Department of Chemical Engineering and Bioengineering Program, Lehigh University, Bethlehem, PA 18015, USA.
Proc Natl Acad Sci U S A. 2013 Jun 25;110(26):10541-5. doi: 10.1073/pnas.1304587110. Epub 2013 Jun 10.
We show that a drop of liquid a few hundred microns in diameter placed under a solid, elastic, thin film (∼10 μm thick) causes it to bulge by tens of microns. The deformed shape is governed by equilibrium of tensions exerted by the various interfaces and the solid film, a form of Neumann's triangle. Unlike Young's equation, which specifies the contact angles at the junction of two fluids and a (rigid) solid, and is fundamentally underdetermined, both tensions in the solid film can be determined here if the liquid-vapor surface tension is known independently. Tensions in the solid film have a contribution from elastic stretch and a constant residual component. The residual component, extracted by extrapolation to films of vanishing thickness and supported by analysis of the elastic deformation, is interpreted as the solid-fluid surface tension, demonstrating that compliant thin-film structures can be used to measure solid surface tensions.
我们证明，直径几百微米的液滴置于固体、弹性、薄膜（约 10 微米厚）下会导致其凸起数十微米。变形形状由各种界面和固体膜产生的张力平衡决定，这是一种 Neumann 三角形形式。与指定两种液体和（刚性）固体交界处接触角的杨氏方程不同，杨氏方程是基本欠定的，而在这里，如果独立地知道液体-蒸汽表面张力，则可以确定固体膜中的两个张力。固体膜中的张力有一个来自弹性拉伸的贡献和一个恒定的残余分量。残余分量通过对厚度趋于零的薄膜进行外推得到，并通过对弹性变形的分析得到支持，被解释为固-液表面张力，证明了顺应性薄膜结构可用于测量固体表面张力。
