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Morphological evolution of microscopic dewetting droplets with slip

Published online by Cambridge University Press:  04 September 2017

Tak Shing Chan Open the ORCID record for Tak Shing Chan [Opens in a new window] ,
Joshua D. McGraw ,
Thomas Salez ,
Ralf Seemann  and
Martin Brinkmann
Tak Shing Chan*
Affiliation:
Experimental Physics, Saarland University, D-66041 Saarbrücken, Germany
Joshua D. McGraw
Affiliation:
Département de Physique, Ecole Normale Supérieure/PSL Research University, CNRS, 24 rue Lhomond, 75005 Paris, France
Thomas Salez
Affiliation:
Laboratoire de Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI Paris, PSL Research University, Paris, France Global Station for Soft Matter, Global Institution for Collaborative Research and Education, Hokkaido University, Sapporo, Japan
Ralf Seemann
Affiliation:
Experimental Physics, Saarland University, D-66041 Saarbrücken, Germany
Martin Brinkmann
Affiliation:
Experimental Physics, Saarland University, D-66041 Saarbrücken, Germany
*
†Email address for correspondence: tak.chan@physik.uni-saarland.de
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Abstract

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 $\tilde{b}$ 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 $\tilde{b}_{m}\approx O(0.1{-}1)$ 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 $\tilde{b}_{m}$. Around $\tilde{b}_{m}$, 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 $\tilde{b}\gg \tilde{b}_{m}$, friction at the substrate for $\tilde{b}\approx \tilde{b}_{m}$ and shear flows for $\tilde{b}\ll \tilde{b}_{m}$. Following the changes between these dominant dissipation mechanisms, our study indicates a crossover to the quasistatic regime when $\tilde{b}$ is many orders of magnitude smaller than $\tilde{b}_{m}$.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Contact lines Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
Papers
Information
Journal of Fluid Mechanics , Volume 828 , 10 October 2017 , pp. 271 - 288
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© 2017 Cambridge University Press 

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