Abstract
Thin polymer films on hydrophobic substrates are susceptible to rupture and hole formation. This, in turn, initiates a complex dewetting process, which ultimately leads to characteristic droplet patterns. Experimental and theoretical studies suggest that the type of droplet pattern depends on the specific interfacial condition between the polymer and the substrate. Predicting the morphological evolution over long timescales and on the different length scales involved is a major computational challenge. In this study, a highly adaptive numerical scheme is presented, which allows for following the dewetting process deep into the nonlinear regime of the model equations and captures the complex dynamics, including the shedding of droplets. In addition, our numerical results predict the previously unknown shedding of satellite droplets during the destabilization of liquid ridges that form during the late stages of the dewetting process. While the formation of satellite droplets is well known in the context of elongating fluid filaments and jets, we show here that, for dewetting liquid ridges, this property can be dramatically altered by the interfacial condition between polymer and substrate, namely slip. This work shows how dissipative processes can be used to systematically tune the formation of patterns.
Highlights
The no-slip condition is widely accepted as an appropriate boundary condition for flows of Newtonian liquids sheared along a solid surface
The primary problem is to resolve the length scales associated with nanoscopic residual layers that remain after the film has dewetted, typically about ∼ 0.1 − 1 nm up to thickness of about ∼ 10 − 1,000 nm of the growing rim, and to account for the slip length in the range of 1 − 1,000 nm and the length scale of the resulting instability of 103 − 104 nm
Our solution of the thin-film model in Eq 5 is based on a P2 finite element method (FEM), where the fourth-order equation is split into a system of two second-order equations
Summary
Dewetting is the hydrodynamic process where a uniform layer of liquid destabilizes and decays into distinct patterns of stationary droplets by virtue of interfacial and intermolecular energies These patterns can be predicted theoretically, and their evolution can be followed numerically in striking similarity to experimental results. A closer look at experimental results confirms these predictions In other contexts, such as liquid jets or fluid filaments, formation of satellite droplets during rupture is well known, and their destabilization was observed to have a rich structure of intermediate asymptotic regimes [e.g., the works by Tjahjadi et al [27], Eggers and Villermaux [28], and Castrejon-Pita et al [29]].
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