A contact theory for surface tension driven systems
A contact theory for surface tension driven systems
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DOI：
10.1177/1081286514521230
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发表时间：
2016-03
影响因子：
2.6
通讯作者：
R. Sauer
中科院分区：
文献类型：
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作者：
R. Sauer
本文提出了表面张力驱动系统接触的一般模型描述。考虑与可变形固体基底接触的液滴的示例系统。这可以很容易地修改为考虑两种液体或两种固体接触。表面运动学，表面张力的建模必不可少的，在这里描述曲线坐标。特别是建模的重点是接触边界处的接触条件，在接触边界处可能会形成润湿脊。它示出，在准静态和超弹性的情况下，控制方程可以从一个全球性的潜在的，占接触，以及在体积和表面域的能量存储。共推导出21个欧拉-拉格朗日方程。除了这些强形式的方程，控制弱形式以及它的完全线性化，这是计算方法所需要的，也进行了讨论。它示出的控制方程可以进一步简化成一组减少的方程，然后适合于一个有效的计算实现系统。这里不讨论计算求解方法，因为目前的重点是理论及其含义。尽管如此，给出了一些关于解析解的评论，以及一个简单的计算例子。这项工作的一个辅助好处是系统的运动学和本构方程的变化和线性化的总结。
This paper presents a general model description for the contact of surface tension driven systems. The example system of a liquid droplet in contact with a deformable solid substrate is considered. This can be easily modified to consider two liquids or two solids in contact. The surface kinematics, essential to the modeling of surface tension, are described here in curvilinear coordinates. In particular modeling focus are the contact conditions at the contact boundary, where a wetting ridge may develop. It is shown that in the case of quasi-statics and hyperelasticity the governing equations can be derived from a global potential that accounts for contact as well as the energy storage within the bulk and surface domains. Altogether, 21 Euler–Lagrange equations are derived in this manner. Apart from these strong form equations, the governing weak form as well as its complete linearization, which are required for computational methods, are also discussed. It is shown that the governing equations can be further simplified into a reduced set of equations that are then suitable for an efficient computational implementation of the system. Computational solution methods are not discussed here, as the present focus is on the theory and its implications. A few remarks on analytical solutions, as well as a simple computational example, are given nonetheless. An auxiliary benefit of this work is a summary of the variation and linearization of the kinematical and constitutive equations of the system.