Keywords: micro-electro-mechanical systems, micro-pump, electromechanical coupling, dynamic pull-in, adhesion energy, stiction.

Micro-pumps are essential components in micro-electro-mechanical systems (MEMS), such as integrated drug delivery systems and cooling circuits for micro-electronics [1]. This paper refers to a special kind of micro-pump, actuated by an electrostatic mechanism, which may involve particular advantages from the industrial point of view. In electrostatic micro-pumps, a planar shell is actuated by the application of appropriate voltage on two opposite electrodes. The fluid in the reservoir is forced to flow in the micro-channels due to pressure difference induced by the plate deflection in the pump chamber [2].

In this work, focus is on the mechanical response of the pump chamber. The design procedure of such device should be based on multi-physics simulations, coupling electrostatic, structural and fluid dynamic phenomena. Analytical and numerical approaches have been exploited with the aim of understanding the behaviour of actuated plates in different load conditions. In order to obtain preliminary results and to understand the fundamentals of the mechanical response, a simplified finite element model has been devised, taking into account the interaction with the electric field and the fluid flow in the chamber. The results have been compared to those obtained, for simple systems, using analytical methods and fully coupled finite element codes.

The stable regime, when the applied voltage is lower than the so-called static pull-in voltage, is investigated in a quasi-static conventional framework. Subsequently, the dynamic behaviour of the structure is explored, leading to the identification of a dynamic pull-in voltage which is dependent on the quality factor. Attention is paid to the pull-in phenomena in non-linear dynamics, with the aim of controlling this feature and eventually to take advantage of it. The numerical outcomes are discussed and compared with those available in the literature for similar micro-systems. The results obtained are of wider applicability, in view of the fact that electrostatically actuated plates are key components of many other micro-devices, such as pressure sensors, microphones, microswitches.

The analysis of the device is completed by the evaluation of adhesion energy between the plate and the substrate, after contact has been reached because of pull-in. This study is essential in order to evaluate the so-called "stiction" of the plate and its release after capacitor deactivation. The adhesion energy is evaluated on the basis of the method proposed in [3]. In this way, it is possible to assess the risk of permanent adhesion for different geometries of the micro-plate.

1

B.D. Iverson, S.V. Garimella, "Recent advances in microscale pumping technologies: a review and evaluation", Microfluidics and Nanofluidics 130, 917-942, 2008. doi:10.1007/s10404-008-0266-8

2

E. Bertarelli, R. Ardito, E. Bianchi, K. Laganà, F. Procopio, L. Baldo, A. Corigliano, G. Dubini, R. Contro, "A computational study for design optimization of an electrostatic micro-pump in stable and pull-in regime", AES Technical Reviews B: International Journal of Advances in Mechanics and Applications of Industrial Materials, 2, 19-25, 2010.

3

R. Ardito, A. Corigliano, A. Frangi, "Multiscale Finite Element models for predicting spontaneous adhesion in MEMS", Mécanique & Industries, 11(3-4), 177-182, 2010. doi:10.1051/meca/2010028

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