Spout states in the selective withdrawal of immiscible fluids through a nozzle suspended above a two-fluid interface

In selective withdrawal, fluid is withdrawn through a nozzle suspended above the flat interface separating two immiscible, density-separated fluids of viscosities nu(upper) and nu(lower) = lambda nu(upper). At low withdrawal rates, the interface gently deforms into a hump. At a transition withdrawal rate, a spout of the lower fluid becomes entrained with the flow of the upper one into the nozzle. When lambda=0.005, the spouts at the transition are very thin with features that are over an order of magnitude smaller than any observed in the humps. When lambda=20, there is an intricate pattern of hysteresis and a spout appears which is qualitatively different from those seen at lower lambda. No corresponding qualitative difference is seen in the hump shapes.