Active Stokesian dynamics

We present a comprehensive computational study of the short-time transport properties of bidisperse hard-sphere 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 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.

The characteristics and differences in the two approximations. i.e., the additivity of forces and the additivity of velocities, on which Stokesian dynamics methods are based, have been investigated. To do so, Stokesian dynamics simulations of a ferromagnetic colloidal dispersion have been carried out for a simple shear flow, and the aggregate structures and the averaged viscosities have been evaluated, From the results of aggregate structures in equilibrium, the results obtained by the additivity of forces are quantaively different from those by the approximation of ignoring hydrodynamic interactions, although a qualitative agreement is recognized. The results obtained by the additivity of velocities give medium characteristics between the two above approximations. This difference in characeristics between the two additivity approximations and that of ignoring hydrodynamics becomes clearer as the influences of the shear flow dominate those of magnetic forces more significantly. From the results of transient characteristics from an initial state, the results of the additivity of velocities agree well with those of the additivity of forces. In contrast, the results without hydrodynamic interactions deviate from those of the two additivity approximations at a time step when a nearly particle particle touching situation starts to appear.

A scalable parallel Stokesian Dynamics method for the simulation of colloidal suspensions

We use lattice Boltzmann simulations, in conjunction with Ewald summation methods, to investigate the role of hydrodynamic interactions in colloidal suspensions of dipolar particles, such as ferrofluids. Our work addresses volume fractions phi of up to 0.20 and dimensionless dipolar interaction parameters lambda of up to 8. We compare quantitatively with Brownian dynamics simulations, in which many-body hydrodynamic interactions are absent. Monte Carlo data are also used to check the accuracy of static properties measured with the lattice Boltzmann technique. At equilibrium, hydrodynamic interactions slow down both the long-time and the short-time decays of the intermediate scattering function S(q, t), for wavevectors close to the peak of the static structure factor S(q), by a factor of roughly two. The long-time slowing is diminished at high interaction strengths, whereas the short-time slowing (quantified via the hydrodynamic factor H(q)) is less affected by the dipolar interactions, despite their strong effect on the pair distribution function arising from cluster formation. Cluster formation is also studied in transient data following a quench from lambda = 0; hydrodynamic interactions slow the formation rate, again by a factor of roughly two.

The self-diffusivity of Brownian hard spheres in a simple shear flow is studied by numerical simulation. Particle trajectories are calculated by Stokesian dynamics, with an accurate representation of the suspension hydrodynamics that includes both many-body interactions and lubrication. The simulations are of a monolayer of identical spheres as a function of the Péclet number: Pe =γ̇a2/D0, which measures the relative importance of shear and Brownian forces. Here γ̇ is the shear rate, a the particle radius, and D0 the diffusion coefficient of a single sphere at infinite dilution. In the absence of shear, using only hydrodynamic interactions, the simulations reproduce the pair-distribution function of the equivalent hard-disk system. Both short- and long-time self-diffusivities are determined as a function of the Péclet number. The results show a clear transition from a Brownian motion dominated regime (Pe<1) to a hydrodynamically dominated regime (Pe>10) with a dramatic change in the behavior of the long-time self-diffusivity.

Brownian Dynamics Simulations of Ferromagnetic Colloidal Dispersions in a Simple Shear Flow

A new Stokesian dynamics (SD) algorithm for Brownian suspensions is presented. The implementation is based on the recently developed accelerated Stokesian dynamics (ASD) simulation method [Sierou and Brady, J. Fluid Mech. 448, 115 (2001)] for non-Brownian particles. As in ASD, the many-body long-range hydrodynamic interactions are computed using fast Fourier transforms, and the resistance matrix is inverted iteratively, in order to keep the computational cost O(N log N). A fast method for computing the Brownian forces acting on the particles is applied by splitting them into near- and far-field contributions to avoid the O(N3) computation of the square root of the full resistance matrix. For the near-field part, representing the forces as a sum of pairwise contributions reduces the cost to O(N); and for the far-field part, a Chebyshev polynomial approximation for the inverse of the square root of the mobility matrix results in an O(N1.25 log N) computational cost. The overall scaling of the method is thus roughly of O(N1.25 log N) and makes possible the simulation of large systems, which are necessary for studying long-time dynamical properties and/or polydispersity effects in colloidal dispersions. In this work the method is applied to study the rheology of concentrated colloidal suspensions, and results are compared with conventional SD. Also, a faster approximate method is presented and its accuracy discussed.

The rheological properties of particulate dispersions containing aggregate structures were theoretically investigated in this study. Under the assumption of Stokes flow, the viscosity of fluids with fine particles was derived by a theoretical method based on the multipole expansion in reciprocal space. In this method, many-body hydrodynamic interactions were considered as the multipole-expanded moment of the force density at the surface of the particles. It is possible to calculate the viscosity of particulate suspensions by considering higher-order moments. The viscosity of monodisperse particulate suspensions was calculated under various conditions. To verify the accuracy of the calculation, the viscosity of uniformly distributed particulate suspensions was calculated, and the results were compared with the experimental results of previous studies. The calculated viscosities were in good agreement with the experimental results for a wide range of particle volumetric concentrations. The viscosity of aggregated suspensions was also calculated to examine the mechanism of viscosity change. The viscosity was systematically calculated with changing the aggregate size and particle concentration. The results indicate that the hydrodynamic effect is not significant on the viscosity change by aggregation, which is contrary to the assumption of previous viscosity models. The calculation results suggest that the increase in the viscosity of aggregated suspensions is instead caused by the direct influence of inter-particle forces.

Hydrodynamic and electrokinetic effects on the dynamics of charged colloids andmacromolecules

A particle mesh Ewald (PME) Stokesian dynamics algorithm has been developed to model hydrodynamic interactions in suspensions of non-spherical dicolloidal particles. Dicolloids, which have recently been synthesized by a number of independent research groups (Johnson, van Kats & van Blaaderen (Langmuir, vol. 21, 2005, p. 11510), Mocket al. (Langmuir, vol. 22, 2006, p. 4037), Kim, Larsen & Weitz (J. Am. Chem. Soc., vol. 128, 2006, p. 14374)), consist of two intersecting spheres of varying radii and centre-to-centre separation. One-body resistance tensors and disturbance velocity fields are computed for general linear flows using a superposition of Stokes singularities along the symmetry axis of the dicolloid particles. The coefficients and the locations of the singularities are optimized to minimize the norm of the velocity error on the particle surface. The one-body solution provides all coefficients required for the far-field many-body interactions in the Stokesian dynamics algorithm. These generalize the analytical results for spheres employed in the classic algorithm. Modified lubrication interaction tensors are developed for dicolloids for the singular near-field lubrication interactions. Accuracy of the one-body solutions and two-body generalized Stokesian dynamics solutions are validated by comparison with high-precision numerical solutions computed with the spectral boundary element method of Muldowney & Higdon (J. Fluid Mech., vol. 298, 1995, p. 167). The newly developed PME Stokesian dynamics algorithm was used to study transport properties in dicolloidal suspensions over a range of volume fractions (φ ≤ 0.5). The effects of the degree of anisotropy on the properties of the suspension are discussed. For these mildly anisotropic particles, the transport properties remain close to those of spheres, however certain interesting trends emerge, with non-monotonic viscosity dependence as a function of increasing aspect ratio. The minimum viscosity in concentrated suspensions is lower than that for spheres with equal volume fraction over a range of volume fractions.

A Stokesian dynamics approach for simulation of magnetic particle suspensions

The interaction between passive and active/driven particles has introduced a new way to control colloidal suspension properties from particle aggregation to crystallization. Here, we focus on the hydrodynamic interaction between a single rotational driven particle and a suspension of passive particles near the floor. Using experiments and Stokesian dynamics simulations that account for near-field lubrication, we demonstrate that the flow induced by the driven particle can induce long-ranged rearrangement in a passive suspension. We observe an accumulation of passive particles in front of the driven particle and a depletion of passive particles behind the driven particle. This restructuring generates a pattern that can span a range more than 10 times the driven particles radius. We further show that size scale of the pattern is only a function of the particles height above the floor.

Many-body hydrodynamic interactions between spherical drops in an emulsion

Collective diffusion of charged spheres in the presence of hydrodynamic interaction

Interactions between hard spheres sedimenting at low Reynolds number