  Experimental studies of the variation of the mean square displacement (MSD)
of a particle in a confined colloid suspension that exhibits density variations
on the scale length of the particle diameter are not in agreement with the
prediction that the spatial variation in MSD should mimic the spatial variation
in density. The predicted behavior is derived from the expectation that the MSD
of a particle depends on the system density and the assumption that the force
acting on a particle is a point function of position. The experimental data
come from studies of the MSDs of particles in narrow ribbon channels and
between narrowly spaced parallel plates, and from new data, reported herein, of
the radial and azimuthal MSDs of a colloid particle in a dense colloid
suspension confined to a small circular cavity. In each of these geometries a
dense colloid suspension exhibits pronounced density oscillations with spacing
of a particle diameter. We remove the discrepancy between prediction and
experiment using the Fisher-Methfessel interpretation of how local equilibrium
in an inhomogeneous system is maintained to argue that the force acting on a
particle is delocalized over a volume with radius equal to a particle diameter.
Our interpretation has relevance to the relationship between the scale of
inhomogeneity and the utility of translation of the particle MSD into a
position dependent diffusion coefficient, and to the use of a spatially
dependent diffusion coefficient to describe mass transport in a heterogeneous
system.
