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We present a comprehensive study of the slip and flow of concentrated colloidal suspensions using cone-plate rheometry and simultaneous confocal imaging. In the colloidal glass regime, for smooth, non-stick walls, the solid nature of the suspension causes a transition in the rheology from Herschel-Bulkley (HB) bulk flow behavior at large stress to a Bingham-like slip behavior at low stress, which is suppressed for sufficient colloid-wall attraction or colloid-scale wall roughness. Visualization shows how the slip-shear transition depends on gap size and the boundary conditions at both walls and that partial slip persist well above the yield stress. A phenomenological model, incorporating the Bingham slip law and HB bulk flow, fully accounts for the behavior. Microscopically, the Bingham law is related to a thin (sub-colloidal) lubrication layer at the wall, giving rise to a characteristic dependence of slip parameters on particle size and concentration. We relate this to the suspensions osmotic pressure and yield stress and also analyze the influence of van der Waals interaction. For the largest concentrations, we observe non-uniform flow around the yield stress, in line with recent work on bulk shear-banding of concentrated pastes. We also describe residual slip in concentrated liquid suspensions, where the vanishing yield stress causes coexistence of (weak) slip and bulk shear flow for all measured rates.
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We image the flow of a nearly random close packed, hard-sphere colloidal suspension (a `paste) in a square capillary using confocal microscopy. The flow consists of a `plug in the center while shear occurs localized adjacent to the channel walls, reminiscent of yield-stress fluid behavior. However, the observed scaling of the velocity profiles with the flow rate strongly contrasts yield-stress fluid predictions. Instead, the velocity profiles can be captured by a theory of stress fluctuations originally developed for chute flow of dry granular media. We verified this behavior both for smooth and rough boundary conditions.
We study the flow of concentrated hard-sphere colloidal suspensions along smooth, non-stick walls using cone-plate rheometry and simultaneous confocal microscopy. In the glass regime, the global flow shows a transition from Herschel-Bulkley behavior at large shear rate to a characteristic Bingham slip response at small rates, absent for ergodic colloidal fluids. Imaging reveals both the `solid microstructure during full slip and the local nature of the `slip to shear transition. Both the local and global flow are described by a phenomenological model, and the associated Bingham slip parameters exhibit characteristic scaling with size and concentration of the hard spheres.
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 Mazurs method [Physica 120A, 388 (1983) & 126A, 349 (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 Mazurs $deltagamma$-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 $deltagamma$ 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 $40%$.
We review recent advances in imaging the flow of concentrated suspensions, focussing on the use of confocal microscopy to obtain time-resolved information on the single-particle level in these systems. After motivating the need for quantitative (confocal) imaging in suspension rheology, we briefly describe the particles, sample environments, microscopy tools and analysis algorithms needed to perform this kind of experiments. The second part of the review focusses on microscopic aspects of the flow of concentrated model hard-sphere-like suspensions, and the relation to non-linear rheological phenomena such as yielding, shear localization, wall slip and shear-induced ordering. Both Brownian and non-Brownian systems will be described. We show how quantitative imaging can improve our understanding of the connection between microscopic dynamics and bulk flow.
We study the pressure-driven flow of concentrated colloids confined in glass micro-channels at the single particle level using fast confocal microscopy. For channel to particle size ratios $a/bar{D} lesssim 30$, the flow rate of the suspended particles shows fluctuations. These turn into regular oscillations for higher confinements ($a/bar{D} simeq 20$). We present evidence to link these oscillations with the relative flow of solvent and particles (permeation) and the effect of confinement on shear thickening.
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