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Particle mesh Ewald Stokesian dynamics simulations for suspensions of non-spherical particles

Published online by Cambridge University Press:  04 April 2011

A. KUMAR  and
J. J. L. HIGDON
A. KUMAR
Affiliation:
Department of Chemical and Biomolecular Engineering, University of Illinois, Urbana, IL 61801, USA
J. J. L. HIGDON*
Affiliation:
Department of Chemical and Biomolecular Engineering, University of Illinois, Urbana, IL 61801, USA
*
†Email address for correspondence: jhigdon@uiuc.edu
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Abstract

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), Mock et 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.

JFM classification

Low-Reynolds-number flows: Stokesian dynamics Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 675 , 25 May 2011 , pp. 297 - 335
Copyright
Copyright © Cambridge University Press 2011

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