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

We 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.

Experimental Study of Rimming Flows of Two Liquids in a Partially Filled Horizontally Rotating Cylinder

An experimental study was carried out to examine the flow patterns and the stability of rimming flows of two liquids in partially-filled horizontally rotating cylinders. Pure water and oil were considered as non-miscible liquids; the third phase in the cylinder was normal air. The effect of cylinder aspect ratio (length to diameter) was investigated, too. Significant mixing and de-mixing phenomena were observed between both liquids, and interesting transition processes occurred in the rotating multi-phase flow. The liquid configuration and flow characteristics were systematically visualized, and the resulting vibration spectra and Campbell diagrams were also obtained. It was found that the existence of a special sub-synchronous vibration was intimately connected with the transition to the rimming flow state. In contrast to the simple expectation, the experimental results indicated that non-trivial turbulent flow was present in the liquid domain even in case of the rimming flow state for high running speed. This is fully in contrast to the common assumption of a primary rigid-body motion of the liquid at this running speed level.

Steady rimming flows with surface tension

We examine steady flows of a thin film of viscous fluid on the inside of a cylinder with horizontal axis, rotating about this axis. If the amount of fluid in the cylinder is sufficiently small, all of it is entrained by rotation and the film is distributed more or less evenly. For medium amounts, the fluid accumulates on the ‘rising’ side of the cylinder and, for large ones, pools at the cylinder's bottom. The paper examines rimming flows with a pool affected by weak surface tension. Using the lubrication approximation and the method of matched asymptotics, we find a solution describing the pool, the ‘outer’ region, and two transitional regions, one of which includes a variable (depending on the small parameter) number of asymptotic zones.