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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 $40%$.
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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.
We present a comprehensive computational study of the short-time transport properties of bidisperse neutral colloidal suspensions and the corresponding porous media. Our study covers bidisperse particle size ratios up to $4$, and total volume fractions up to and beyond the monodisperse hard-sphere close packing limit. The many-body hydrodynamic interactions are computed using conventional Stokesian Dynamics (SD) via a Monte-Carlo approach. We address suspension properties including the short-time translational and rotational self-diffusivities, the instantaneous sedimentation velocity, the wavenumber-dependent partial hydrodynamic functions, and the high-frequency shear and bulk viscosities; and porous media properties including the permeability and the translational and rotational hindered diffusivities. We carefully compare the SD computations with existing theoretical and numerical results. For suspensions, we also explore the range of validity of various approximation schemes, notably the Pairwise Additive (PA) approximations with the Percus-Yevick structural input. We critically assess the strengths and weaknesses of the SD algorithm for various transport properties. For very dense systems, we discuss in detail the interplay between the hydrodynamic interactions and the structures due to the presence of a second species of a different size.
Discontinuous shear thickening (DST) observed in many dense athermal suspensions has proven difficult to understand and to reproduce by numerical simulation. By introducing a numerical scheme including both relevant hydrodynamic interactions and granularlike contacts, we show that contact friction is essential for having DST. Above a critical volume fraction, we observe the existence of two states: a low viscosity, contactless (hence, frictionless) state, and a high viscosity frictional shear jammed state. These two states are separated by a critical shear stress, associated with a critical shear rate where DST occurs. The shear jammed state is reminiscent of the jamming phase of granular matter. Continuous shear thickening is seen as a lower volume fraction vestige of the jamming transition.
We report on a comprehensive theory-simulation-experimental study of collective and self-diffusion in suspensions of charge-stabilized colloidal spheres. In simulation and theory, the spheres interact by a hard-core plus screened Coulomb pair potential. Intermediate and self-intermediate scattering functions are calculated by accelerated Stokesian Dynamics simulations where hydrodynamic interactions (HIs) are fully accounted for. The study spans the range from the short-time to the colloidal long-time regime. Additionally, Brownian Dynamics simulation and mode-coupling theory (MCT) results are generated where HIs are neglected. It is shown that HIs enhance collective and self-diffusion at intermediate and long times, whereas at short times self-diffusion, and for certain wavenumbers also collective diffusion, are slowed down. MCT significantly overestimate the slowing influence of dynamic particle caging. The simulated scattering functions are in decent agreement with our dynamic light scattering (DLS) results for suspensions of charged silica spheres. Simulation and theoretical results are indicative of a long-time exponential decay of the intermediate scattering function. The approximate validity of a far-reaching time-wavenumber factorization of the scattering function is shown to be a consequence of HIs. Our study of collective diffusion is amended by simulation and theoretical results for the self-intermediate scattering function and the particle mean squared displacement (MSD). Since self-diffusion is not assessed in DLS measurements, a method to deduce the MSD approximately in DLS is theoretically validated.
Colloidal Laves phases (LPs) of $MgCu_2$ type are promising precursors for diamond structure photonic materials. They have been predicted for hard sphere binary mixtures, but not yet observed. We here report a time resolved static light scattering study on their formation in a binary mixture of buoyant experimental hard sphere approximants (size ratio $Gamma=0.77$, molar fraction of small spheres $x_S = 0.76$) for volume fractions between melting and the glass transition. In line with theoretical expectation, all samples form LPs of $MgZn_2$ structure on the time scale of weeks to months. $MgNi_2$ structures are absent, $MgCu_2$ structures and randomly stacked LPs prevail at elevated volume fraction. The addition of small amounts of non-adsorbing polymer switches the interaction to depletion attractive and results in significantly accelerated crystallization kinetics and improved crystal quality.
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