  A jet of non-Brownian particles confined in a thin cell and driven by
gravitational force is studied both numerically and theoretically. We present a
theoretical scheme aimed to describe such a system in the Stokes regime. We
focus on the dynamics of the interface between the suspension and the pure
fluid. Numerical simulations solving Newton's equations for all particles show
that the jet free surface becomes unstable: the fastest growing modes at small
sizes coarsen up to the largest structures reaching the jet lateral scale. In
the bulk, structural waves develop and travel at slightly slower speed than the
jet average fall. An analytical model, based on hydrodynamic-like equations for
the suspension, is derived and predicts the development of the interfacial
instability. It captures in essence, the collective effects driving the
interface destabilization i.e. the long range hydrodynamic interactions coupled
with the abrupt interface, and no analogous to a surface tension is found.
