Linear stability analysis of a sharp-interface model for dewetting thin films

Abstract

The stability of the receding front at the growing rim of a thin liquid film dewetting from a substrate is studied. The underlying forces that drive the dewetting motion are given by the intermolecular potential between the liquid film and the substrate. The role of slippage in the emerging instability is studied via a sharp-interface model for the dewetting thin film, which is derived from the lubrication model via matched asymptotic expansions. Using the separation of the time-scale for the slow growth of the rim and the time-scale on which the rim destabilises, the sharp-interface results are compared to earlier results for the lubrication model and good agreement for the unstable modes is obtained. The main advantage of the sharp-interface model is that it allows for the derivation of traveling solutions for the base state and subsequently a systematic linear stability analysis via normal modes. Interestingly, unlike the dispersion relations that are typically encountered for the well-known finger-instability in thin-film flows, where the dependence of the growth rate on the wave number is quadratic, here it is linear.Keywords Asymptotic methods · High-order nonlinear boundary-value problems · Sharp-interface model · Stability analysis · Thin liquid films

Stability Analysis of Unsteady, Nonuniform Base States in Thin Film Equations

“…In addition to the typically expected even powers ofQ, the expansion also contains odd powers ofQ which is due to the fact that the eigenvalueλ = 0 atQ = 0 is degenerate, i.e., belongs to a Jordan block. This is very similar to the situation found for dewetting a liquid in a slip-dominated case [23]. Proceeding as in that reference, we obtain the valueλ 1 = (3/2) 1/2 = 1.22; details are given in Appendix C. Good agreement with the numerically found eigenvalues up toQ = 0.3 is seen in Figure 4(left) for the positive value forλ 1 .…”

“…However, this concept has to be reconsidered for problems where the correspond-a suitably chosen comoving frame of reference, and a normal-mode ansatz is possible again. Using scaling arguments to take into account the evolving base state, the amplification of a perturbation was inferred from the resulting spectrum [23,34]. A related approach was followed for a model of anisotropic solid dewetting in [9].…”

Deformation and dewetting of thin liquid films induced by moving gas jets

“…Three nucleated dry-spots grow with an initial dewetting speed of approximately 850 lm/s. The dewetting rims of the receding contact lines are corrugated and exhibit a well-known rim instability [50][51][52][53]. The fastest growing wavelength k max for this instability was found to depend on the width b of the rim and the contact angle h, according to k max /b = b(h).…”

An anisotropic phase-field model for solid-state dewetting and its sharp-interface limit

“…While the dynamical evolution has many similarities with the dewetting of liquid thin films, which has been investigated in numerous theoretical and experimental studies [2,28,50,51] and recently reviewed in [8], solid dewetting has not received as much attention. The physical mechanisms for the mass transport underlying the dewetting of solid films is also quite different and it is based on capillarity driven surface diffusion [26,57,61].…”