Temporal and spatial dependence of hydrodynamic correlations: Simulation and experiment

Diffusion and sedimentation in colloidal suspensions using multiparticle collision dynamics with a discrete particle model

We study self-diffusion and sedimentation in colloidal suspensions of nearly hard spheres using the multiparticle collision dynamics simulation method for the solvent with a discrete mesh model for the colloidal particles (MD+MPCD). We cover colloid volume fractions from 0.01 to 0.40 and compare the MD+MPCD simulations to experimental data and Brownian dynamics simulations with free-draining hydrodynamics (BD) as well as pairwise far-field hydrodynamics described using the Rotne-Prager-Yamakawa mobility tensor (BD+RPY). The dynamics in MD+MPCD suggest that the colloidal particles are only partially coupled to the solvent at short times. However, the long-time self-diffusion coefficient in MD+MPCD is comparable to that in experiments, and the sedimentation coefficient in MD+MPCD is in good agreement with that in experiments and BD+RPY, suggesting that MD+MPCD gives a reasonable description of hydrodynamic interactions in colloidal suspensions. The discrete-particle MD+MPCD approach is convenient and readily extended to more complex shapes, and we determine the long-time self-diffusion coefficient in suspensions of nearly hard cubes to demonstrate its generality.

Autonomously Probing Viscoelasticity in Disordered Suspensions

Recent experiments show a strong rotational diffusion enhancement for self-propelled microrheological probes in colloidal glasses. Here, we provide microscopic understanding using simulations with a frictional probe-medium coupling that converts active translation into rotation. Diffusive enhancement emerges from the medium's disordered structure and peaks at a second-order transition in the number of contacts. Our results reproduce the salient features of the colloidal glass experiment and support an effective description that is applicable to a broader class of viscoelastic suspensions.

Rheology of colloidal suspensions in confined flow: Treatment of hydrodynamic interactions in particle-based simulations inspired by dynamical density functional theory

We investigate the microstructure and rheology of a hard-sphere suspension in a Newtonian fluid confined in a cylindrical channel and undergoing pressure-driven flow using Monte Carlo simulations. We develop a hydrodynamic framework inspired by dynamical density functional theory approaches in which the contributions due to various flow-induced hydrodynamic interactions (HI) are included in the form of thermodynamic work done by these HI-derived forces in displacing the hard spheres. Using this framework, we can self-consistently determine the effect of the local microstructure on the average flow field, and vice versa, and coevolve the inhomogeneous density distribution and the flattening velocity profile with increase in the density of suspended particles. Specifically, we explore the effect on the local microstructure due to the inclusion of forces arising from confinement-induced inertial effects, forces due to solvent-mediated interparticle interactions, and the dependence of the diffusivity on the local density. We examine the dependence of the apparent viscosity of the suspension on the volume fraction of hard spheres in the cylinder, the flow rate, and the diameter of the cylinder and investigate their effects on the local microstructure.

Short- and long-time diffusion and dynamic scaling in suspensions of charged colloidal particles

We report on a comprehensive theory-simulation-experimental study of collective and self-diffusion in concentrated suspensions of charge-stabilized colloidal spheres. In theory and simulation, the spheres are assumed to interact directly by a hard-core plus screened Coulomb effective pair potential. The intermediate scattering function, f_c(q, t), is calculated by elaborate accelerated Stokesian dynamics (ASD) simulations for Brownian systems where many-particle hydrodynamic interactions (HIs) are fully accounted for, using a novel extrapolation scheme to a macroscopically large system size valid for all correlation times. The study spans the correlation time range from the colloidal short-time to the long-time regime. Additionally, Brownian Dynamics (BD) simulation and mode-coupling theory (MCT) results of f_c(q, t) are generated where HIs are neglected. Using these results, the influence of HIs on collective and self-diffusion and the accuracy of the MCT method are quantified. It is shown that HIs enhance collective and self-diffusion at intermediate and long times. At short times self-diffusion, and for wavenumbers outside the structure factor peak region also collective diffusion, are slowed down by HIs. MCT significantly overestimates the slowing influence of dynamic particle caging. The dynamic scattering functions obtained in the ASD simulations are in overall good agreement with our dynamic light scattering (DLS) results for a concentration series of charged silica spheres in an organic solvent mixture, in the experimental time window and wavenumber range. From the simulation data for the time derivative of the width function associated with f_c(q, t), there is indication of long-time exponential decay of f_c(q, t), for wavenumbers around the location of the static structure factor principal peak. The experimental scattering functions in the probed time range are consistent with a time-wavenumber factorization scaling behavior of f_c(q, t) that was first reported by Segrè and Pusey [Phys. Rev. Lett. 77, 771 (1996)] for suspensions of hard spheres. Our BD simulation and MCT results predict a significant violation of exact factorization scaling which, however, is approximately restored according to the ASD results when HIs are accounted for, consistent with the experimental findings for f_c(q, t). Our study of collective diffusion is amended by simulation and theoretical results for the self-intermediate scattering function, f_s(q, t), and its non-Gaussian parameter α₂(t) and for the particle mean squared displacement W(t) and its time derivative. Since self-diffusion properties are not assessed in standard DLS measurements, a method to deduce W(t) approximately from f_c(q, t) is theoretically validated.

Short-time diffusion in concentrated bidisperse hard-sphere suspensions

Diffusion in bidisperse Brownian hard-sphere suspensions is studied by Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical scheme for colloidal short-time dynamics, based on Beenakker and Mazur's method [Physica A 120, 388-410 (1983); 126, 349-370 (1984)]. Two species of hard spheres are suspended in an overdamped viscous solvent that mediates the salient hydrodynamic interactions among all particles. In a comprehensive parameter scan that covers various packing fractions and suspension compositions, we employ numerically accurate SD simulations to compute the initial diffusive relaxation of density modulations at the Brownian time scale, quantified by the partial hydrodynamic functions. A revised version of Beenakker and Mazur's δγ-scheme for monodisperse suspensions is found to exhibit surprisingly good accuracy, when simple rescaling laws are invoked in its application to mixtures. The so-modified δγ scheme predicts hydrodynamic functions in very good agreement with our SD simulation results, for all densities from the very dilute limit up to packing fractions as high as 40%.

Short-time rheology and diffusion in suspensions of Yukawa-type colloidal particles

A comprehensive study is presented on the short-time dynamics in suspensions of charged colloidal spheres. The explored parameter space covers the major part of the fluid-state regime, with colloid concentrations extending up to the freezing transition. The particles are assumed to interact directly by a hard-core plus screened Coulomb potential, and indirectly by solvent-mediated hydrodynamic interactions. By comparison with accurate accelerated Stokesian Dynamics (ASD) simulations of the hydrodynamic function H(q), and the high-frequency viscosity η(∞), we investigate the accuracy of two fast and easy-to-implement analytical schemes. The first scheme, referred to as the pairwise additive (PA) scheme, uses exact two-body hydrodynamic mobility tensors. It is in good agreement with the ASD simulations of H(q) and η(∞), for smaller volume fractions up to about 10% and 20%, respectively. The second scheme is a hybrid method combining the virtues of the δγ scheme by Beenakker and Mazur with those of the PA scheme. It leads to predictions in good agreement with the simulation data, for all considered concentrations, combining thus precision with computational efficiency. The hybrid method is used to test the accuracy of a generalized Stokes-Einstein (GSE) relation proposed by Kholodenko and Douglas, showing its severe violation in low salinity systems. For hard spheres, however, this GSE relation applies decently well.

Dynamics of permeable particles in concentrated suspensions

We calculate short-time diffusion properties of suspensions of porous colloidal particles as a function of their permeability, for the full fluid-phase concentration range. The particles are modeled as spheres of uniform permeability with excluded volume interactions. Using a precise multipole method encoded in the HYDROMULTIPOLE program, results are presented for the hydrodynamic function, H(q) , sedimentation coefficient, and self-diffusion coefficients with a full account of many-body hydrodynamic interactions. While self-diffusion and sedimentation are strongly permeability dependent, the wave-number dependence of the hydrodynamic function can be reduced by appropriate shifting and scaling, to a single master curve, independent of permeability. Generic features of the permeable sphere model are discussed.

Collective diffusion in charge-stabilized suspensions: Concentration and salt effects

The authors present a joint experimental-theoretical study of collective diffusion properties in aqueous suspensions of charge-stabilized fluorinated latex spheres. Small-angle x-ray scattering and x-ray photon correlation spectroscopy have been used to explore the concentration and ionic-strength dependence of the static and short-time dynamic properties including the hydrodynamic function H(q), the wave-number-dependent collective diffusion coefficient D(q), and the intermediate scattering function over the entire accessible range. They show that all experimental data can be quantitatively described and explained by means of a recently developed accelerated Stokesian dynamics simulation method, in combination with a modified hydrodynamic many-body theory. In particular, the behavior of H(q) for de-ionized and dense suspensions can be attributed to the influence of many-body hydrodynamics, without any need for postulating hydrodynamic screening to be present, as it was done in earlier work. Upper and lower boundaries are provided for the peak height of the hydrodynamic function and for the short-time self-diffusion coefficient over the entire range of added salt concentrations.

Many-body hydrodynamic interactions in charge-stabilized suspensions

In this joint experimental-theoretical work we study hydrodynamic interaction effects in dense suspensions of charged colloidal spheres. Using x-ray photon correlation spectroscopy we have determined the hydrodynamic function H(q), for a varying range of electrosteric repulsion. We show that H(q) can be quantitatively described by means of a novel Stokesian dynamics simulation method for charged Brownian spheres, and by a modification of a many-body theory developed originally by Beenakker and Mazur. Very importantly, we can explain the behavior of H(q) for strongly correlated particles without resorting to the controversial concept of hydrodynamic screening, as was attempted in earlier work by Riese [Phys. Rev. Lett. 85, 5460 (2000)].

Diffusion and microstructural properties of solutions of charged nanosized proteins: Experiment versus theory

We have reanalyzed our former static small-angle x-ray scattering and photon correlation spectroscopy results on dense solutions of charged spherical apoferritin proteins using theories recently developed for studies of colloids. The static structure factors S(q), and the small-wave-number collective diffusion coefficient D(c) determined from those experiments are interpreted now in terms of a theoretical scheme based on a Derjaguin-Landau-Verwey-Overbeek-type continuum model of charged colloidal spheres. This scheme accounts, in an approximate way, for many-body hydrodynamic interactions. Stokesian dynamics computer simulations of the hydrodynamic function have been performed for the first time for dense charge-stabilized dispersions to assess the accuracy of the theoretical scheme. We show that the continuum model allows for a consistent description of all experimental results, and that the effective particle charge is dependent upon the protein concentration relative to the added salt concentration. In addition, we discuss the consequences of small ions dynamics for the collective protein diffusion within the framework of the coupled-mode theory.

Self-diffusion in dilute colloidal suspensions with attractive potential interactions

The colloidal short-time self-diffusivity D(s)(s)(phi) is significantly retarded relative to hard sphere suspensions for the case of interparticle potential interactions induced by a nonadsorbing polymer. A comparison of diffusing wave spectroscopy measurements with direct calculations of D(s)(s)(phi) demonstrates that depletion effects on structure explain the observed retardation. We show that coexistence boundaries place unexpectedly severe constraints on the amount of D(s)(s)(phi) retardation possible for stable suspensions. The measured retardation is demonstrated to be an indicator of suspension metastability.

Probe size effects on the microrheology of associating polymer solutions

Diffusing wave spectroscopy has been used to investigate the thermally driven displacement of colloidal particles dispersed in solutions of associating polymers (APs). The effect of varying colloidal probe size on the measured particle displacements is studied in particular. Recent theories of microrheology are examined in light of the observed effects. The associating polymer used in this research was a linear polyethylene oxide (PEO) chain (molecular weight 35 000 g/mole) with a Cl14 aliphatic group appended to each end of the PEO. Above a critical concentration, the associating polymers display linear viscoelasticity consistent with the Maxwell model. The concentration of aqueous AP solutions was varied from 0.25 to 4.0 wt. %. At low concentration of APs, the mean square displacement of the colloidal beads was indistinguishable from simple Brownian diffusion in the aqueous solvent. However, at concentrations greater than 0.5 wt. %, the mean square displacement differed from simple diffusion in a way that was found to be consistent with the Maxwell model linear viscoelasticity (LVE) of the AP solutions. Significantly, for the most concentrated solutions, as the probe particle size was varied from 0.3 to 2.2 microm, the observed mean square displacement deviated substantially from the generalized Stokes-Einstein behavior predicted by microrheological theories. Our experiments showed that these deviations could not be attributed to specific physicochemical interactions at the probe-matrix interface, since observed mean square displacements were independent of different probe surface chemistries studied. Moreover, this particle size effect was not observed in semidilute, high molecular weight PEO solutions (molecular weight 4.0 x 10(6) g/mole). We concluded that possible effects of AP network compressibility and AP depletion at the probe surface could not account for the observed particle size effects. We examined recent reports of the structural heterogeneity in AP solutions for their possible connection to our observation of the breakdown of the generalized Stokes-Einstein equation for this system. Numerical conversion of the microscopic results to the linear viscoelastic moduli, G'(omega) and G"(omega), by means of a constrained regularization method (CONTIN), demonstrates that the experiments with larger probe particles are most consistent with the single-mode Maxwell model LVE observed by macroscopic mechanical rheology.

Diffusing wave spectroscopy and small-angle neutron scattering from concentrated colloidal suspensions

We have studied the properties of dense colloidal suspensions with a combination of small-angle neutron scattering (SANS) and diffusing wave spectroscopy (DWS). Contrary to single light scattering, DWS provides dynamic information on length scales, from 1 to 100 nm, comparable to SANS. This offers a unique range of accessible length and time scales perfectly suited for the (noninvasive) investigation of highly concentrated systems. By this we obtain valuable information about the structural properties and the short-time diffusion of electrostatically stabilized, but strongly screened, hard-sphere-like colloidal suspensions with volume fractions up to 30%. We furthermore discuss the consequences of local structural ordering on the optical properties, such as optical density and polarization. Quantitative agreement is found when comparing transmission measurements (optical density) with parameter-free numerical calculations based on the structural characterization from SANS.

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.

The Application of Diffusing-Wave Spectroscopy to Monitor the Phase Behavior of Emulsion-Polysaccharide Systems

Droplet aggregation is an important cause of instability in emulsions because it may, on one hand, lead to an increased creaming rate, resulting in fast separation of a concentrated emulsion phase (creamed layer). On the other hand, it may also lead to the formation of a stabilizing, droplet-based network. Early detection of instability is often difficult due to the high turbidity and viscosity of more concentrated food emulsions. The applicability of diffusing-wave spectroscopy (DWS) for monitoring droplet aggregation and creaming was studied using a model system consisting of a protein-stabilized emulsion, to which a soluble polymer ("thickener") was added. This addition leads to an increased solvent viscosity and may induce droplet aggregation. In addition, the redistribution process of emulsion droplets in aggregating concentrated emulsions was directly observed by confocal scanning laser microscopy (CSLM). By DWS the decrease of the droplet mobility caused by the viscosity increase of the continuous phase could be separated from the effect of droplet aggregation. Moreover, a distinction could be made between aggregation, leading to increased creaming rates and that leading to the formation of a stabilizing droplet network. The potential of DWS for in situ measurement of the stability of concentrated emulsions is discussed. Copyright 2000 Academic Press.

Optical Polydispersity and Contrast Variation Effects in Colloidal Dispersions

We present a theoretical study on the effect of refractive index variations on static and dynamic light scattering in size-polydisperse suspensions of sterically and charge-stabilized colloidal particles with an internal optical structure (core-shell model) and size-dependent refractive indices. The equilibrium microstructure and the short-time dynamics of these optically, size-, and interaction-polydisperse systems are calculated using hypernetted chain and Percus-Yevick integral equation schemes. Our calculations show that, close to an index matching point, the scattered intensity I(k), the measurable structure factor SM(k), and the measurable hydrodynamic function HM(k) become very sensitive to the refractive index contrast with respect to the solvent. For this purpose, various definitions of index matching points are analyzed, and the strong relative enhancement of the incoherent part of the scattered intensity close to the matching points is discussed. For charge-stabilized systems we show that the anomalous behaviour of I(k) and HM(k) in the matching regime of the solvent refractive index can be well described by a simple approximative scheme, which can be easily implemented. Consequences of our study for scattering experiments aimed to determine particle sizes or structural properties of colloidal dispersions are discussed. Copyright 1998 Academic Press.