Droplet-induced abnormal bending of micro-beams

Abstract

We present a theoretical study of the abnormal deformation of micro-beams induced by a droplet placed on their top/bottom surfaces. The bending moments and deflections of the micro-beams are derived in consideration of the surface tension and Laplacian pressure difference of the droplet. The deflection curves show that the cantilever inevitably tilts upwards with a droplet on its top surface, and most parts of the simply supported beam and clamped–clamped beam will bend upwards when a droplet is adhered to their bottom surfaces. These anomalous deformation behaviors have been verified by our finite element simulations. We also demonstrate what extent of the boundary conditions will affect the deflection curves of the micro-beams during the variation of the droplet’s parameters. Understanding this abnormal bending mechanism of the beams can be beneficial to some industry applications, such as the micro-electro-mechanical systems (MEMS) and the micro/nano-measurement, which can provide the inspiration of engineering more precision micro-sensors.

Keywords:

• surface tension
• Laplacian pressure difference
• analytical solution
• numerical simulation
• boundary conditions

Acknowledgements

The authors are grateful for National Natural Science Foundation of China (11272357 and 11102140), the Doctoral Fund of Ministry of Education of China (20110141120024), and opening project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) (Grant No. KFJJ12-11M). Jianlin Liu also acknowledges the supporting of BK scholarship from Seoul National University.