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.
We
develop a scaling theory that predicts the dynamics of symmetric
and asymmetric unentangled liquid coacervates formed by solutions
of oppositely charged polyelectrolytes. Symmetric coacervates made
from oppositely charged polyelectrolytes consist of polycations and
polyanions with equal and opposite charge densities along their backbones.
These symmetric coacervates can be described as mixtures of polyelectrolytes
in the quasi-neutral regime with a single correlation length. Asymmetric
coacervates are made from polycations and polyanions with unequal
charge densities. The difference in charge densities results in a
double semidilute structure of asymmetric coacervates with two correlation
lengths, one for the high-charge-density and the other for the low-charge-density
polyelectrolytes. We predict that the double semidilute structure
in asymmetric coacervates results in a dynamic coupling, which increases
the friction of the high-charge-density polyelectrolyte. This dynamic
coupling increases the contribution to the zero-shear viscosity of
the high-charge-density polyelectrolyte. The diffusion coefficient
of the high-charge-density polyelectrolyte is predicted to depend
on the concentration and degree of polymerization of the low-charge-density
polyelectrolyte in the coacervate if the size of the low-charge-density
polymer is smaller than the correlation length of the high-charge-density
polymer. We also predict a non-monotonic salt concentration dependence
of the zero-shear viscosity of asymmetric coacervates.
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