  Interacting Fermi gases with equal populations but unequal masses are
investigated at zero temperature using local density approximation and the
hydrodynamic theory of superfluids in the presence of harmonic trapping.
  We derive the conditions of energetic stability of the superfluid
configuration with respect to phase separation and the frequencies of the
collective oscillations in terms of the mass ratio and the trapping frequencies
of the two components. We discuss the behavior of the gas after the trapping
potential of a single component is switched off and show that, near a Feshbach
resonance, the released component can still remain trapped due to many-body
interaction effects. Explicit predictions are presented for a mixture of $^6$Li
and $^{40}$K with resonant interaction.
