Taylor–Culick retractions and the influence of the surroundings

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.

Inertio-capillary rebound of a droplet impacting a fluid bath

“…(2020) and recently by Sanjay et al. (2022 b ). With different symbolic definitions for underlying colour functions representing the droplet and the bath in the VOF framework, the algorithm ensures that numerically induced coalescence is avoided, and the entrapped gas region between the impacting drop and the pool is well resolved throughout the studied motion.…”

“…The implementation described above is made available to interested users at https://github.com/rcsc-group/ BouncingDroplets. A particularity of our set-up lies in the integration of the recent functionality developed for non-coalescence scenarios, as previously employed by Ramírez-Soto et al (2020) and recently by Sanjay et al (2022b). With different symbolic definitions for underlying colour functions representing the droplet and the bath in the VOF framework, the algorithm ensures that numerically induced coalescence is avoided, and the entrapped gas region between the impacting drop and the pool is well resolved throughout the studied motion.…”

Drop impact on viscous liquid films

“…(E a t (t/τ γ = 4) ≈ 0.01E 0 ). Readers are referred to Landau & Lifshitz (1987), Wildeman et al (2016), Ramírez-Soto et al (2020 and Sanjay et al (2022) for details of energy budget calculations.…”

When does an impacting drop stop bouncing?

“…Upon impact, the liquid first spreads (Philippi, Lagrée & Antkowiak 2016;Gordillo, Sun & Cheng 2018) until it reaches its maximal extent (Clanet et al 2004;Laan et al 2014;Wildeman et al 2016;Gordillo, Riboux & Quintero 2019). It then recoils, following a Taylor-Culick-type retraction parallel to the substrate (Taylor 1959;Culick 1960;Bartolo, Josserand & Bonn 2005;Deka & Pierson 2020;Pierson et al 2020;Sanjay et al 2022), and ultimately bounces off in an elongated shape perpendicular to the substrate (Richard & Quéré 2000;Yarin 2006;Josserand & Thoroddsen 2016).…”

“…2020; Sanjay et al. 2022), and ultimately bounces off in an elongated shape perpendicular to the substrate (Richard & Quéré 2000; Yarin 2006; Josserand & Thoroddsen 2016).…”