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Issue 46, 2015
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Planar equilibrium shapes of a liquid drop on a membrane

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Abstract

The equilibrium shape of a small liquid drop on a smooth rigid surface is governed by the minimization of energy with respect to the change in configuration, represented by the well-known Young's equation. In contrast, the equilibrium shape near the line separating three immiscible fluid phases is determined by force balance, represented by Neumann's Triangle. These two are limiting cases of the more general situation of a drop on a deformable, elastic substrate. Specifically, we have analyzed planar equilibrium shapes of a liquid drop on a deformable membrane. We show that to determine its equilibrium shape one must simultaneously satisfy configurational energy and mechanical force balance along with a constraint on the liquid volume. The first condition generalizes Young's equation to include changes in stored elastic energy upon changing the configuration. The second condition generalizes the force balance conditions by relating tensions to membrane stretches via their constitutive elastic behavior. The transition from Young's equation to Neumann's triangle is governed by the value of the elasto-capillary number, β = TRo/μh, where TRo is twice the surface tension of the solid–vapor interface, μ is the shear modulus of the membrane, and h is its thickness.

Graphical abstract: Planar equilibrium shapes of a liquid drop on a membrane

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Supplementary files

Article information


Submitted
26 Aug 2015
Accepted
11 Sep 2015
First published
14 Sep 2015

Soft Matter, 2015,11, 8960-8967
Article type
Paper
Author version available

Planar equilibrium shapes of a liquid drop on a membrane

C. Hui and A. Jagota, Soft Matter, 2015, 11, 8960
DOI: 10.1039/C5SM02157J

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