Bidisperse Colloidal Suspensions Research Articles

Simulation of bidisperse colloidal centrifugal sedimentation using a mixture viscosity model

Understanding the sedimentation behavior of bidisperse colloidal suspensions is critical in determining their stability and separation. While centrifugation is often used to accelerate separation, the settling of bidisperse colloids and their phase separation under these conditions is complex and difficult to predict explicitly. As an alternative, this work proposes a one-dimensional advection-diffusion model that uses an effective maximum volume fraction with a bidisperse viscosity scheme, which reflects important characteristics of bidisperse sedimentation while remaining computationally efficient. The influence of Derjaguin–Landau–Verwey–Overbeek interactions on packing fraction and dispersion viscosity is also considered. A numerical implementation is described using an adaptive finite-difference solver, which can be used for concentration profile and settling rate prediction of both species under variable acceleration. Validation experiments with silica suspensions in two size ratios (500:800 and 100:500 nm) and various total concentrations are performed using an analytical centrifuge, with results also being compared to Richardson–Zaki empirical predictions. The model is shown to be a very good fit to the data for both size ratio dispersions at three mixing ratios, with differences <10%. Slightly higher levels of variation were detected for the 500:800 nm system, owing to the smaller size ratio and resulting greater effect of uncounted secondary hydrodynamic factors, which enables the limits of the mixture viscosity model to be established. Nevertheless, this work highlights that mixture viscosity modeling combined with effective maximum volume fraction modifications can provide critical insights into the effect of bidisperse suspension dynamics on separation efficiencies.

Characterising the sedimentation of bidisperse colloidal silica using analytical centrifugation

This study investigates the settling behaviour of bidisperse colloidal silica suspensions in two different size ratios (100:500 nm and 500:800 nm) with various mixture ratios and volume fractions, using an analytical photocentrifuge. For dilute systems, translation of settling rate profiles to size distributions resulted in more accurate measurements for both monodisperse and bidisperse systems than using dynamic light scattering, in comparison to SEM. However, a critical limitation was also observed, as distinction between upper (smaller particle) and lower (larger particle) interfaces could only be measured for total volume fractions <∼0.02. For 500:800 mixtures, results were compared with Richardson-Zaki and modified Batchelor model predictions. The Batchelor model proved more accurate at predicting the lower interface rate, while both models over predicted the upper interface, likely due to increased drag that was most evident with higher fractions of smaller particles. For 100:500 cases, higher centrifugal rotation speeds were required to settle the 100 nm particles, and the influence of Brownian motion was evident. It was also found that the smaller particles obtained a lower initial settling rate than its terminal velocity, due to induced anisotropic effects or backflow from the 500 nm fraction, which was again more evident with a greater proportion of smaller particles.

Stationary and oscillatory convection in bidisperse colloidal suspension

Stationary and oscillatory convection in bidisperse colloidal suspension

Onset of Convection in Bidisperse Colloidal Suspension

Onset of Convection in Bidisperse Colloidal Suspension

Simulation Study of Structural and Dynamic Properties of Bi-Disperse Colloidal Suspensions

We used Brownian Dynamic simulation to study structural and dynamic properties of bi-disperse colloidal suspensions. The size ratio of large to small particles in the bi-disperse colloidal suspension is set at 5:1 and 10:1. We studied the interaction of aggregates (clusters) formed through DLVO (Derjaguin, Landau, Verwey and Overbeek) and soft sphere interactions in a bi-disperse suspension. The dynamic properties of bi-disperse is correlated by varying the size ratio of bi-disperse particles, it is found that the mobility is decreased at size ratio of large to small particles is 5:1. This is despite the percolating particle gels formation was disrupted by larger particles at higher size ratio.

Segregation in Drying Binary Colloidal Droplets.

When a colloidal suspension droplet evaporates from a solid surface, it leaves a characteristic deposit in the contact region. These deposits are common and important for many applications in printing, coating, or washing. By the use of superamphiphobic surfaces as a substrate, the contact area can be reduced so that evaporation is almost radially symmetric. While drying, the droplets maintain a nearly perfect spherical shape. Here, we exploit this phenomenon to fabricate supraparticles from bidisperse colloidal aqueous suspensions. The supraparticles have a core–shell morphology. The outer region is predominantly occupied by small colloids, forming a close-packed crystalline structure. Toward the center, the number of large colloids increases and they are packed amorphously. The extent of this stratification decreases with decreasing the evaporation rate. Complementary simulations indicate that evaporation leads to a local increase in density, which, in turn, exerts stronger inward forces on the larger colloids. A comparison between experiments and simulations suggest that hydrodynamic interactions between the suspended colloids reduce the extent of stratification. Our findings are relevant for the fabrication of supraparticles for applications in the fields of chromatography, catalysis, drug delivery, photonics, and a better understanding of spray-drying.

Differential dynamic microscopy of bidisperse colloidal suspensions

Research tasks in microgravity include monitoring the dynamics of constituents of varying size and mobility in processes such as aggregation, phase separation, or self-assembly. We use differential dynamic microscopy, a method readily implemented with equipment available on the International Space Station, to simultaneously resolve the dynamics of particles of radius 50 nm and 1 μm in bidisperse aqueous suspensions. Whereas traditional dynamic light scattering fails to detect a signal from the larger particles at low concentrations, differential dynamic microscopy exhibits enhanced sensitivity in these conditions by accessing smaller wavevectors where scattering from the large particles is stronger. Interference patterns due to scattering from the large particles induce non-monotonic decay of the amplitude of the dynamic correlation function with the wavevector. We show that the position of the resulting minimum contains information on the vertical position of the particles. Together with the simple instrumental requirements, the enhanced sensitivity of differential dynamic microscopy makes it an appealing alternative to dynamic light scattering to characterize samples with complex dynamics.

Hydrodynamic segregation in a bidisperse colloidal suspension in microchannel flow: A theoretical study.

Colloids in suspension exhibit shear-induced migration towards regions of low viscous shear. In dense bidisperse colloidal suspensions under pressure driven flow large particles can segregate in the center of a microchannel and the suspension partially demixes. To develop a theoretical understanding of these effects, we formulate a phenomenological model for the particle currents based on the work of Phillips et al. [Phys. Fluids 4, 30 (1992)]. We also simulate hard spheres under pressure-driven flow in two and three dimensions using the mesoscale simulation technique of multi-particle collision dynamics. Using a single fit parameter for the intrinsic diffusivity, our theory accurately reproduces the simulated density profiles across the channel. We present a detailed parameter study on how a monodisperse suspension enriches the channel center and quantitatively confirm the experimental observation that a binary colloidal mixture partially segregates into its two species. In particular, we always find a strong accumulation of large particles in the center. Qualitative differences between two and three dimensions reveal that collective diffusion is more relevant in two dimensions.

Hierarchical microstructures formed by bidisperse colloidal suspensions within colloid-in-liquid crystal gels.

Past studies have reported that colloids of a single size dispersed in the isotropic phase of a mesogenic solvent can form colloid-rich networks (and gels) upon thermal quenching of the system across the isotropic-nematic phase boundary of the mesogens. Herein we report the observation and characterization of complex hierarchical microstructures that form when bidisperse colloidal suspensions of nanoparticles (NPs; iron oxide with diameters of 188 ± 20 nm or poly(methyl methacrylate) with diameters of 150 ± 15 nm) and microparticles (MPs; polystyrene with diameters of 2.77 ± 0.20 μm) are dispersed in the isotropic phase of 4-pentyl-4'-cyanobiphenyl (5CB) and thermally quenched. Specifically, we document microstructuring that results from three sequential phase separation processes that occur at distinct temperatures during stepwise cooling of the ternary mixture from its miscibility region. The first phase transition demixes the system into coexisting MP-rich and NP-rich phases; the second promotes formation of a particle network within the MP-rich phase; and the third, which coincides with the isotropic-to-nematic phase transition of 5CB, produces a second colloidal network within the NP-rich phase. We quantified the dynamics of each demixing process by using optical microscopy and Fourier transform image analysis to establish that the phase transitions occur through (i) surface-directed spinodal decomposition, (ii) spinodal decomposition, and (iii) nucleation and growth, respectively. Significantly, the observed series of phase transitions leads to a hierarchical organization of cellular microstructures not observed in colloid-in-liquid crystal gels formed from monodisperse colloids. The results of this study suggest new routes to the synthesis of colloidal materials with hierarchical microstructures that combine large surface areas and organized porosity with potential applications in catalysis, separations, chemical sensing, or tissue engineering.

Dielectric spectroscopy of bidisperse colloidal suspensions

Dielectric spectroscopy is used to measure the complex permittivity of bidisperse colloidal suspensions over the frequency range 2.5kHz⩽ω/2π⩽10MHz using the spectrometer design of Hollingsworth and Saville (A.D. Hollingsworth, D.A. Saville, J. Colloid Interface Sci., 2003). Dielectric spectra of monodisperse polystyrene spheres of two diameters (530nm and 1μm) are fit to electrokinetic theory using the surface charge density as an adjustable parameter. Quantitative agreement is found in the dielectric increment and also for the conductivity increment, after considering the effect of added counterions and nonspecific adsorption. Bidisperse suspension spectra are a linear superposition of each particle’s dielectric response. The results provide a simple method to extend standard electrokinetic theory based on a single particle size to dilute suspensions with many particle sizes and verify the sensitivity of the spectrometer.

Irreversible Rearrangements, Correlated Domains, and Local Structure in Aging Glasses

Bidisperse colloidal suspensions of temperature-sensitive microgel spheres were quenched from liquid to glass states by a rapid temperature drop, and then the glass was permitted to age. Irreversible rearrangements, events that dramatically change a particle's local environment, were observed to be closely related to dynamic heterogeneity. The rate of these irreversible events decreased during aging and the the number of particles required to move as part of these irreversible rearrangements increased. Thus, the slowing dynamics of aging were governed by growing, correlated domains of particles. Additionally, short-range order developed, and a spatial decay length scale associated with orientational order was found to grow during aging.

Effect of small particles on the near-wall dynamics of a large particle in a highly bidisperse colloidal solution

We consider the hydrodynamic effect of small particles on the dynamics of a much larger particle moving normal to a planar wall in a highly bidisperse dilute colloidal suspension of spheres. The gap h(0) between the large particle and the wall is assumed to be comparable to the diameter 2a of the smaller particles so there is a length-scale separation between the gap width h(0) and the radius of the large particle b>>h(0). We use this length-scale separation to develop a new lubrication theory which takes into account the presence of the smaller particles in the space between the larger particle and the wall. The hydrodynamic effect of the small particles on the motion of the large particle is characterized by the short time (or high frequency) resistance coefficient. We find that for small particle-wall separations h(0), the resistance coefficient tends to the asymptotic value corresponding to the large particle moving in a clear suspending fluid. For h(0)>>a, the resistance coefficient approaches the lubrication value corresponding to a particle moving in a fluid with the effective viscosity given by the Einstein formula.

A New Model System for Diffusion NMR Studies of Concentrated Monodisperse and Bidisperse Colloids

A method to prepare monodisperse and simultaneously NMR-visible and fluorescent colloidal particles is described, and a systematic approach to obtain spectrally resolved diffusion coefficient for every component in a monodisperse colloidal suspension is presented. We also prepared bidisperse colloidal suspensions, where each colloid component has a distinct NMR spectral signature, and obtained the diffusion coefficients of both colloid species simultaneously in concentrated colloidal suspensions, with volume fractions between 20 and 50%. The colloidal model system developed in this work enables the study of colloidal phase behavior in binary mixtures for different number and size ratios.

Depletion forces near a soft surface

We investigate excluded-volume effects in a bidisperse colloidal suspension near a flexible interface. Inspired by a recent experiment by Dinsmore et al. [Phys. Rev. Lett. 80, 409 (1998)], we study the adsorption of a mesoscopic bead on the surface and show that depletion forces could in principle lead to particle encapsulation. We then consider the effect of surface fluctuations on the depletion potential itself and construct the density profile of a polymer solution near a soft interface. Surprisingly we find that the chains accumulate at the wall, whereas the density displays a deficit of particles at distances larger than the surface roughness. This nonmonotonic behavior demonstrates that surface fluctuations can have major repercussions on the properties of a colloidal solution. On average, the additional contribution to the Gibbs adsorbance is negative. The amplitude of the depletion potential between a mesoscopic bead and the surface increases accordingly.

Investigation of Particle Interactions in Dense Colloidal Suspensions Using Frequency Domain Photon Migration: Bidisperse Systems

The frequency domain photon migration (FDPM) technique was employed for investigation of particle interactions of dense, bidisperse, polystyrene samples of differring volume ratios of small to large particle sizes. The particle interactions of bidisperse systems were evaluated from the angular integrated structure factors, 〈S(q)〉 , which were extracted from FDPM measurements of scattering properties at high volume fractions ranging from 0.1 to 0.3. The FDPM-measured 〈S(q)〉 were then compared with theoretical predictions using the full binary hard sphere Percus−Yevick (HSPY) model, as well as the decoupling approximation (DA) and the local monodisperse approximation (LMA) models. The influence of differing volume ratios of colloid sizes on structure factors at differing wavelengths was also investigated. Results show that the interactions between small and large particles significantly impact the structure factors as well as the scattering properties in dense bidisperse colloidal suspensions. Furthermore, ...

Depletion and Structural Forces between Two Macrosurfaces Immersed in a Bidisperse Colloidal Suspension

Recent experiments on the thinning of liquid films formed from colloidal suspensions carried out in our laboratory [Nikolov, A., and Wasan, D. T., J. Colloid Interface Sci.133, 1 (1989); Langmuir8, 2985 (1992)] have revealed the pronounced effect of the presence of bidisperse-sized particles on the film stability. To shed more light on the role of the size bidispersity on the film properties, we performed a statistical mechanics study of a model system that consists of a binary hard-sphere mixture with a size ratio of 1 : 10 between two planar surfaces. The variations of the particle local densities, excess surface coverage, film disjoining pressure, and film interaction energy per unit area with separation between the surfaces in the presence of monodisperse and bidisperse particles have been investigated. A repulsive depletion interaction (depletion stabilization) between the surfaces in the case of a bidisperse suspension has been observed at separations of about one layer of the larger particles.

Assembly of Binary Colloidal Structures via Specific Biological Adhesion

We present a novel approach to the fabrication of binary colloidal materials where specific biomolecular cross-linking drives the self-assembly of bidisperse colloidal suspensions. In particular, we have employed low-affinity immune system carbohydrate-selectin interactions to mediate the heterotypic assembly of binary colloidal structures. Using small (0.94 μm) and larger (5.5 μm) diameter particles coated with complementary chemistry, we show that a progressive series of structures, such as colloidal micelles (a large particle coated with smaller particles), colloidal clusters, rings, and elongated chains, can be made by decreasing the number fraction, NA/NB, of small (A) to large (B) particles (200 ≥ NA/NB ≥ 2) at low total volume fraction (φΤ = 10-4−10-3). The assembly is due to specific molecular interactions, as control experiments in which the molecules are blocked or eliminated do not lead to the assembly of these structures. The size of the structures can be modulated by time or total volume frac...

Triplet depletion forces from density functional optimization

A novel density functional theory optimization technique, based on Rosenfeld's “fundamental measure ” theory for hard-core particles and the use of an adaptive real-space grid, is developed to investigate highly asymmetric binary mixtures of hard spheres as models of bidisperse colloidal suspensions. The method is applied to the calculation of pair and triplet depletion forces between large colloids in a bath of much smaller colloidal particles. The computed pair forces are in generally good agreement with theoretical predictions and previous Monte Carlo work. The triplet forces, explicitly calculated for the first time, are an order of magnitude weaker than the much-studied pair interactions, and appear to be attractive.

Osmotic depletion, non-additivity and phase separation

A brief discussion is given of the subtle interplay between non-additivity of hard sphere diameters and the osmotic depletion effect, and their influence on phase separation in bidisperse colloidal suspensions.