  We study a two-dimensional model for a long cylindrical stiff charged
macroion immersed in a charge-asymmetric electrolyte with charge ratio +2/-1.
The model is integrable and it allows an exact analytical determination of the
effective charge of the macroion, which characterizes the electrostatic
potential at large distances (compared to the screening length) from the
macroion. At at high coulombic coupling, this model predicts charge inversion:
for a highly negatively charged macroion, the effective charge could become
positive, indicating an overscreening of the macroion by the divalent
counterions. By studying the behavior of the coions and counterions density
profiles close to the macroion, we show that the counterion condensation
threshold is shifted to a lower value in absolute value. This plays an
important role in the charge inversion phenomenon.
