Nonlinear rupture of thin liquid films on solid surfaces

Stabilization mechanisms in the evolution of thin liquid-films

In recent years, there has been great interest in using control theory to alter the stability regimes of fluid systems. A flow property is measured at a point and relayed back to a control that alters a condition that opposes the instability, thereby postponing its onset. Here, we discuss an alternative to postponing and even eliminating instabilities without the need for measuring properties or designing control strategies: a shear flow imposed upon a system produces an interfacial viscous-capillary wave which, in the nonlinear regime, is capable of postponing or even eliminating the incipient instability. The literature shows several examples, whereby Rayleigh break-up of capillary jets is eliminated, van der Waals dry-out of a film is removed and thermocapillary instability is avoided by the application of a suitable surface shear or an imposed fluid flow. The stabilization mechanism is closely linked to the behaviour of the lower-order terms governing the evolution of the liquid–gas interface profile, providing an estimate for the time scales and shear strength involved. Our intention here is to develop a unified theoretical framework for the study of a large number of thin liquid-film configurations and related systems.

Instability, self-organization and pattern formation in thin soft films

The free surface of a thin soft polymer film is often found to become unstable and self-organizes into various meso-scale structures. In this article we classify the instability of a thin polymer film into three broad categories, which are: category 1: instability of an ultra-thin (<100 nm) viscous film engendered by amplification of thermally excited surface capillary waves due to interfacial dispersive van der Waals forces; category 2: instability arising from the attractive inter-surface interactions between the free surface of a soft film exhibiting room temperature elasticity and another rigid surface in its contact proximity; and category 3: instability caused by an externally applied field such as an electric field or a thermal gradient, observed in both viscous and elastic films. We review the salient features of each instability class and highlight how characteristic length scales, feature morphologies, evolution pathways, etc. depend on initial properties such as film thickness, visco-elasticity (rheology), residual stress, and film preparation conditions. We emphasize various possible strategies for aligning and ordering of the otherwise isotropic structures by combining the essential concepts of bottom-up and top-down approaches. A perspective, including a possible future direction of research, novelty and limitations of the methods, particularly in comparison to the existing patterning techniques, is also presented for each setting.

Rupture of thin liquid films: generalization of weakly nonlinear theory

In this paper, we investigate the rupture dynamics of thin liquid films driven by intermolecular forces via weakly nonlinear bifurcation analysis. The dynamic equations governing slow dynamics of the perturbation amplitude of the near-critical mode corresponding to several models describing the evolution of thin liquid films in different physical situations appear to have the same structure. When antagonistic (attractive and repulsive) molecular forces are considered, nonlinear saturation of the instability becomes possible, while the boundary of this supercritical bifurcation is determined solely by the form of the intermolecular potential. The rupture time estimate obtained in closed form shows an excellent agreement with the results of the previously reported numerical simulations of the strongly nonlinear coupled evolution equations upon fitting the amplitude of the small initial perturbation. We further extend the weakly nonlinear analysis of the film dynamics and apply the Galerkin approximation to derive the amplitude equation(s) governing the dynamics of the fastest growing linear mode far from the instability threshold. The comparison of the rupture time derived from this theory with the results of numerical simulations of the original nonlinear evolution equations shows a very good agreement without any adjustable parameters.

Rupture of thin films with resonant substrate patterning

We study the stability and rupture of thin liquid films on patterned substrates. It is shown that striped patterning on a length scale comparable to that of the spinodal instability leads to a resonance effect and an imperfect bifurcation of equilibrium film shapes. Weakly nonlinear analysis gives predictions for film shapes, stability, growth rates, and rupture times, which are confirmed by numerical solution of the thin-film equation. Film behavior is qualitatively different in the resonant patterning regime, but with sufficiently large domains rupture occurs on a spinodal length scale regardless of patterning. Instabilities transverse to the patterning are examined and shown to behave similarly as disturbances to films on uniform substrates. We explain some previously reported effects in terms of the imperfect bifurcation.