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We study the capillary forces acting on sub-millimeter particles (0.02−0.6 mm) trapped at a liquid−liquid interface due to gravity-induced interface deformations. An analytical procedure is developed to solve the linearized capillary (Young−Laplace) equation and calculate the forces for an arbitrary number of particles, allowing also for a background curvature of the interface. The full solution is expressed in a series of Bessel functions with coefficients determined by the contact angle at the particle surface. For sub-millimeter spherical particles, it is shown that the forces calculated using the lowest order term of the full solution (linear superposition approximation; LSA) are accurate to within a few percents. Consequently the many particle capillary force is simply the sum of the isolated pair interactions. To test these theoretical results, we use video microscopy to follow the motion of individual particles and pairs of interacting particles at a liquid−liquid interface with a slight macroscopic background curvature. Particle velocities are determined by the balance of capillary forces and viscous drag. The measured velocities (and thus the capillary forces) are well described by the LSA solution with a single fitting parameter.

Flow electrification in nonaqueous suspensions has been scarcely reported in the literature but can significantly affect colloidal stability and (phase) behavior, perhaps even without being recognized. We have observed it in shear flow experiments on concentrated binary suspensions of hydrophobized silica particles in chloroform. In this low-polarity solvent, electrical charges on the large-particles' surfaces manifest themselves via long-ranged forces, because hardly any screening can take place through counterions. By shearing the suspension for a prolonged time, we could demonstrate that the effective interactions between the large particles change from weakly attractive (due to the small particles) to strongly repulsive (due to acquired Coulomb interactions). One of the conditions required for flow electrification was the presence of a glass surface in the shear cell. A spectacular manifestation of the phenomenon was observed with confocal video microscopy. First, the formation of large-particle aggregates was seen, while subsequently (over a long shearing time) the aggregates disintegrated into small entities, mostly primary particles. The spatial distribution of these entities in the quiescent state after stopping the flow showed evidence for acquired long-range repulsion. The occurrence of flow electrification was further corroborated by control experiments, where no flow was imposed, antistatic agent was added, or the glass bottom was coated with a conducting (indium tin oxide, ITO) layer:  here, the aggregates kept growing until they became very large. To further diagnose the phenomenon, we have also done experiments in which an external electric field was applied (via the ITO layer) to an aggregated suspension. When the lower electrode was given the lowest potential, the aggregates were found to move away from the bottom and disintegrate. The qualitative similarity hereof with the flow electrification experiment suggests that in the latter, the glass acquired negative charges. After prolonged application of an external electric field, we observed segregation into regions enriched in large particles and regions completely depleted of them. In the quiescent fluid these regions exist as isolated units, but in shear flow they merge into bands, a behavior which resembles shear banding.

We used video microscopy to study the behavior of aggregating suspensions in shear flow. Suspensions consisted of 920 nm diameter silica spheres, dispersed in a methanol/bromoform solvent, to which poly(ethylene glycol) (M = 35.000 g) was added to effect weak particle aggregation. With our solvent mixture, the refractive index of the particles could be closely matched, to allow microscopic observations up to 80 μm deep into the suspension. Also the mass density is nearly equal to that of the particles, thus allowing long observation times without problems due to aggregate sedimentation. Particles were visualized via fluorescent molecules incorporated into their cores. Using a fast confocal scanning laser microscope made it possible to characterize the (flowing) aggregates via their contour-area distributions as observed in the focal plane. The aggregation process was monitored from the initial state (just after adding the polymer), until a steady state was reached. The particle volume fraction was chosen at 0.001, to obtain a characteristic aggregation time of a few hundred seconds. On varyiation of polymer concentration, cP (2.2−12.0 g/L), and shear rate, γ (3−6/s), it was observed that the volume-averaged size, Dv, in the steady state became larger with polymer concentration and smaller with shear rate. This demonstrates that the aggregate size is set by a competition between cohesive forces caused by the polymer and rupture forces caused by the flow. Also aggregate size distributions were be measured (semiquantitatively). Together with a description for the internal aggregate structure they allowed a modeling of the complete aggregation curve, from t = 0 up to the steady state. A satisfactory description could be obtained by describing the aggregates as fractal objects, with Df = 2.0, as measured from CSLM images after stopping the flow. In this modeling, the fitted characteristic breakup time was found to increase with cP.

Concentrated suspensions of hard spheres with a bimodal size distribution provide a system with a very rich behavior, which largely still has to be explored. We present here an experimental study, focused at the kinetics of aggregation between the large spheres, as caused by the presence of the small spheres. At high concentrations of the small particles, the pair potential between the large spheres is considered to contain not only an attractive well in the contact region but also a repulsive barrier at larger separations. This barrier was confirmed to be present in our system and was seen to have a profound influence on the initial aggregation rate. To test the adequacy of the binary hard sphere (BHS) model to describe our system, we have performed quantitative measurements and modeling of the rate of aggregate formation. Three-dimensional video microscopy, with a spatial resolution at the level of single (large) particles, allowed us to determine the time evolutions for monomer, dimer, and trimer number densities. By fitting these to theoretical model expressions, characteristic times were extracted and translated into stability ratios. The experiments were performed with colloidal silica spheres, having respective diameters of 920 and 50 nm for the large and small particles. Particle volume fractions ranged from 0.01 to 0.35% for the large particles and from 30 to 40% for the small particles. Besides experiments under quiescent conditions, we also performed measurements in flow, for Peclet numbers up to 20. The time evolutions of the various aggregation number densities were found to correspond well with Smoluchowski theory. The stability ratio W was found to increase sharply with small-particle concentration, in correspondence with the predictions. The magnitudes of the experimental W were found to be 4−11 (2−3) times larger than those predicted for a BHS in quiescent fluid (under shear).

Linear and nonlinear rheological behavior of a suspension of polymer-coated colloidal spheres was experimentally investigated for systems with a polymer layer thickness comparable to the core size of the particles. The low shear plateau of the flow curves increases 5 orders of magnitude with increasing concentration in a very narrow range around a critical concentration. Below this critical concentration, the dependence of the low shear viscosity on concentration differs significantly from hard sphere behavior. Above the critical concentration, low shear viscosity plateaus were observed, too, followed by an extreme shear thinning in which the shear stress was virtually constant. In this concentration range, hysteresis was observed. The behavior at high shear rates was captured with lubrication-based modeling. Viscoelastic behavior could only be measured at concentrations above the transition. The observed storage moduli were virtually frequency independent. Their concentration dependence was satisfactorily described with a model based on the work of Elliott and Russel [see:  J. Rheol. 1998, 42, 361.]. An essential ingredient of this model is the radial pair distribution function, g(r12). Using Monte Carlo simulations to calculate g(r12), both ordered and disordered structures were found above a concentration close to the critical concentration found from the flow curves. These structure differences caused only a marginal difference in calculated values for the storage modulus.

The elastic moduli of polymerically stabilized suspensions consisting of colloidal silica particles coated with endgrafted PDMS (Mn = 80 000) in heptane, were measured as a function of concentration. And the elastic modulus at high frequency %@mt;sys@%%@ital@%G%@rsf@%%@/xs;55;%lnwidth@%‘%@/xs;63;(%lnwidth-x55)@%%@mh;-x63@%%@sb@%∞%@sbx@%%@mx@% was quantitatively described by model calculations with microscopic parameters. In the modeling of %@mt;sys@%%@ital@%G%@rsf@%%@/xs;55;%lnwidth@%‘%@/xs;63;(%lnwidth-x55)@%%@mh;-x63@%%@sb@%∞%@sbx@%%@mx@% we essentially followed the method of Elliott and Russel [Elliott, S. L.; Russel, W. B. J. Rheology 1998, 42, 361]. To suit our case of strongly curved polymer layers, we made adaptations in the description of both the pair potential and hydrodynamic interactions. Anticipating that the predicted %@mt;sys@%%@ital@%G%@rsf@%%@/xs;55;%lnwidth@%‘%@/xs;63;(%lnwidth-x55)@%%@mh;-x63@%%@sb@%∞%@sbx@%%@mx@% is sensitive to the modeling of the polymer brush, we explored two different models to predict the pair potential and the polymer layer thickness:  a numerical self-consistent field lattice model [Wijmans, C. M.; Zhulina, E. B. Macromolecules 1993, 26, 7214] and an analytical method based on the approach of Li and Witten [Li, H.; Witten, T. A. Macromolecules 1994, 27, 449]. The polymer models were used separately in the model calculations for %@mt;sys@%%@ital@%G%@rsf@%%@/xs;55;%lnwidth@%‘%@/xs;63;(%lnwidth-x55)@%%@mh;-x63@%%@sb@%∞%@sbx@%%@mx@% with the magnitude of their parameters obtained from (elaborate) characterizations of the particles. Both models result in a quantitative description of the experimental %@mt;sys@%%@ital@%G%@rsf@%%@/xs;55;%lnwidth@%‘%@/xs;63;(%lnwidth-x55)@%%@mh;-x63@%%@sb@%∞%@sbx@%%@mx@% and thickness of the polymer layer.

Rheological behavior of a dispersion of small nearly-unilamellar phospholipid bilayer vesicles has been investigated. We conducted steady-state shear experiments and linear viscoelastic experiments. In the dilute and semidilute regime the rheological behavior is similar to that of a hard-sphere dispersion as reported in the literature for viscoelastic measurements, but now also observed in steady shear experiments. The effect of the main acyl-chain phase transition, taking place at 23 °C, can be described with an increase of the effective volume fraction. As a result, with temperature variation one can obtain effective volume fractions larger than the maximum packing fraction for hard spheres. Near and above the maximum packing fraction a dynamic yield stress τy and a frequency independent storage modulus G‘ develop. In this concentration regime the rheological behavior is determined by the interplay between vesicle deformation and the intervesicle interaction, and so far, there is no indication which phenomenon is dominant. A comparison with recently reported measurements suggests that G‘ is proportional to a^-3, where a is the vesicle radius. Furthermore, we show that τy ≈ γcG‘ which is in agreement with theory. Here τy is the dynamic yield stress and γc the critical strain which indicates the transition to nonlinear behavior in a viscoelastic experiment. There is a striking resemblance between our high concentration results and those reported in literature for vesicles in the so-called onion phase. To the best of our knowledge this is the first rheological study for concentrated nearly-unilamellar vesicle dispersions with volume fraction and temperature as variables.