Numerical Solution of a Nonlinear One-Dimensional System of Differential Equations Describing the Motion of a Free Thin Film

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.

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“…Its full description is given in [8]. A finite-difference conservative implicit scheme on staggered grids, of accuracy O(∆x + ∆t), is applied.…”

Section: Static Solution and Relaxationmentioning

confidence: 99%

“…In the case of a laterally bounded film by a solid boundary, the dynamics of a planar film is studied numerically in [7], [8] and [9]. In the last work, the electrostatic and steric repulsive components are included into the disjoining pressure.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and Stability of Free Thin Films

Tabakova¹,

Todorov²,

Christov³

2010

AIP Conference Proceedings

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“…(3.1) and (3.2), with initial and boundary conditions, Eqs. (3.4)-(3.6), can be solved numerically by appropriate conservative finite difference scheme on staggered grids and iterative algorithms [52]. Here, we develop a faster numerical method briefly described in Appendix B.…”

Section: One-dimensional Thin Liquid Films Attached To Framesmentioning

confidence: 99%