The Plateau–Rayleigh instability of a liquid column underlies a variety of fascinating phenomena that can be observed in everyday life. In contrast to the case of a free liquid cylinder, describing the evolution of a liquid layer on a solid fibre requires consideration of the solid–liquid interface. Here we revisit the Plateau–Rayleigh instability of a liquid coating a fibre by varying the hydrodynamic boundary condition at the fibre–liquid interface, from no slip to slip. Although the wavelength is not sensitive to the solid–liquid interface, we find that the growth rate of the undulations strongly depends on the hydrodynamic boundary condition. The experiments are in excellent agreement with a new thin-film theory incorporating slip, thus providing an original, quantitative and robust tool to measure slip lengths.
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.
A viscous liquid film coating a fibre becomes unstable and decays into droplets due to the Rayleigh-Plateau instability (RPI). Here, we report on the generation of uniform droplets on a hydrophobized fibre by taking advantage of this effect. In the late stages of liquid column breakup, a three-phase contact line can be formed at one side of the droplet by spontaneous rupture of the thinning film. The resulting capillary imbalance leads to droplet propulsion along the fibre. We study the dynamics and the dewetting speed of the droplet as a function of molecular weight as well as temperature and compare to a force balance model based on purely viscous dissipation.
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