Three-dimensional modelling of maximum fluid load on horizontally rotating cylinder

Abstract

It is a well-known fact that when a rod coated with a viscous liquid such as honey is rotated at a sufficiently high speed, the liquid will stop draining. However, when the liquid is left on the rod for a sufficiently long time, fluid will accumulate in bands around the cylinder. When these bands reach a sufficiently large amplitude, the fluid will drain from the rod. While previous literature has explored the formation and growth of these bands, none has explored the conditions under which the fluid in these bands will drain. In this paper, we make use of linear stability analysis to find the growth rate of the band and hence, the time taken for the band to reach the critical amplitude before draining occurs. We verify this approximation with full 3D simulations. Afterwards, this is used to plot a phase plot to identify if the fluid is draining at a specific point in time. We come to the compelling conclusion that the inevitable formation of bands on the rod will invariably lead to fluid drainage. This has important implications for rolling-coating operations where a uniform fluid coating is required as the coating will need to be complete before the fluid accumulates in bands.