Taylor-Culick retractions and the influence of the surroundings

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) >> 1), namely We(f) similar to Oh(s)(-2) and Ca-s similar to Oh(s)(0) for the two-phase Taylor-Culick configuration, and We(f) similar to Oh(s)(-)(1) an d Ca-s Oh(s)(1/)(2) for the three-phase Taylor-Culick configuration.

Automated summary

The retraction velocity of a liquid film is affected by the presence of an external viscous medium, with the speed depending on the dissipation within that medium. This study examines the retraction of a liquid film in a viscous oil ambient and between air and a viscous oil. The dependence of retraction velocity on oil viscosity is weaker when the film is sandwiched between air and oil. This weaker dependence arises from the localization of viscous dissipation near the three-phase contact line.