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.     

Kinetic analyses of colloidal crystallization in shear flow

Colloidal crystallization kinetics is studied in the shear flow of a suspension of colloidal silica spheres (110 nm in diameter), using a continuously-circulating type of stopped flow cell system. The crystallization rate from a suspension containing a small amount of nuclei and/or single crystals is high compared with that from a suspension containing no nuclei and/or single crystals. Crystal growth takes place at shear rates smaller than 3.4 s^–1 and at sphere concentrations higher than a volume fraction of 0.004.     

On the collision efficiency in polymer flocculation of colloidal particles

The applicability of the conventional collision efficiency approach for the case where the collision of colloidal particles is not necessary for the rate-determining step is examined. On the basis of a dynamical treatment, we show that the fundamental assumption made in the conventional analysis may lead to a significant error. Depending upon the ratio of the number of sites on the colloidal surfaces to the number of polymer molecules, and the relative magnitudes of the desorption rate constant and the adsorption rate constant, the collision efficiency calculated by the conventional analysis may be either underestimated or overestimated. The present approach yields the temporal variation of the distribution of the fractional surface coverage. It can be shown that if the number of colloidal particles is large, using the mean fractional surface coverage instead of the exact distribution of the fractional surface coverage is sufficient for the evaluation of the collision efficiency.     

Crystallization kinetics of colloidal spheres under stationary shear flow

A systematic experimental study of dispersions of charged colloidal spheres is presented on the effect of steady shear flow on nucleation and crystal growth rates. In addition, the nonequilibrium phase diagram as it relates to the melting line is measured. Shear flow is found to strongly affect induction times, crystal growth rates, and the location of the melting line. The main findings are that (1) the crystal growth rate for a given concentration exhibits a maximum as a function of the shear rate; (2) contrary to the monotonic increase in the growth rate with increasing concentration in the absence of flow, a maximum of the crystal growth rate as a function of concentration is observed for sheared systems; and (3) the induction time for a given concentration exhibits a maximum as a function of the shear rate. These findings are partly explained on a qualitative level.     

Breakage rate of colloidal aggregates in shear flow through stokesian dynamics

We study the first breakage event of colloidal aggregates exposed to shear flow by detailed numerical analysis of the process. We have formulated a model, which uses stokesian dynamics to estimate the hydrodynamic interactions among the particles in a cluster, van der Waals interactions and Born repulsion to describe the normal interparticle interactions, and the tangential interactions through discrete element method to account for contact forces. Fractal clusters composed of monodisperse spherical particles were generated using different Monte Carlo methods, covering a wide range of cluster masses (N(sphere) = 30-215) and fractal dimensions (d(f) = 1.8-3.0). The breakup process of these clusters was quantified for various flow magnitudes (γ), under both simple shear and extensional flow conditions, in terms of breakage rate constant (K(B)), mass distribution of the produced fragments (FMD, f(m,k)), and critical stable aggregate mass (N(c)), defined as the largest cluster mass that does not break under defined flow conditions. The breakage rate K(B) showed a power law dependence on the product of the aggregate size and the applied stress, with values of the corresponding exponents depending only on the aggregate fractal dimension and the type of flow field, whereas the prefactor of the power law relation also depends on the size of the primary particles comprising a cluster. The FMD was fitted by Schultz-Zimm distribution, and the parameter values showed an analogous dependence on the product of the aggregate size and the applied stress similar to the rate constant. Finally, a power law relation between the applied stress and corresponding largest stable aggregate mass was found, with an exponent value depending on the aggregate fractal dimension. This unique and detailed analysis of the breakage process can be directly utilized to formulate a breakage kernel used in solving population balance equations.     

Interaction of micrometer-scale particles with nanotextured surfaces in shear flow

Dynamic particle adhesion from flow over collecting surfaces with nanoscale heterogeneity occurs in important natural systems and current technologies. Accurate modeling and prediction of the dynamics of particles interacting with such surfaces will facilitate their use in applications for sensing, separating, and sorting colloidal-scale objects. In this paper, the interaction of micrometer-scale particles with electrostatically heterogeneous surfaces is analyzed. The deposited polymeric patches that provide the charge heterogeneity in experiments are modeled as 11-nm disks randomly distributed on a planar surface. A novel technique based on surface discretization is introduced to facilitate computation of the colloidal interactions between a particle and the heterogeneous surface based on expressions for parallel plates. Combining these interactions with hydrodynamic forces and torques on a particle in a low Reynolds number shear flow allows particle dynamics to be computed for varying net surface coverage. Spatial fluctuations in the local surface density of the deposited patches are shown responsible for the dynamic adhesion phenomena observed experimentally, including particle capture on a net-repulsive surface.     

Adsorption and desorption of colloidal particles on glass in a parallel plate flow chamber—Influence of ionic strength and shear rate

The adsorption and desorption rates of 736 nm diameter polystyrene particles on glass were studiedin situ using a parallel plate flow chamber and automated image analysis. Adsorption and desorption rates were measured simultaneously during deposition, enabling the determination of initial deposition rates, blocked areas per particle, desorption rate coefficients, and the number of adhering particles in the stationary state. Deposition experiments were done from suspensions with different potassium nitrate concentrations (1, 10 and 50 mM) and at varying shear rates (15 to 200 s^–1). The initial deposition rate, the desorption rate, the blocked area per particle and the number of adhering particles in the stationary state showed major variations with the shear rate and the ionic strength of the suspension. At low ionic strength, the number of adhering particles showed an oscillatory behavior in time, presumably due to a varying interaction between particle and collector surface. Blocked areas, determined from deposition kinetics, ranged 705 to 2374 cross-sections at low ionic strength, and from 10 to 564 at high ionic strength and corresponded well with those estimated from local pair distribution functions which were obtained from an analysis of the spatial arrangement of the adhering particles.     

Electrically induced colloidal clusters for generating shear mixing and visualizing flow in microchannels

When aqueous suspensions of 1 μm, negatively charged polystyrene particles are subject to a 1 kHz alternating electric field of strength greater than 7 kV(rms) m(-1), dynamic elliptical clusters of particles spontaneously form. With potential applications in microchannel fluidics in mind, we characterize how cluster formation and particle circulation, driven by induced dipole-dipole interactions, is critically dependent on time, field strength, electrolyte concentration, and cell thickness. Logarithmic growth of cluster size is observed, and particle velocity within the clusters is found to be proportional to cluster length. Increasing cell thickness from 10 to 60 μm increases the projected cluster area but decreases cluster aspect ratio as the result of changing particle dispersal rates. Clusters are shown to generate significant fluid shear suitable for microchannel mixing applications. These clusters are observed to distort under transverse fluid flow and, above a critical flow rate, to undergo a transition to form regularly spaced particle streams, which may be suitable for two-dimensional visualization of fluid flow.     

Analysis of colloidal particles V. size-exclusion chromatography of colloidal semiconductor particles

An HPLC technique for the size determination of colloidal cadmium sulphide and zinc sulphide in a diameter range from 20 down to 2 nm using silica with pore sizes from 30 to 100 nm is described. The growth of the particles during the run was suppressed by the addition of stabilizers to the eluent and by the use of reversed-phase silica as the stationary phase for inorganic stabilizers. The calibration of the column sets by electron microscopy resulted in a linear relationship between the logarithm of the particle diameter and the elution time. The analysis was carried out within 4–10 min. The lateral resolution lay between 1.3% for larger particles and 1.9% for smaller particles. Below a diameter of 13 nm these values were better than those found from electron microscopy. From the comparison of the calibration lines for various colloidal materials, the differences in their electrical double layers could be estimated. The limitations of the method are discussed and the size-exclusion chromatographic and electron microscopic methods are compared.     

Characterization of the flow of anisotropic colloidal particles using energy-dispersive X-ray diffraction

The technique of energy-dispersive X-ray diffraction to study the orientation of microscopic crystalline particles dispersed in a liquid has been described recently. This complements previous neutron diffraction studies by permitting measurements at higher spatial resolution. Work with synchrotron radiation and high-energy X-rays has allowed studies on liquid dispersions flowing in pipes with a thickness of about 1 cm and a spatial resolution of 100 mum. Kaolinite is often found as a dispersion of monocrystalline, microscopic plates. The crystallographic layer structure is commensurate with the particle shape: the 00l direction is normal to the plane of the plates. Measurements of diffraction of the flowing liquid dispersion in a pipe oriented in various directions to the incident beam can be used to deduce the average orientation and order parameters of the particles. The competing effects of alignment with walls and in flow fields were observed. Further work has measured the orientation near a bend in a pipe.     

Friction of rodlike particles adsorbed to a planar surface in shear flow

A planar hard surface covered with elongated stiff rodlike particles in shear flow is considered in the low-Reynolds-number regime assuming low particle surface coverage. The particles are modeled as straight chains of spherical beads. Multipole expansion of the Stokes equations (the accurate HYDROMULTIPOLE algorithm) is applied to evaluate the hydrodynamic force exerted by the fluid on the rodlike particles, depending on their shape, i.e., on the number of beads and their orientation with respect to the wall and to the ambient shear flow.     

Dynamics of colloidal particles in ice

We use x-ray photon correlation spectroscopy (XPCS) to probe the dynamics of colloidal particles in polycrystalline ice. During freezing, the dendritic ice morphology and rejection of particles from the ice created regions of high particle density, where some of the colloids were forced into contact and formed disordered aggregates. The particles in these high density regions underwent ballistic motion, with a characteristic velocity that increased with temperature. This ballistic motion is coupled with both stretched and compressed exponential decays of the intensity autocorrelation function. We suggest that this behavior could result from ice grain boundary migration.     

Nonlinear electrophoresis of colloidal particles

Advances over the past decade in nonlinear electrophoresis of charged, dielectric colloidal particles in aqueous electrolytes are reviewed. Here, the word nonlinear refers to the fact that the ratio of the electrophoretic speed of the particle to the magnitude of the applied electric field—the electrophoretic mobility—is not independent of field strength. This is in stark contrast to the vast majority of work on (linear) colloidal electrophoresis over the last century, where the mobility is assumed to be a material property dependent only on the particle–electrolyte combination. The present discussion is focused on: (i) experimental measurements of the field-dependent mobility; (ii) an asymptotic scheme to calculate the mobility in the common thin-Debye-layer limit; and (iii) computations of nonlinear electrophoresis from numerical solution of the electrokinetic equations. The article concludes with suggestions for future work in this evolving area of colloid science.     

Lateral migration and focusing of colloidal particles and DNA molecules under viscoelastic flow

Much difficulty has been encountered in manipulating small-scale materials, such as submicron colloidal particles and macromolecules (e.g., DNA and proteins), in microfluidic devices since diffusion processes due to thermal (Brownian) motion become more pronounced with decreasing particle size. Here, we present a novel approach for the continuous focusing of such small-scale materials. First, we successfully focused fluorescent submicron polystyrene (PS) beads along equilibrium positions in microchannels through the addition of a small amount water-soluble polymer [500 ppm poly(ethylene oxide) (PEO)]. Lateral migration velocity significantly depends upon the viscoelastic effect (Weissenberg number: Wi) and the aspect ratio of particle size to channel height (a/h). Interestingly, focusing using viscoelastic flows was also observed for flexible DNA molecules (λ-DNA and T4-DNA), which have radii of gyration (R(g)) of approximately 0.69 μm and 1.5 μm, respectively. This small-scale material manipulation using medium viscoelasticity will contribute to the design of nanoparticle separation and genomic mapping devices.     

Anisotropic colloidal particles in critical fluids

We consider anisotropic colloidal particles with dumbbell or lens shapes that are immersed in a critical binary fluid mixture. The orientation-dependent long-ranged universal interactions mediated by the critical solvent between a particle and a wall or between two particles are investigated for mesoscopic particle sizes small compared to the correlation length and interparticle distances. Exact results are obtained using a "small particle operator expansion." The amplitudes of the isotropic and anisotropic operators in the expansion depend on the size and aspect ratio of the dumbbell or lens and are determined by density profiles in the Ising model at the critical point in a wedge geometry with symmetry-breaking fixed-spin boundary conditions. Dumbbells and ellipsoids with a symmetry preserving surface are also considered.     

Preparation of monodispersed colloidal particles

The procedures and the backgrounds for the formation of monodispersed colloidal particles are reviewed, along with the personal view of the author's own, by classifying a wide variety of the systems. This article consists of the size distribution control for uniform colloidal systems with typical examples, including homogeneous and heterogeneous systems, and the crystal habit control of monodispersed particles.