Inertial instability of flows on the inside or outside of a rotating horizontal cylinder

Abstract

AbstractWe consider thin liquid films on the inside (rimming flows) or outside (coating flows) of a cylinder with horizontal axis, rotating about this axis. If the liquid’s net volume is small, such films are known to evolve towards a steady state with a smooth surface, whereas, for larger amounts, the flow develops a ‘shock’ similar to a tidal bore. In this work, smooth films are shown to be unstable. Since the strongest instability occurs at wavelengths comparable to the film’s thickness, our analysis is based on the full Navier–Stokes equations, not on the lubrication approximation (which has been traditionally used in this problem). It is also shown that, for cylinders of sufficiently small radii, the instability can be suppressed by surface tension.