentation of nanoparticles is analyzed by invoking the fundamental considerations of agglomeration-deagglomeration kinetics of the particulate phases. The model demonstrates the effect of particle volume fraction, particle size, and aggregate structure on the sedimentation velocity of the suspended nanoparticles. Predictions from the present model agree well with the experimental results reported in the literature.     

Local phase transitions in driven colloidal suspensions

Using dynamical density functional theory and Brownian dynamics simulations, we investigate the influence of a driven tracer particle on the density distribution of a colloidal suspension at a thermodynamic state point close to the liquid side of the binodal. In bulk systems, we find that a localised region of the colloid-poor phase, a ‘cavitation bubble’, forms behind the moving tracer. The extent of the cavitation bubble is investigated as a function of both the size and velocity of the tracer. The addition of a confining boundary enables us to investigate the interaction between the local phase instability at the substrate and that at the particle surface. When both the substrate and tracer interact repulsively with the colloids we observe the formation of a colloid-poor bridge between the substrate and the tracer. When a shear flow is applied parallel to the substrate the bridge becomes distorted and, at sufficiently high shear-rates, disconnects from the substrate to form a cavitation bubble.     

Propagation of hydrodynamic interactions in colloidal suspensions

We describe direct measurements of the dynamics of two colloidal spheres before hydrodynamic interactions have had time to fully develop. We find that the dynamics of the two spheres are coupled at times significantly shorter than tau(nu), the time required for vorticity to diffuse between the two spheres. From the distance dependence of the measured coupling, we infer that hydrodynamic interactions develop in a sonic time scale.     

Diffusion of colloidal particles in swimming suspensions

Previously, we have proposed to analyse the hydrodynamic interactions in a suspension of swimmers with respect to an effective hydrodynamic diffusion coefficient, which only considers the fluctuating motion caused by the stirring of the fluid. In this work, we study the diffusion of colloidal particles immersed in a bath of swimmers. To accurately resolve the many-body hydrodynamic interactions responsible for this diffusion, we use a direct numerical simulation scheme based on the smooth profile method. We consider a squirmer model for the self-propelled swimmers, as it accurately reproduces the flow field generated by real microorganisms, such as bacteria or spermatozoa. We show that the diffusion coefficients of the colloids are comparable with the effective diffusion coefficients of the swimmers, provided that the concentration of swimmers is high enough. At low concentrations, the difference in the way colloids and swimmers react to the flow leads to a reduction in the diffusion coefficient of the colloids. This is clearly seen in the appearance of a negative-correlation region for the velocity-correlation function of the colloids, which does not exist for the swimmers.     

Partial clustering in binary two-dimensional colloidal suspensions

Strongly interacting binary mixtures of superparamagnetic colloidal particles confined to a two-dimensional water-air interface are examined by theory, computer simulation, and experiment. The mixture exhibits a partial clustering in equilibrium: in the voids of the matrix of unclustered big particles, the small particles form subclusters with a spongelike topology which is accompanied by a characteristic small-wave vector peak in the small-small structure factor. This partial clustering is a general phenomenon occurring for strongly coupled negatively nonadditive mixtures.     

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.     

Elastic properties of 2D colloidal crystals from video microscopy

Elastic constants of two-dimensional (2D) colloidal crystals are determined by measuring strain fluctuations induced by Brownian motion of particles. Paramagnetic colloids confined to an air-water interface of a pendant drop are crystallized under the action of a magnetic field, which is applied perpendicular to the 2D layer. Using video microscopy and digital image processing we measure fluctuations of the microscopic strain obtained from random displacements of the colloidal particles from their mean (reference) positions. From these we calculate system-size dependent elastic constants, which are extrapolated using finite-size scaling to obtain their values in the thermodynamic limit. The data are found to agree rather well with zero-temperature calculations.     

Fractal structure of the crystalline-nuclei boundaries in 2D colloidal crystallization: Computer simulations

By performing 2D kinetic Monte Carlo simulations of colloidal crystallization we found that the boundaries of the crystalline nuclei are not only rough, as obtained by experimentalists, but fractal, whose value (_df$d_f$) we calculated. The corresponding boundary for the crystals, above the critical size (_Nc$N_c$), is also fractal but smoother. A knowledge of the particles coordinates during the crystallization process allows us to calculate the _Nc$N_c$, the line tension (γ) and the chemical potential difference (Δμ) between the two phases. However, different from the experimentalists procedure, we found that the boundary fractalities are needed to derive γ and Δμ.