Viscous dissipation dictates Taylor-Culick type retractions

Surface tension minimizes the surface area of a ruptured liquid film resulting in a spontaneous retraction. For a long film surrounded by passive gaseous medium (like air), the retraction speed is known to approach a constant Taylor-Culick velocity (given by v_TC = (2γ/(ρh₀))^0.5 for a sheet of thickness, h₀, density ρ, and surface tension coefficient γ). This velocity is independent of the viscosity of both the film as well as the surrounding. In the present work, we study similar retraction dynamics of a liquid film (i) surrounded by a viscous medium (oil) and (ii) sandwiched between a passive (air) and a viscous media (oil). We show that the film in these configurations still retracts with a constant velocity that scales linearly with v_TC. However, the prefactor depends on the viscosity of the oil bath, η_s. The dependence is stronger in case of first configuration (i, v ∽ 1/η_s) as compared to the second (ii, v ∽ 1/η_s^0.5). This difference arises due to the localization of the viscous dissipation near the three-phase contact line in the second configuration. We look at the overall energy budgets to provide insights into the dynamics of this process.