  In protoplanetary disks the aerodynamical friction between particles and gas
induces a variety of instabilities that facilitate planet formation. Of these
we examine the so-called `secular gravitational instability' (SGI) in the
two-fluid approximation, deriving analytical expressions for its stability
criteria and growth rates. Concurrently, we present a physical explanation of
the instability that shows how it manifests upon an intermediate range of
lengthscales exhibiting geostrophic balance in the gas component. In contrast
to a single-fluid treatment, the SGI is quenched within a critical disk radius,
as large as 10 AU and 30 AU for cm and mm sized particles respectively,
although establishing robust estimates is hampered by uncertainties in the
parameters (especially the strength of turbulence) and deficiencies in the
razor-thin disk model we employ. It is unlikely, however, that the SGI is
relevant for well-coupled dust. We conclude by applying these results to the
question of planetesimal formation and the provenance of large-scale dust
rings.
