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The structure and dynamics of confined suspensions of particles of arbitraryshape is of interest in multiple disciplines, from biology to engineering.Theoretical studies are often limited by the complexity of long-rangeparticle-particle and particle-wall forces, including many-body fluctuatinghydrodynamic interactions. Here, we report a computational study on thediffusion of spherical and cylindrical particles confined in a sphericalcavity. We rely on an Immersed-Boundary General geometry Ewald-like method tocapture lubrication and long-range hydrodynamics, and include appropriatenon-slip conditions at the confining walls. A Chebyshev polynomialapproximation is used to satisfy the fluctuation-dissipation theorem for theBrownian suspension. We explore how lubrication, long-range hydrodynamics,particle volume fraction and shape affect the equilibrium structure and thediffusion of the particles. It is found that once the particle volume fractionis greater than $10\%$, the particles start to form layered aggregates thatgreatly influence particle dynamics. Hydrodynamic interactions stronglyinfluence the particle diffusion by inducing spatially dependent short-timediffusion coefficients, stronger wall effects on the particle diffusion towardsthe walls, and a sub-diffusive regime --caused by crowding-- in the long-timeparticle mobility. The level of asymmetry of the cylindrical particlesconsidered here is enough to induce an orientational order in the layeredstructure, decreasing the diffusion rate and facilitating a transition to thecrowded mobility regime at low particle concentrations. Our results offerfundamental insights into the diffusion and distribution of globular andfibrillar proteins inside cells.

Structure and dynamics of hydrodynamically interacting finite-size Brownian particles in a spherical cavity: spheres and cylinders