Ju l 2 01 5 Slip-Mediated Dewetting of Polymer Microdroplets

Classical models for wetting predict that an infinite work is required to move a three-phase contact line, defined as the line where a liquid-vapor interface intersects a solid surface. Assuming a slip boundary condition, in which the liquid slides against the solid, such an unphysical prediction is avoided. In this article, we present the results of experiments in which a contact line moves and where slip is a dominating and controllable factor. Spherical cap shaped polystyrene microdroplets, with non-equilibrium contact angle, are placed on solid self-assembled monolayer coatings from which they dewet. The relaxation is monitored using in situ atomic force microscopy, and the results are in agreement with scaling analysis and boundary element numerical integration of the governing Stokes equations, including a Navier slip boundary condition. We find that slip has a strong influence on the droplet evolutions, both on the transient non-spherical shapes and contact line dynamics. Unexpected flow phenomena emerge when the size of a liquid system is reduced below a certain length scale, typically on the order of a few to hundreds of nanometers [1–3]. Approaching this scale, effects associated with interfaces become increasingly important. One such effect is slip, wherein fluid slides along a solid confining boundary. Examples include flow of single-component [4, 5] and complex fluids [6, 7] in microand nano-channels, as well as dewetting [8, 9] and interfacial instabilities [10] of molten polymer films. The present work demonstrates that the relaxation of micron-sized droplets in contact with a solid planar surface is strongly influenced by slip effects. The no-slip boundary condition assumes no relative motion between liquid and solid at the phase boundary. This condition was historically assumed to be valid in all practical cases [3]. However, the no-slip condition is an empirical assumption and Experimental Physics, Saarland University, D-66041 Saarbrücken, Germany Max Planck Institute for Dynamics and SelfOrganization (MPIDS), 37077 Göttingen, Germany PCT Lab, UMR Gulliver 7083, ESPCI Paristech, PSL Research University, Paris, France email: j.mcgraw@physik.uni-saarland.de recent experimental techniques [1–3] have reached nanometric resolution, allowing for a critical assessment of this hypothesis at microscopic length scales. Slip lengths – defined as the distance beyond the solid over which a linear extrapolation of the velocity field reaches zero [11] – on the order of tens of nanometers for small-molecule liquids [1–3,12–15] and gases [16,17], and up to a couple of hundred nanometers [18–20], are now commonly reported. In dewetting thin polymer films, where the molecules are larger and highly coupled to the bulk liquid [21–23], slip lengths up to tens of micrometers have been reported [9, 10, 24–29]. Given the existence of such boundary conditions, it is relevant to ask what effect slip might have on the motion of a three-phase contact line. On one hand, a no-slip boundary condition at the contact line leads to a non-integrable divergence of the stress, and thus implies that moving a contact line requires infinite work. On the other hand, in common experience we are surrounded by liquid interfaces moving along solid surfaces, from water droplets on a wind screen, to the displacement of air by liquid through a capillary or porous medium. This apparent paradox [30] of contact line