  We extend the classical Gouy-Chapman model of two planar parallel interacting
double-layers, which is used as a first approximation to describe the force
between colloidal particles, by considering the finite-thickness of the
colloids. The formation of two additional double layers due to this finite
thickness, modifies the interaction force compared to the Gouy-Chapman case, in
which the colloids are semi-infinite objects. In this paper we calculate this
interaction force and some other size-dependent properties using a mean field
level of description, based on the Poisson-Boltzmann (PB) equation. We show
that in the case of finite-size colloids, this equation can be set in a closed
form depending on the geometrical parameters and on their surface charge. The
corresponding linear (Debye-Huckel) theory and the well-known results for
semi-infinite colloids are recovered from this formal solution after taking
appropriate limits. We use a density functional corresponding to the PB level
of description to show how in the case when the total colloidal charge is
fixed, it redistribute itself on their surfaces to minimize the energy of the
system depending on the afore mentioned parameters. We study how this charge
relaxation affects the colloidal interactions.
