Spout States in the Selective Withdrawal System

In selective withdrawal, fluid is withdrawn through a nozzle suspended above the flat interface separating two immiscible, density-separated fluids of viscosities ${\nu }_{upper}$ and ${\nu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.