Many-body hydrodynamic interactions in suspensions

We consider hydrodynamic interactions between N rigid bodies of arbitrary shape immersed in an incompressible fluid. We study the generalized mobility matrix relating the translational and rotational velocities and the symmetric force dipole moments to the forces, the torques and the strain of an incident flow field. We show that the elements of the mobility matrix may be obtained as matrix elements of an operator related to the friction kernel. This allows a multiple scattering expansion of the mobility matrix.     

Many-body hydrodynamic interactions in charge-stabilized suspensions

In this joint experimental-theoretical work we study hydrodynamic interaction effects in dense suspensions of charged colloidal spheres. Using x-ray photon correlation spectroscopy we have determined the hydrodynamic function H(q), for a varying range of electrosteric repulsion. We show that H(q) can be quantitatively described by means of a novel Stokesian dynamics simulation method for charged Brownian spheres, and by a modification of a many-body theory developed originally by Beenakker and Mazur. Very importantly, we can explain the behavior of H(q) for strongly correlated particles without resorting to the controversial concept of hydrodynamic screening, as was attempted in earlier work by Riese [Phys. Rev. Lett. 85, 5460 (2000)].     

Propagation of hydrodynamic interactions in colloidal suspensions

We describe direct measurements of the dynamics of two colloidal spheres before hydrodynamic interactions have had time to fully develop. We find that the dynamics of the two spheres are coupled at times significantly shorter than tau(nu), the time required for vorticity to diffuse between the two spheres. From the distance dependence of the measured coupling, we infer that hydrodynamic interactions develop in a sonic time scale.     

Effective screening of hydrodynamic interactions in charged colloidal suspensions

We investigate the hydrodynamic interaction in suspensions of charged colloidal silica spheres. The volume fraction as well as the range of the electrostatic repulsion between the spheres is varied. Using a combination of dynamic x-ray scattering, cross-correlated dynamic light scattering, and small angle x-ray scattering, the hydrodynamic function H(q) is determined experimentally. The effective hydrodynamic interactions are found to be screened, if the range of the direct interaction is relatively long and the static density correlations are strong. This observation of effective hydrodynamic screening is in marked contrast to hard-sphere-like systems.     

GPU-accelerated simulation of colloidal suspensions with direct hydrodynamic interactions

Solvent-mediated hydrodynamic interactions between colloidal particles can significantly alter their dynamics. We discuss the implementation of Stokesian dynamics in leading approximation for streaming processors as provided by the compute unified device architecture (CUDA) of recent graphics processors (GPUs). Thereby, the simulation of explicit solvent particles is avoided and hydrodynamic interactions can easily be accounted for in already available, highly accelerated molecular dynamics simulations. Special emphasis is put on efficient memory access and numerical stability. The algorithm is applied to the periodic sedimentation of a cluster of four suspended particles. Finally, we investigate the runtime performance of generic memory access patterns of complexity O(N ²) for various GPU algorithms relying on either hardware cache or shared memory.     

Modeling of concentrated suspensions

The constitutive equation of a concentrated suspension of spherical particles in a Newtonian medium is derived. To this end the method of local volume averaging is employed. To calculate the contribution of the particles to the stress tensor it is assumed that the stress generated in the interstitial holes between the particles is negligible compared to the stress generated in !he narrow gaps separating the particles. The use of the resulting expression is demonstrated with two examples on a cubical arrangement of particles: pure shear and simple shear. Furthermore, the validity of the lubrication approximation employed in this work is checked against the results derived by Nunan and Keller for periodic suspensions.     

Simulation method of colloidal suspensions with hydrodynamic interactions: fluid particle dynamics

We develop a new simulation method of colloidal suspensions, which we call a "fluid particle dynamics" (FPD) method. This FPD method, which treats a colloid as a fluid particle, removes the difficulties stemming from a solid-fluid boundary condition in the treatment of hydrodynamic interactions between the particles. The importance of interparticle hydrodynamic interactions in the aggregation process of colloidal particles is demonstrated as an example. This method can be applied to a wide range of problems in colloidal science.     

Sol-Gel transition of concentrated colloidal suspensions

Diffusing-wave spectroscopy (DWS) was used to follow the sol-gel transition of concentrated colloidal suspensions. We present a new technique based on a sandwich of two scattering cells aimed to overcome the problem of nonergodicity in DWS of solidlike systems. Using this technique we obtain quantitative information about the microscopic dynamics all the way from an aggregating suspension to the final gel, thereby covering the whole sol-gel transition. At the gel point a dramatic change of the particle dynamics from diffusion to a subdiffusive arrested motion is observed. A critical-power-law behavior is found for the time evolution of the maximum mean square displacement delta(2) probed by a single particle in the gel.     

Towardsab Initio simulations of concentrated suspensions

Determination of many-body interactions between particles of arbitrary shape in a viscous fluid is a key problem in the simulation of concentrated suspensions. Three-dimensional flows involving such complex fluid-solid boundaries are beyond the scope of spatial methods, even on supercomputers. Boundary integral methods convert the three-dimensional PDE to a two-dimensional integral equation. Unfortunately, conventional boundary methods yield Fredholm integral equations of the first kind, and dense linear systems which are too large for accurate solution. We have pursued a different boundary integral formulation, which yields Fredholm integral equations of the second kind; these arc amenable to iterative solution. The velocity representation involves a compact operator, so a discrete spectrum results. Wielandt deflations give dramatic reductions in the spectral radius and accurate solutions are obtained after only a few iterations (typically less than 10). An analytic construction of the spectrum for sphere sphere interactions confirms these numerical results. The mathematics is similar to that encountered in the mixing ofd-atomic orbitals to form bonding/antibonding molecular orbitals in transition metals. The memory-saving version of our code can be implemented directly on a dedicated MicroVAX to solve problems involving clusters of less than a dozen particles. For a fixed number of processors, the algorithm grows essentially asN ², whereN is the system size, so computational times are readily estimated on more powerful super-minicomputers and supercomputers using standard dot-product benchmarks. The algorithm is especially ideal for gigaflop and teraflop parallel array processors under construction in a number of computer companies; an analysis of the spectrum reveals that asynchronous iterative methods will converge, leading the way to a rigorous formulation of screening concepts for suspended particles of arbitrary shape.     

Viscosity minimum in bimodal concentrated suspensions under shear

We study a model of concentrated suspensions under shear in two dimensions. Interactions between suspended particles are dominated by direct-contact viscoelastic forces and the particles are neutrally bouyant. The bimodal suspensions consist of a variable proportion between large and small droplets, with a fixed global suspended fraction. Going beyond the assumptions of the classical theory of Farris (R.J. Farris, Trans. Soc. Rheol. 12, 281 (1968)), we discuss a shear viscosity minimum, as a function of the small-to-large-particle ratio, in shear geometries imposed by external body forces and boundaries. Within a linear-response scheme, we find the dependence of the viscosity minimum on the imposed shear and the microscopic drop friction parameters. We also discuss the viscosity minimum under dynamically imposed shear applied by boundaries. We find a reduction of macroscopic viscosity with the increase of the microscopic friction parameters that is understood using a simple two-drop model. Our simulation results are qualitatively consistent with recent experiments in concentrated bimodal emulsions with a highly viscous or rigid suspended component. Received 28 June 2002 RID="a" ID="a"e-mail: ernesto@pion.ivic.ve     

Determination of optical constants of latex in concentrated suspensions

The possibility of taking into account concentration effects in the determination of optical constants of latex in the visible and near IR regions of the spectrum is demonstrated, and the limits of applicability of the methods proposed for this purpose are determined. The limiting concentration of particles in suspensions for which these effects should be taken into account depend on the particle size. Using latex as an example, ways of increasing the accuracy of reconstruction of optical constants of weakly absorbing particles of micron and submicron size are shown. Similar concentration effects can take place in the study of blood substituents, proteins, and other weakly absorbing particles in weakly absorbing media.     

Dilatant flow of concentrated suspensions of rough particles

The flow anisotropy of a concentrated colloidal suspension at the jamming transition is studied. It is shown that the use of rough spherical particles reduces the hydrodynamic lubrication forces between adjacent colloids and makes possible the study of the stress tensor anisotropy. At low shear rates, the suspension exerts an attractive force between two opposite surfaces, whereas at higher shear rates it becomes dilatant. Direct confocal microscopy observation of the particles organization reveal that crystallites form at high shear rate.     

Colloidal interactions in suspensions of rods

We report direct measurements of entropic interactions of colloidal spheres in suspensions of rodlike fd bacteriophage. We investigate the influence of sphere size, rod concentration, and ionic strength on these interactions. Although the results compare favorably with a recent calculation, small discrepancies reveal entropic effects due to rod flexibility. At high salt concentrations, the potential turns repulsive as a result of viral adsorption on the spheres and viral bridging between the spheres.     

Nonequilibrium Brownian dynamics simulations of shear thinning in concentrated colloidal suspensions

The effect of interparticle forces on shear thinning in concentrated aqueous and nonaqueous colloidal suspensions was studied using nonequilibrium Brownian dynamics. Hydrodynamic interactions among particles were neglected. Systems of 108 particles were studied at volume fractions of 0.2 and 0.4. For the nonaqueous systems, shear thinning could be correlated with the gradual breakup of small flocs present because of the weak, attractive secondary minimum in the interparticle potential. At the highest shear rate for=0.4, the particles were organized into a hexagonally packed array of strings. For the strongly repulsive aqueous systems, the viscosity appeared to be a discontinuous function of the shear rate. For=0.4, this discontinuity coincided with a transition from a disordered state to a lamellar structure for the suspension.