  In this paper we develop statistical mechanical tools to describe the
intermediate- and long-time collective- and self-diffusion properties of a
liquid of strongly-interacting hollow spherical particles (shells), each
bearing a smaller solid sphere (yolk) in its interior. To decouple two complex
effects we assume that the hydrodynamic interactions can be accounted for
through the effective short-time self-diffusion coefficients $D^0_s$ and
$D^0_y$ that describe the short-time Brownian motion of the yolk and the shell
particles, and develop a self-consistent generalized Langevin equation theory
to describe the intermediate- and long-time effects of the direct shell-shell,
yolk-shell and yolk-yolk interactions. In a concrete application, we consider
the simplest yolk-shell model system involving purely repulsive hard-body
interactions between all (shell and yolk) particles. Using a softened version
of these interparticle potentials we perform Brownian dynamics simulations to
determine the mean squared displacement of both types of particles, as well as
the intermediate scattering function of the yolk-shell complex. We compare the
theoretical and simulation results between them, and with the results for the
same system in the absence of yolks. We find that the yolks, which have no
effect on the shell-shell static structure, influences the dynamic properties
in a predictable manner, fully captured by the theory.
