  Using a solvable model, the two-dimensional two-component plasma, we study a
Coulomb gas confined in a disk and in an annulus with boundaries that can
adsorb some of the negative particles of the system. We obtain explicit
analytic expressions for the grand potential, the pressure and the density
profiles of the system. By studying the behavior of the disjoining pressure we
find that without the adsorbing boundaries the system is naturally unstable,
while with attractive boundaries the system is stable because of a positive
contribution from the surface tension to the disjoining pressure. The results
for the density profiles show the formation of a positive layer near the
boundary that screens the adsorbed negative particles, a typical behavior in
charged systems. We also compute the adsorbed charge on the boundary and show
that it satisfies a certain number of relations, in particular an
electro-neutrality sum rule.
