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Register a new userShort-time transport properties of bidisperse suspensions and porous media: a Stokesian Dynamics study
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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.
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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 $40%$.
In 1983 Felderhof, Ford and Cohen gave microscopic explanation of the famous Clausius-Mossotti formula for the dielectric constant of nonpolar dielectric. They based their considerations on the cluster expansion of the dielectric constant, which relates this macroscopic property with the microscopic characteristics of the system. In this article, we analyze the cluster expansion of Felderhof, Ford and Cohen by performing its resummation (renormalization). Our analysis leads to the ring expansion for the macroscopic characteristic of the system, which is an expression alternative to the cluster expansion. Using similarity of structures of the cluster expansion and the ring expansion, we generalize (renormalize) the Clausius-Mossotti approximation. We apply our renormalized Clausius-Mossotti approximation to the case of the short-time transport properties of suspensions, calculating the effective viscosity and the hydrodynamic function with the translational self-diffusion and the collective diffusion coefficient. We perform calculations for monodisperse hard-sphere suspensions in equilibrium with volume fraction up to 45%. To assess the renormalized Clausius-Mossotti approximation, it is compared with numerical simulations and the Beenakker-Mazur method. The results of our renormalized Clausius-Mossotti approximation lead to comparable or much less error (with respect to the numerical simulations), than the Beenakker-Mazur method for the volume fractions below $ phi approx 30% $ (apart from a small range of wave vectors in hydrodynamic function). For volume fractions above $phi approx 30 %$, the Beenakker-Mazur method gives in most cases lower error, than the renormalized Clausius-Mossotti approximation.
The motion of active polymers in a porous medium is shown to depend critically on flexibilty, activity and degree of polymerization. For given Peclet number, we observe a transition from localisation to diffusion as the stiffness of the chains is increased. Whereas stiff chains move almost unhindered through the porous medium, flexible ones spiral and get stuck. Their motion can be accounted for by the model of a continuous time random walk with a renewal process corresponding to unspiraling. The waiting time distribution is shown to develop heavy tails for decreasing stiffness, resulting in subdiffusive and ultimately caged behaviour.
In this work we develop the Spectral Ewald Accelerated Stokesian Dynamics (SEASD), a novel computational method for dynamic simulations of polydisperse colloidal suspensions with full hydrodynamic interactions. SEASD is based on the framework of Stokesian Dynamics (SD) with extension to compressible solvents, and uses the Spectral Ewald (SE) method [Lindbo & Tornberg, J. Comput. Phys. 229 (2010) 8994] for the wave-space mobility computation. To meet the performance requirement of dynamic simulations, we use Graphic Processing Units (GPU) to evaluate the suspension mobility, and achieve an order of magnitude speedup compared to a CPU implementation. For further speedup, we develop a novel far-field block-diagonal preconditioner to reduce the far-field evaluations in the iterative solver, and SEASD-nf, a polydisperse extension of the mean-field Brownian approximation of Banchio & Brady [J. Chem. Phys. 118 (2003) 10323]. We extensively discuss implementation and parameter selection strategies in SEASD, and demonstrate the spectral accuracy in the mobility evaluation and the overall $mathcal{O}(Nlog N)$ computation scaling. We present three computational examples to further validate SEASD and SEASD-nf in monodisperse and bidisperse suspensions: the short-time transport properties, the equilibrium osmotic pressure and viscoelastic moduli, and the steady shear Brownian rheology. Our validation results show that the agreement between SEASD and SEASD-nf is satisfactory over a wide range of parameters, and also provide significant insight into the dynamics of polydisperse colloidal suspensions.
There was an error in data reduction, resulting in incorrect values for the normal stress differences $N_1$ and $N_2$ shown in Figs. 7-10, and the corrected figures are shown here. In particular, the algebraic sign of $N_1$ is changed, as are the relative magnitudes of $N_1$ and $N_2$. The negative values of $N_1$ for these non-shear-thickening suspensions are larger in magnitude than those reported by other workers, but both $N_1$ and $N_2$ are in general agreement with the accelerated Stokesian Dynamics calculations of Sierou and Brady [1].
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