可伸长弹性软薄膜的毛细黏附

Capillary Adhesion of a Non-linearly Elastic Soft Membrane

软薄膜的毛细黏附问题在微机电系统(MEMS)、生物系统中大量存在,同时在薄膜的生产工艺中也至关重要。研究了任意形状的软薄膜在毛细力作用下的黏附,建立了相应的能量泛函,推导出了薄膜的挠度曲线以及相应的横截条件。并针对圆形软薄膜的毛细黏附,求解其挠曲线、横截条件,从而得到其临界黏附半径。计算中引入了表征黏附半径以及表面张力、薄膜张力组合的无量纲参数,得到了薄膜能够发生毛细黏附的参数临界值。这些分析对于工程设计,以及MEMS、生物系统的毛细黏附等有一定的参考价值。

Capillary adhesion of a soft thin membrane exists widely in MEMS technology and biological system, which is also vital for the fabrication of membranes. In this paper, capillary adhesion of a soft membrane with an arbitrary shape under capillary force is investigated. An energy model of the membrane/substrate system is developed, as to derive the deflection curve and the corresponding controversality conditions. The derivation results and the critical capillary adhesion radius of a circular soft membrane are also determined. In the calculation, critical parameters of the membrane are obtained in terms of a non-dimensional parameter, which represents the capillary adhesion radius, surface tension, and tension force of the membrane. These theoretical analyses may be beneficial to engineering applications and micro/nano-measurements.