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

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.

Creeping motion of a solid particle inside a spherical elastic cavity: II. Asymmetric motion

“…in agreement with the results by Aponte-Rivera and Zia [80][81][82], who provided the elements of the grand mobility tensor for general motion inside a rigid cavity. Interestingly, the particle mobility in the limit of infinite stiffness is found to be always larger than that inside a rigid cavity with no-slip velocity boundary condition on its interior surface.…”

Creeping motion of a solid particle inside a spherical elastic cavity

“…The latter is valid when particle radius is very small compared to that of the cavity. In addition, a combination of multipole expansion and Faxén's theorem has been used by Zia and collaborators [41,42], providing the elements of the grand mobility tensor of finitesized particles moving inside a rigid spherical cavity. Additional works addressed the low-Reynolds-number locomotion inside a viscous drop [43][44][45], or the dynamics of a particleencapsulating droplet in flow [46,47].…”

Impact of polydispersity and confinement on diffusion in hydrodynamically interacting colloidal suspensions

“…Entropic and hydrodynamic effects underlie these rich behaviours: size intermixing reduces free energy to permit higher packing fractions; non-continuum colloidal interactions lead to vitrification rather than crystallization; and hydrodynamic asymmetry effects and depletion forces lead to margination and viscosity changes. Given the recently demonstrated interplay between spherical confinement and these microscopic forces (Aponte-Rivera, Su & Zia 2018), it is likely that new behaviours resulting from a coupling between confinement and polydispersity will affect the particle dynamics. The study of particle dynamics in confinement presents some of the same challenges as in the study of particle dynamics in unconfined suspensions, and presents new challenges as well.…”

“…Our confined Stokesian dynamics algorithm models Brownian motion, many-body hydrodynamic interactions, confinement and crowding, but thus far could not represent polydisperse particle size (Aponte-Rivera & Zia 2016; Aponte-Rivera et al. 2018). Size polydispersity is a non-trivial extension of both the hydrodynamics theoretical framework and the computational algorithm.…”