We present the 2-D, two fluid (ions + neutrals) numerical simulations that we are carrying out in order to study the ambipolar filamentation process, in which a magnetized, partially ionized plasma is stirred by turbulence in the ambipolar frequency range. The higher turbulent velocity of the neutrals in the most ionized regions gives rise to a non-linear force driving them out of these regions, and causes the ions and the magnetic flux to condense in the most ionized regions, resulting in a filamentary structure where initial ionization inhomogeneities are amplified. This mechanism might help to explain some features observed in magnetized and partially ionized astrophysical plasmas as the interstellar medium.