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 and Tornberg (2010) [29]] 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 and Brady (2003) [39]. We extensively discuss implementation and parameter selection strategies in SEASD, and demonstrate the spectral accuracy in the mobility evaluation and the overall O(N log 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.

Nanoparticles dispersed in polymer melts have recently been shown to decrease the bulk viscosity. This contradicts expectations based on Einstein's well-known theory for effective viscosity of dilute, random dispersions of rigid spheres in Newtonian fluids. In this paper, we examine a continuum hydrodynamic model where a layer of polymer at the nanoparticle-polymer interface has a different viscosity and density than the bulk polymer. When the layer thickness is greater than the nanoparticle radius, and the layer viscosity is lower than that of the bulk polymer, the intrinsic viscosity is comparable to the unexpectedly large, negative values reported experimentally by Mackay and coworkers. Accordingly, our continuum hydrodynamic model attributes a bulk viscosity reduction to a lower melt viscosity at the nanoparticle-polymer interface. Such a reduction has been ascribed to the Rouse dynamics of polymer chains at the nanoparticle-polymer interface. Fitting the theory to experimental data reveals a simple correlation between the reduced viscosity layer thickness, polymer chain size, entanglement tube diameter, and nanoparticle size and concentration. Our calculations support the arguments of Mackay and coworkers that nanoparticle inclusions significantly influence the polymer chain conformation in melts, even when the inclusion volume fraction is very small.

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. C 2015 AIP Publishing LLC. [http://dx

Embedding colloidal particles in polymeric hydrogels often endows the polymer skeleton with appealing characteristics for microfluidics and biosensing applications. This theoretical study provides a rigorous foundation for interpreting active electrical microrheology and electroacoustic experiments on such materials. In addition to viscoelastic properties of the composites, these techniques sense physicochemical characteristics of the particle–polymer interface. Wang & Hill (Soft Matter, vol. 4, 2008, p. 1048) studied the steady response of a rigid, impenetrable sphere in a compressible hydrogel skeleton. Here, we extend their analysis to arbitrary frequencies, showing, in general, how the frequency response depends on the particle size and charge, ionic strength of the electrolyte and elastic and hydrodynamic characteristics of the polymer skeleton. Our calculations capture the transition from quasi-steady compressible to quasi-steady incompressible dynamics as the frequency passes through the reciprocal draining time of the gel. Above the reciprocal draining time, the skeleton and fluid move in unison, so the dynamics are incompressible and, thus, given to an excellent approximation by the well-known dynamic electrophoretic mobility but with the Newtonian shear viscosity replaced by a complex, frequency-dependent value.

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