open access

https://hdl.handle.net/2115/68436

Morphological evolution of microscopic dewetting droplets with slip

英語

interfacial flows (free surface)

2017-09-04

Cambridge University Press

Journal of Fluid Mechanics

828

271-288

<Abstract 1>We investigate the dewetting of a droplet on a smooth horizontal solid surface for different slip lengths and equilibrium contact angles. Specifically, we solve for the axisymmetric Stokes flow using the boundary element method with (i) the Navier-slip boundary condition at the solid/liquid boundary and (ii) a time-independent equilibrium contact angle at the contact line. When decreasing the rescaled slip length b˜ with respect to the initial central height of the droplet, the typical non-sphericity of a droplet first increases, reaches a maximum at a characteristic rescaled slip length b˜m ≈(O.0:1–1) and then decreases. Regarding different equilibrium contact angles, two universal rescalings are proposed to describe the behaviour of the non-sphericity for rescaled slip lengths larger or smaller than b˜m. Around Qbm, the early time evolution of the profiles at the rim can be described by similarity solutions. The results are explained in terms of the structure of the flow field governed by different dissipation channels: elongational flows for b˜ 》 b˜m, friction at the substrate for b˜≈ b˜m and shear flows for b˜《 b˜m. Following the changes between these dominant dissipation mechanisms, our study indicates a crossover to the quasistatic regime when b˜is many orders of magnitude smaller than b˜m.<Abctract 2>In many macroscopic dynamic wetting problems, it is assumed that the macroscopic interface is quasistatic, and the dissipation appears only in the region close to the contact line. When approaching the moving contact line, a microscopic mechanism is required to regularize the singularity of viscous dissipation. On the other hand, if the characteristic size of a fluidic system is reduced to a range comparable to the microscopic regularization length scale, the assumption that viscous effects are localized near the contact line is no longer justified. In the present work, such microscopic length is the slip length. Our recent study on dewetting polymer microdroplets demonstrated that slip plays a dominant role in the shape evolution as the droplet relaxes toward equilibrium (McGraw et al. 2016). The transient profiles of the droplet were found to be highly non-spherical, meaning that the evolution is not quasistatic. In the present theoretical study, we investigate the dewetting of a droplet using the boundary element method. Specifically, we solve for the axisymmetric Stokes flow with i) the Navier-slip boundary condition at the solid/liquid boundary, and ii) a time-independent microscopic contact angle at the contact line. The profile evolution is computed for different slip lengths and equilibrium contact angles. When decreasing the slip length, the typical nonsphericity first increases, reaches a maximum at a characteristic slip length ˜bm, and then decreases. Regarding different equilibrium contact angles, two universal rescalings are proposed to describe the behavior for slip lengths larger or smaller than ˜bm. Around ˜bm, the early time evolution of the profiles at the rim can be described by similarity solutions. The results are explained in terms of the structure of the flow field governed by different dissipation channels: viscous elongational flows for large slip lengths, friction at the substrate for intermediate slip lengths, and viscous shear flows for small slip lengths. Following the transitions between these dominant dissipation mechanisms, our study indicates a crossover to the quasistatic regime when the slip length is small compared to the droplet size.

学術雑誌論文

Accepted Manuscript

This article has been published in a revised form in Journal of Fluid Mechanics [http://doi.org/10.1017/jfm.2017.515. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © 2017 Cambridge University Press

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