On the breakup of fluid films of finite and infinite extent

Abstract

We study the dewetting process of thin fluid films that partially wet a solid surface. Using a long-wave ͑lubrication͒ approximation, we formulate a nonlinear partial differential equation governing the evolution of the film thickness, h. This equation includes the effects of capillarity, gravity, and an additional conjoining/disjoining pressure term to account for intermolecular forces. We perform standard linear stability analysis of an infinite flat film, and identify the corresponding stable, unstable, and metastable regions. Within this framework, we analyze the evolution of a semi-infinite film of length L in one direction. The numerical simulations show that for long and thin films, the dewetting fronts of the film generate a pearling process involving successive formation of ridges at the film ends and consecutive pinch-off behind these ridges. On the other hand, for shorter and thicker films, the evolution ends up by forming a single drop. The time evolution as well as the final drops pattern show a competition between the dewetting mechanisms caused by nucleation and by free surface instability. We find that precise computations, requiring quadrupole precision of computer arithmetic, are often needed to avoid spurious results.

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

“…Above a critical translation speed, however, a thin liquid film is left on the wafer, that spontaneously breaks up, dewets and leads to undesirable residual droplets on the substrate. Similar film rupture and dewetting phenomena have been described for thin layers of polymer melts [18][19][20][21][22][23][24][25][26][27], metals [28][29][30][31][32] and oil films submersed in water [33][34][35].…”

Comparison of Navier-Stokes simulations with long-wave theory: Study of wetting and dewetting

“…Note that here we are assuming a dependence on θ eq in the form of (tan 2 θ eq )/2 instead of (1 − cos θ eq ) as usually seen in the literature. 24,30 In fact, the former dependence comes directly from using the linearized form of the free surface curvature, 31 which is consistent with the hypothesis of small slope in the L-W approximation, while the latter is derived when using the complete (nonlinear) form. The connection between K and θ eq has been recently discussed in more detail in Ref.…”

“…29 Instead of characterizing the interaction by means of A, it is also possible to relate K with the equilibrium contact angle, θ eq , as discussed in some detail in, e.g., Ref. 24. Briefly, through the "augmented" Young-Laplace condition, which assumes a local equilibrium of pressures, one obtains K = tan 2 (θ eq )/(2Mh * ), where M = (n − m)/((m − 1)(n − 1)); we use (n, m) = (3, 2), and h * = 10 −3 except if specified differently.…”

“…We continue by describing the L-W model which also uses the slip model for consistency with the VoF based solver, and specifies the contact angle via a disjoining pressure approach, discussed in some detail in, e.g., Ref. 24. In Sec.…”

“…24 and the references therein). Using the time and length scales defined previously, the resulting (nondimensional) equation for the fluid thickness, h = h(x, y, t), …”