Ribbing instability in the rotating drag-out problem

We study experimentally and numerically the flow around a rotating wheel, when this wheel is partially immersed in a liquid reservoir. Two liquids are used: water, and an 80 times more viscous mixture of water and UCON oil. For large enough rotation rates, the initially 2D liquid film entrained along the wheel destabilizes into several parallel liquid ribs. These ribs are reminiscent of the fingers forming in the printer's instability, but in a strongly inertial limit. We measure the spacing between these ribs as a function of wheel velocity, viscosity and depth of immersion (up to 50% of wheel radius). A 3D numerical simulation is carried out with Basilisk for the conditions of the experiment: this simulation shows a good agreement with experimental results, and yields insight into the mechanism of rib formation. We will show that this mechanism relies on the variations of pressure within the liquid film, as it is extracted from the bath. We will discuss the implications of this mechanism for predicting the wavelength of this ribbing instability.