| Authors: Kiran Singh† Tae-Hong Kim∗ Ho-Young Kim∗ Dominic Vella† †OCCAM, The Mathematical Institute, University of Oxford, UK ∗Seoul National University, Seoul, South Korea Abstract: MEMS (or micro-electromechanical) devices present the potential for significant miniaturisation of mechan- ical and electrical components. However fabrication failure rates of these devices are high, and often attributed to the wetting and drying processes involved in fabrication. At micron scales the capillary forces at the evaporating air-liquid interface can cause the minute flexible structures to bend; if the components stick together or break the operation of the device is compromised. A key focus of this work is to understand this sticking of flexible beams due to surface tension forces: a combination of elasticity and capillarity that is often known as elasto-capillarity. A key question is: On what time scale does sticking occur? We present a lubrication theory model of the liquid dynamics, coupled to the elasticity of the beams to address this question. The characteristic time scale that emerges from this model for an isolated pair of beams sticking together is too short to account for experimental observations. However, by incorporating evaporation we show that it is, in principle, possible to prevent sticking altogether by evaporating sufficiently quickly. The difference between predicted and observed timescales leads us to consider multi-body interactions. We develop a toy model of the system and show that structures can spontaneously rearrange into clusters, where the characteristic cluster size depends upon the stiffness of the structures relative to the surface tension of the liquid. This picture is consistent with experiments on multiple coalescing fibres [1]. The numerical model is then used to demonstrate that multi-body effects can indeed decelerate the onset of elastocapillary instabilities by several orders of magnitude. Although our work is principally motivated by MEMS applications, similar phenomenon are observed over length scales that range from nanometres to several centimetres [2], suggesting a larger remit for the approach and results developed here. REFERENCES [1] B. Jose, B. Roman, L. Moulin, and A. Boudaoud. Elastocapillary coalescence in wet hair. Nature, 432:690, 2004. [2] B. Roman and B. Jose. Elasto-capillarity: deforming an elastic structure with a liquid droplet. J. Phys: Condens Matter, 22:493101, 2010. |
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