  We study the homogenization of a diffusion process which takes place in a
binary structure formed by an ambiental connected phase surrounding a
suspension of very small spheres distributed in an $\veps$-periodic network.
The asymptotic distribution of the concentration is determined for both phases,
as $\veps\to 0$, assuming that the suspension has mass of unity order and
vanishing volume. Three cases are distinguished according to the values of a
certain limit capacity. When it is positive and finite, the macroscopic system
involves a two-concentration system, coupled through a term accounting for the
non local effects. In the other two cases, where the capacity is either
infinite or going to zero, although the form of the system is much simpler,
some peculiar effects still account for the presence of the suspension.
