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Equilibrium structure and diffusion in concentrated hydrodynamically interacting suspensions confined by a spherical cavity

Published online by Cambridge University Press:  11 December 2017

Christian Aponte-Rivera ,
Yu Su  and
Roseanna N. Zia Open the ORCID record for Roseanna N. Zia [Opens in a new window]
Christian Aponte-Rivera
Affiliation:
Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca NY 14850, USA
Yu Su
Affiliation:
Robert Frederick Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca NY 14850, USA
Roseanna N. Zia*
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford CA 94305, USA
*
†Email address for correspondence: rzia@stanford.edu
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Abstract

The short- and long-time equilibrium transport properties of a hydrodynamically interacting suspension confined by a spherical cavity are studied via Stokesian dynamics simulations for a wide range of particle-to-cavity size ratios and particle concentrations. Many-body hydrodynamic and lubrication interactions between particles and with the cavity are accounted for utilizing recently developed mobility and resistance tensors for spherically confined suspensions (Aponte-Rivera & Zia, Phys. Rev. Fluids, vol. 1(2), 2016, 023301). Study of particle volume fractions in the range $0.05\leqslant \unicode[STIX]{x1D719}\leqslant 0.40$ reveals that confinement exerts a qualitative influence on particle diffusion. First, the mean-square displacement over all time scales depends on the position in the cavity. Additionally, at short times, the diffusivity is anisotropic, with diffusion along the cavity radius slower than diffusion tangential to the cavity wall, due to the anisotropy of hydrodynamic coupling and to confinement-induced spatial heterogeneity in particle concentration. The mean-square displacement is anisotropic at intermediate times as well and, surprisingly, exhibits superdiffusive and subdiffusive behaviours for motion along and perpendicular to the cavity radius respectively, depending on the suspension volume fraction and the particle-to-cavity size ratio. No long-time self-diffusive regime exists; instead, the mean-square displacement reaches a long-time plateau, a result of entropic restriction to a finite volume. In this long-time limit, the higher the volume fraction is, the longer the particles take to reach the long-time plateau, as cooperative rearrangements are required as the cavity becomes crowded. The ordered dynamical heterogeneity seen here promotes self-organization of particles based on their size and self-mobility, which may be of particular relevance in biophysical systems.

JFM classification

Complex Fluids: Colloids Low-Reynolds-number flows: Stokesian dynamics Complex Fluids: Suspensions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 836 , 10 February 2018 , pp. 413 - 450
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Copyright
© 2017 Cambridge University Press 

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Aponte-Rivera et al. supplementary movie

Stokesian dynamics simulation with full, many-body hydrodynamic and lubrication interactions for a spherically confined, concentrated colloidal suspension. The no-slip and no-flux confining cavity is rigorously modeled via newly developed hydrodynamic mobility couplings. Model can simulate volume fractions up to maximum packing and arbitrary particle-to-cavity size ratio. Shown here is equilibrium diffusion for 30% volume fraction and particles 10% of cavity size.”

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