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Multiple equilibria in a simple elastocapillary system

Published online by Cambridge University Press:  28 September 2012

Michele Taroni  and
Dominic Vella
Michele Taroni
Affiliation:
Oxford Centre for Collaborative Applied Mathematics, Mathematical Institute, 24-29 St Giles’, Oxford OX1 3LB, UK
Dominic Vella*
Affiliation:
Oxford Centre for Collaborative Applied Mathematics, Mathematical Institute, 24-29 St Giles’, Oxford OX1 3LB, UK Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Rd, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Interfacial Flows (free surface): Capillary flows Low-Reynolds-number flows: Lubrication theory Micro-/Nano-fluid dynamics: MEMS/NEMS
Type
Papers
Information
Journal of Fluid Mechanics , Volume 712 , 10 December 2012 , pp. 273 - 294
Copyright
©2012 Cambridge University Press

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