The effects of specific interactions in a two dimensional coulombic system axe investigated. In the framework of a field theoretical approach, we have shown that the electric properties of the system are strongly modified when two ionic species have a tendency to demix. By means of a Langevin dynamics, we investigate here a model system where, in the absence of electrostatic interaction, the specific interactions are such that the system demixes. This phase separation cannot take place in the presence of the coulombic potential, as a result of the electroneutrality condition in the system. The snapshots of the system obtained in the sim~ation, show large local concentration inhomogeneities, which are also charge inhomogeneities reminiscent of the tendency of the two species to separate. This is an unusual feature in a charged system, as it corresponds to the gathering of ions of the same sign. These inhomogeneities are constituted by a continuous network of lines of ions of the same species, the adjacent line being of the opposite sign. This structure is similar to a bicontinuous phase. One property of these lines: the average distance between the lines, has been studied by means of a simple field theoretical model. The Hamiltonian includes entropy, electrostatic and specific interactions. In the mean field approximation, we obtain a distance between the lines in agreement with what is found in the simulation.