Analytical model for the deformation of a fluid-fluid interface beneath an AFM probe.
Analytical model for the deformation of a fluid-fluid interface beneath an AFM probe.
复制标题
AFM 探针下方流体-流体界面变形的分析模型。
DOI：
10.1021/la304359h
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
H. Stone
中科院分区：
文献类型：
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作者：
D. Quinn;Jie Feng;H. Stone
我们提出了纳米级固体球体附近的流体-流体界面形状的解析解，这是一种由原子力显微镜常见测量引起的构型。所考虑的力是表面张力、重力和范德华引力。非线性控制方程以前是用匹配渐近展开的方法求解的，这要求表面张力远大于重力，即Bond数远小于1。我们首先使用方程的物理相关缩放来提出这种方法，然后提供一个适用于所有Bond数的新解析解。我们展示了一种具有大有效键数的结构，因此需要我们的新溶液，是铺在固体衬底上的纳米厚的液体膜。考虑了两种分析方法的标度含义，并将两者与完整方程的数值解进行了比较。
We present an analytical solution for the shape of a fluid-fluid interface near a nanoscale solid sphere, which is a configuration motivated by common measurements with an atomic force microscope. The forces considered are surface tension, gravity, and the van der Waals attraction. The nonlinear governing equation has been solved previously using the method of matched asymptotic expansions, and this requires that the surface tension forces far exceed those of gravity, i.e., the Bond number is much less than one. We first present this method using a physically relevant scaling of the equations, then offer a new analytical solution valid for all Bond numbers. We show that one configuration with a large effective Bond number, and thus one requiring our new solution, is a nanothick liquid film spread over a solid substrate. The scaling implications of both analytical methods are considered, and both are compared with numerical solutions of the full equation.