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

TL;DR

This paper investigates how partially wetting liquids behave on a rotating cylinder, analyzing bifurcations and flow transitions as rotation speed and wettability change, using numerical and asymptotic methods.

Contribution

It introduces a detailed bifurcation analysis of partially wetting liquids on a rotating cylinder, highlighting the effects of wettability on flow behavior and depinning transitions.

Findings

Depinning transition occurs for partially wetting liquids with increasing rotation speed.

Bifurcation structures change significantly with wettability.

Numerical continuation and asymptotic analyses support the results.

Abstract

We discuss the behavior of partially wetting liquids on a rotating cylinder using a model that takes into account the effects 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 \bfuwe{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 flow behavior it encodes changes with changing wettability. We employ various numerical continuation techniques that allow us to track stable/unstable steady and time-periodic film and drop thickness profiles. We support our findings by time-dependent numerical simulations and asymptotic analyses of steady and time-periodic profiles for large rotation numbers.