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

Charge inversion of colloids in an exactly solvable model