  We present a new approach to simulating mixtures of gas and dust in smoothed
particle hydrodynamics (SPH). We show how the two-fluid equations can be
rewritten to describe a single-fluid 'mixture' moving with the barycentric
velocity, with each particle carrying a dust fraction. We show how this
formulation can be implemented in SPH while preserving the conservation
properties (i.e. conservation of mass of each phase, momentum and energy). We
also show that the method solves two key issues with the two fluid approach: it
avoids over-damping of the mixture when the drag is strong and prevents a
problem with dust particles becoming trapped below the resolution of the gas.
  We also show how the general one-fluid formulation can be simplified in the
limit of strong drag (i.e. small grains) to the usual SPH equations plus a
diffusion equation for the evolution of the dust fraction that can be evolved
explicitly and does not require any implicit timestepping. We present tests of
the simplified formulation showing that it is accurate in the small
grain/strong drag limit. We discuss some of the issues we have had to solve
while developing this method and finally present a preliminary application to
dust settling in protoplanetary discs.
