Long-wavelength stability of an unsupported multilayer liquid film falling under gravity

The long-wavelength stability of an unsupported multilayer liquid film falling under the effects of gravity and surface tension is investigated. By considering the Navier-Stokes equations for two fluid layers in the high-Reynolds-number and small-aspect-ratio limits the steady-state solutions are obtained. The stability criterion found by Lin (J Fluid Mech 104:111-118, 1981) for a one-layer fluid curtain is generalised to the two-layer case and the criterion for an n-layer curtain is established.