Gravity-driven instability of a thin liquid film underneath a soft solid

S. H. Lee, K. L. Maki, D. Flath, S. J. Weinstein, C. Kealey, W. Li, C. Talbot, and S. Kumar
Phys. Rev. E 90, 053009 – Published 17 November 2014

Abstract

The gravity-driven instability of a thin liquid film located underneath a soft solid material is considered. The equations and boundary conditions governing the solid deformation are systematically converted from a Lagrangian representation to an Eulerian representation, which is the natural framework for describing the liquid motion. This systematic conversion reveals that the continuity-of-velocity boundary condition at the liquid-solid interface is more complicated than has previously been assumed, even in the small-strain limit. We then make clear the conditions under which the commonly used simplified version of this boundary condition is valid. The small-strain approximation, lubrication theory, and linear stability analysis are applied to derive an expression for the growth rate of small-amplitude perturbations. Asymptotic analysis reveals that the coupling between the liquid and solid manifests itself as a lower effective liquid-air interfacial tension that leads to larger instability growth rates. Although this suggests that it is more difficult to maintain a stable liquid coating underneath a soft solid, the effect is expected to be weak for cases of practical interest.

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 13 August 2014

DOI:https://doi.org/10.1103/PhysRevE.90.053009

©2014 American Physical Society

Authors & Affiliations

S. H. Lee1, K. L. Maki2, D. Flath3, S. J. Weinstein4, C. Kealey5, W. Li3, C. Talbot6, and S. Kumar1

  • 1Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455, USA
  • 2School of Mathematical Sciences, Rochester Institute of Technology, Rochester, New York 14623, USA
  • 3Department of Mathematics, Statistics, and Computer Science, Macalester College, St. Paul, Minnesota 55105, USA
  • 4Department of Chemical Engineering, Rochester Institute of Technology, Rochester, New York 14623, USA
  • 5Department of Mathematics, Beloit College, Beloit, Wisconsin 53511, USA
  • 6Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 90, Iss. 5 — November 2014

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×