  The structure and dynamics of confined suspensions of particles of arbitrary
shape is of interest in multiple disciplines, from biology to engineering.
Theoretical studies are often limited by the complexity of long-range
particle-particle and particle-wall forces, including many-body fluctuating
hydrodynamic interactions. Here, we report a computational study on the
diffusion of spherical and cylindrical particles confined in a spherical
cavity. We rely on an Immersed-Boundary General geometry Ewald-like method to
capture lubrication and long-range hydrodynamics, and include appropriate
non-slip conditions at the confining walls. A Chebyshev polynomial
approximation is used to satisfy the fluctuation-dissipation theorem for the
Brownian suspension. We explore how lubrication, long-range hydrodynamics,
particle volume fraction and shape affect the equilibrium structure and the
diffusion of the particles. It is found that once the particle volume fraction
is greater than $10\%$, the particles start to form layered aggregates that
greatly influence particle dynamics. Hydrodynamic interactions strongly
influence the particle diffusion by inducing spatially dependent short-time
diffusion coefficients, stronger wall effects on the particle diffusion towards
the walls, and a sub-diffusive regime --caused by crowding-- in the long-time
particle mobility. The level of asymmetry of the cylindrical particles
considered here is enough to induce an orientational order in the layered
structure, decreasing the diffusion rate and facilitating a transition to the
crowded mobility regime at low particle concentrations. Our results offer
fundamental insights into the diffusion and distribution of globular and
fibrillar proteins inside cells.
