Modeling and simulation of viscoelastic film retraction

In this paper, we investigate the retraction of a circular viscoelastic liquid film with a hole initially present in its center by means of finite element numerical simulations. We study the whole retraction process, aiming at understanding the hole opening dynamics both when the hole does not feel any confinement and when it interacts with the solid wall bounding the film. The retraction behavior is also interpreted through a simple toy model, that highlights the physical mechanism underlying the process. We consider three different viscoelastic constitutive equations, namely, Oldroyd-B, Giesekus (Gsk), and Phan Thien–Tanner (PTT) models, and several system geometries, in terms of the film initial radius and thickness. For each given geometry, we investigate the effects of liquid inertia, elasticity, and flow-dependent viscosity on the dynamics of the hole opening. Depending on the relative strength of such parameters, qualitatively different features can appear in the retracting film shape and dynamics. When inertia is relevant, as far as the opening hole does not interact with the wall bounding the film, the influence of liquid elasticity is very moderate, and the retraction dynamics tends to the one of Newtonian sheets; when the hole starts to interact with the solid wall, hole radius/opening velocity oscillations are detected. Such oscillations are enhanced at increasing elasticity. From the morphological point of view, the formation of a rim at the edge of the retracting film is observed. If inertial forces become less relevant with respect to viscous forces, R-oscillations disappear, the hole opening velocity goes through a maximum and then monotonically decays to zero, and no rim forms during the film retraction. Geometrical changes have the effect of enlarging or reducing the portion of the retraction dynamics not influenced by the presence of the solid wall with respect to the one governed by the hole-wall interactions.