We consider the elastocapillary interaction of a liquid drop placed between two elastic beams, which are both clamped at one end to a rigid substrate. This is a simple model system relevant to the problem of surface-tension-induced collapse of flexible micro-channels that has been observed in the manufacture of microelectromechanical systems (MEMS). We determine the conditions under which the beams remain separated, touch at a point, or stick along a portion of their length. Surprisingly, we show that in many circumstances multiple equilibrium states are possible. We develop a lubrication-type model for the flow of liquid out of equilibrium and thereby investigate the stability of the multiple equilibria. We demonstrate that for given material properties two stable equilibria may exist, and show via numerical solutions of the dynamic model that it is the initial state of the system that determines which stable equilibrium is ultimately reached. © 2012 Cambridge University Press.
|Original language||English (US)|
|Number of pages||22|
|Journal||Journal of Fluid Mechanics|
|State||Published - Sep 28 2012|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This publication was based on work supported in part by Award No KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). We also thank M. Mihelich for his contribution to the early stages of this work as a summer student supported by an Oppenheimer Early Career Fellowship (D.V.), and K. Singh for comments on an earlier draft. Finally, we thank O. E. Jensen for pointing out a discrepancy in earlier versions of our energy calculation.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.