In protoplanetary discs 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. The two-fluid SGI is completely quenched within a critical disc radius, as large as 10 au and 30 au for centimetre- and millimetre-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 disc 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.HNL acknowledges partial funding from Science and Technology Facilities Council (Grant ID: ST/L000636/1), and RR from a Bridgewater summer internship and from Newnham college
