Breakup of ultra-thin liquid films on vertical fiber enhanced by Marangoni effect

Abstract

An ultra-thin liquid film flowing down a vertical uniformly heated cylinder under the influence of gravity is investigated. A thin liquid film model is derived, assuming that the film thickness h is much smaller than the fiber radius a. To predict the breakup of film, the van der Waals attraction, proportional to h-3, is taken into account. Linear stability analysis shows that the Rayleigh-Plateau instability is enhanced by the long-range attractions and Marangoni effect. The spatial-temporal stability analysis shows that the instability is absolute when A+M>0.17 (A is a composite Hamaker number accounting for the strength of van der Waals attractions and M is the Marangoni number). A self-similarity analysis shows that the film thins as h∼(tr-t)1/5 (tr is the breakup time), which is supported by the numerical simulations of the thin film model. Although the scaling is independent on the Marangoni effect, nonlinear simulations demonstrate that the breakup time tr decreases as the Marangoni effect becomes stronger, demonstrating that the breakup process is accelerated by the Marangoni effect. Nonlinear simulation also shows that the thin heated or non-heated film mainly breaks up in the absolutely unstable regime.