  Colloid or nanoparticle mobility under confinement is of central importance
to a wide range of physical and biological processes. Here, we introduce a
minimal model of particles in a hydrodynamic continuum to examine how particle
shape and concentration affect the transport of particles in spherical
confinement. Specifically, an immersed boundary-General geometry Ewald-like
approach is adopted to simulate the dynamics of spheres and cylinders under the
influence of short-and long-range fluctuating hydrodynamic interactions with
appropriate non-slip conditions at the confining walls. An efficient
$\it{O(N)}$ parallel finite element algorithm is used, thereby allowing
simulations at high concentrations, while a Chebyshev polynomial approximation
is implemented in order to satisfy the fluctuation-dissipation theorem. A
concentration-dependent anomalous diffusion is observed for suspended
particles. It is found that introducing cylinders in a background of spheres,
i.e. particles with a simple degree of anisotropy, has a pronounced influence
on the structure and dynamics of the particles. First, increasing the fraction
of cylinders induces a particle segregation effect, where spheres are pushed
towards the wall and cylinders remain near the center of the cavity. This
segregation leads to lower mobility for the spheres relative to that
encountered in a system of pure spheres at the same volume fraction. Second,
the diffusive-to-anomalous transition and the degree of anomaly--quantified by
the power-law exponent in the mean square displacement vs. time relation-both
increase as the fraction of cylinders becomes larger. These findings are of
relevance for studies of diffusion in the cytoplasm, where proteins exhibit a
distribution of size and shapes that could lead to some of the effects
identified in the simulations reported here.
