The influence of a small relative density difference on the displacement of
two miscible liquids is studied experimentally in transparent 2D networks of
micro channels. Both stable displacements in which the denser fluid enters at
the bottom of the cell and displaces the lighter one and unstable displacements
in which the lighter fluid is injected at the bottom and displaces the denser
one are realized. Except at the lowest mean flow velocity U, the average
C(x,t) of the relative concentration satisfies a convection-dispersion
equation. The dispersion coefficient is studied as function of the relative
magnitude of fluid velocity and of the velocity of buoyancy driven fluid
motion. A model is suggested and its applicability to previous results obtained
in 3D media is discussed