Asymptotic behavior of a retracting two-dimensional fluid sheet

Two-dimensional (2D) capillary retraction of a viscous liquid film is studied using numerical and analytical approaches for both diphasic and free surface flows. Full 2D Navier-Stokes equations are integrated numerically for the diphasic case, while one-dimensional (1D) free surface model equations are used for free surface flows. No pinch-off is observed in the film in any of these cases. By means of an asymptotic matching method on the 1D model, we derive an analytical expansion of the film profile for large times. Our analysis shows that three regions with different timescales can be identified during retraction: the rim, the film, and an intermediate domain connecting these two regions. The numerical simulations performed on both models show good agreement with the analytical results. Finally, we report the appearance of an instability in the diphasic retracting film for small Ohnesorge number. We understand this as a Kelvin-Helmholtz instability arising due to the formation of a shear layer in the neck region during the retraction.