Abstract
When a freely suspended liquid film ruptures, it retracts spontaneously under the action of surface tension. If the film is surrounded by air, the retraction velocity is known to approach the constant Taylor–Culick velocity. However, when surrounded by an external viscous medium, the dissipation within that medium dictates the magnitude of the retraction velocity. In the present work, we study the retraction of a liquid (water) film in a viscous oil ambient (two-phase Taylor–Culick retractions), and that sandwiched between air and a viscous oil (three-phase Taylor–Culick retractions). In the latter case, the experimentally measured retraction velocity is observed to have a weaker dependence on the viscosity of the oil phase as compared with the configuration where the water film is surrounded completely by oil. Numerical simulations indicate that this weaker dependence arises from the localization of viscous dissipation near the three-phase contact line. The speed of retraction only depends on the viscosity of the surrounding medium and not on that of the film. From the experiments and the numerical simulations, we reveal unprecedented regimes for the scaling of the Weber number${We}_{f}$of the film (based on its retraction velocity) or the capillary number${Ca}_{s}$of the surroundings versus the Ohnesorge number${Oh}_{s}$of the surroundings in the regime of large viscosity of the surroundings (${Oh}_{s} \gg 1$), namely${We}_{f} \sim {Oh}_{s}^{-2}$and${Ca}_{s} \sim {Oh}_{s}^{0}$for the two-phase Taylor–Culick configuration, and${We}_{f} \sim {Oh}_{s}^{-1}$and${Ca}_{s} \sim {Oh}_{s}^{1/2}$for the three-phase Taylor–Culick configuration.
Funder
FP7 Ideas: European Research Council
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics,Applied Mathematics
Reference106 articles.
1. Revisiting the Taylor–Culick approximation. II. Retraction of a viscous sheet;Deka;Phys. Rev. Fluids,2020
2. Fundamental fluid dynamics challenges in inkjet printing;Lohse;Annu. Rev. Fluid Mech.,2022
3. Théorie mécanique de la chaleur;Dupré;Ann. Chim. Phys.,1867
4. To split or not to split: dynamics of an air disk formed under a drop impacting on a pool;Jian;Phys. Rev. Lett.,2020
5. Popinet, S. & Collaborators 2013–2022 Basilisk. http://basilisk.fr (Last accessed: February 1, 2022).
Cited by
19 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献