Solvable model for electrolytic soap films: the two-dimensional two-component plasma

We study a toy model for electrolytic soap films, the two-dimensional two-component plasma. This model is exactly solvable for a special value of the coulombic coupling constant $\beta q^2=2$. This allows us to compute the disjoining pressure of a film and to study its stability. We found that the Coulomb interaction plays an important role in this stability. Also the adhesivity that measures the attraction of soap anions to the boundaries is very important. For large adhesivity the film is stable, whereas for small adhesivity a collapse could occur. We also study the density and correlations in the film. The charge density near the boundary shows a double layered profile. We show that the charge correlations verify a certain number of sum rules.