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Research Article

. 2014; 2(1): 1-29

Adhesion of Condensed Bodies at Microscale: Variation with Movable Boundary Conditions

Jian-Lin Liu, Jing Sun, Runni Wu, Re Xia.


We review here the recent developments on the adhesion of condensed bodies at microsc]ale, spanning from droplets, microbeams, CNTs (carbon nanotubes) to cells. We first introduce a general method to completely tackle the adhesion problem with movable boundary conditions, from the viewpoint of energy variation. Based on this theoretical framework, we then use the developed line of reasoning to investigate the adhesion behaviors of several condensed systems. According to the variation with movable boundary conditions, the governing equations and transversality conditions of these systems are derived, leading to closed-form problems. The presented method is verified via the concept of energy release rate or J-integral in fracture mechanics. This analysis provides a new approach to explore the mechanism of different systems with similarities as well as to better understand the unification of nature. The analysis results may be beneficial to the design of micro-machined MEMS (micro-electro-mechanical systems) structures, super-hydrophobic materials, nano-structured materials, and hold potential for predicting the adhesion behavior of cells or vesicles.

Key words: CNT adhesion; Variational theory; beam adhesion; cell adhesion; droplet adhesion; transversality condition

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