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, S. Kumar

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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.

Original languageEnglish (US)
Article number053009
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume90
Issue number5
DOIs
StatePublished - Nov 17 2014

Bibliographical note

Publisher Copyright:
© 2014 American Physical Society.

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