Statics and Dynamics of Liquid Barrels in Wedge Geometries

Elfego Ruiz Gutierrez, Ciro Semprebon, Glen McHale, Rodrigo Ledesma Aguilar

Research output: Contribution to journalArticlepeer-review

Abstract

We present a theoretical study of the statics and dynamics of a partially wetting liquid droplet, of equilibrium contact angle θe, confined in a solid wedge geometry of opening angle. We focus on a mostly non-wetting regime, given by the condition θe−β >90◦, where the droplet forms a liquid barrel – a closed shape of positive mean curvature. Using a quasi-equilibrium assumption for the shape of the liquid–gas interface, we compute the changes to the surface energy and pressure distribution of the liquid upon a translation along the symmetry plane of the wedge. Our model is in good agreement with numerical calculations of the surface energy minimisation of static droplets deformed by gravity. Beyond the statics, we put forward a Lagrangian description of the droplet dynamics. We focus on the overdamped limit, where the driving capillary force is balanced by the frictional forces arising from the bulk hydrodynamics, the corner flow near the contact lines and the contact-line friction. Our results provide a theoretical framework to describe the motion of partially wetting liquids in confinement, and can be used to gain further understanding on the relative importance of dissipative processes that span from microscopic to macroscopic length scales.
Original languageEnglish
Pages (from-to)26-57
Number of pages32
JournalJournal of Fluid Mechanics
Volume842
Early online date6 Mar 2018
DOIs
Publication statusPublished - 10 May 2018

Keywords

  • Capillary flows
  • contact lines
  • liquid bridges
  • interfacial flows

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