Scaling and transition structure dependence on the fluid viscosity ratio in the selective withdrawal transition

In the selective withdrawal experiment, fluid is withdrawn through a tube with its tip suspended above a two-fluid interface. At sufficiently high flow rates, the interface undergoes a transition so that the lower fluid is entrained with the upper one, forming a spout. Previous experiments address the scalings and similarity profiles characterizing steady states of the system near the transition for one combination of fluids. In the present study, we show that these scalings and similarity profiles extend to systems with different viscosity ratios. Surprisingly, we find no dependence of the scalings and similarity profiles on the lower fluid viscosity. We use the results of a low-Reynolds-number flow dimensional analysis to show that for different fluid combinations the curves denoting the transition straw height as a function of flow rate can be collapsed. Finally, these results are used to argue that in the low-Reynolds-number regime, the capillary length sets the scale for the final curvature of the interface before the transition.