Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder

Lin T, Rogers S, Tseluiko D, Thiele U

Zusammenfassung

We discuss the behavior of partially wetting liquids on a rotating cylinder using a model that takes into account the e ects of gravity, viscosity, rotation, surface tension, and wettability. Such a system can be considered as a prototype for many other systems where the interplay of spatial heterogeneity and a lateral driving force in the proximity of a first- or second-order phase transition results in intricate behavior. So does a partially wetting drop on a rotating cylinder undergo a depinning transition as the rotation speed is increased, whereas for ideally wetting liquids, the behavior only changes quantitatively. We analyze the bifurcations that occur when the rotation speed is increased for several values of the equilibrium contact angle of the partially wetting liquids. This allows us to discuss how the entire bifurcation structure and the ow behavior it encodes change with changing wettability. We employ various numerical continuation techniques that allow us to track stable/unstable steady and time-periodic lm and drop thickness pro les. We support our ndings by time-dependent numerical simulations and asymptotic analyses of steady and time-periodic pro les for large rotation numbers.