Dynamics and Stability of Free Thin Films

Abstract

The modeling of the free thin film dynamics and stability is usually performed in the framework of the extended lubrication approach, including inertial, viscous, capillary and intermolecular van-der-Waals forces. For films with mobile surfaces, this approach leads to a system of nonlinear PDE for the film thickness and lateral velocities. In the present work the 1D variant of this system is studied numerically in the case of a laterally bounded free film by a frame, with a prescribed wetting angle. A linear and non-linear stability analysis of this problem is performed and their results generalize the stability results obtained for periodic free films by other authors. It is shown that the film rupture can be caused either by the non-existence of a static film shape or by the instability of an existing static shape. It is found that the static film shapes are always stable when subjected to symmetrical disturbances, but can be unstable if asymmetrical disturbances are imposed on them. The latter fact depends on the wetting angle in combination with the action of the van-der-Waals attraction and of the surface tension.

The break-up of free films pulled out of a pure liquid bath

“…For instance, [14] and [15] describe the mechanism of free-film rupture for unbounded films and both highlight the importance of nonlinear contributions to the acceleration of the rupture phenomenon. Similarly, [16] have analysed the stability of free films attached to lateral plates by a given contact angle, the value of which determines whether static solutions are unstable or not under asymmetrical perturbations. However, all these works assume a uniform base state, i.e.…”