MSE10: Elasto-capillarity in MEMS: drying and condensation

Background

Microelectromechanical systems (MEMS) devices present the potential for significant miniaturisation of mechanical and electrical components. However, the small scales involved introduce interactions that are negligible at larger dimensions but that cannot be ignored on the microscale. In particular, during fabrication and usage in humid environments, the surface tension of liquids can bend the minute flexible structures. A more complete theoretical understanding of the interaction between surface tension and elasticity, or ‘elastocapillarity’, is intended as a pathway towards the development of more robust MEMS design solutions.

Techniques and Challenges

We are interested in understanding the dynamics of elastocapillary systems. This involves the combination of elastic beam theory coupled with a lubrication theory assumption. The motion of fluid within the gap is driven by the Laplace pressure at the interface, which in turn deflects the beam. A key challenge is to solve for the beam deflection whilst simultaneously tracking the motion of the interface. This coupling is modelled using a sixth-order nonlinear parabolic partial differential equation (PDE) [1] and the solution of this equation is computed numerically using the method of lines.

Results

So far we have considered the simplest possible situation: a liquid drop placed between two initially parallel fixed-free elastic plates.
Depending upon various parameters, the system can have different equilibrium states: the beams may be slightly deformed or stick together. Even this simple system is surprisingly rich, and in many circumstances there are several equilibrium states. Using a linear stability analysis and full numerical solutions, we have investigated the stability of the multiple equilibria and shown that the stable equilbria chosen depends strongly upon initial conditions.

The Future

Our next step is to model the migration of a droplet beneath a beam, the equilibrium states of which have already been studied [2]. This is of interest from the point of view of understanding how MEMS devices may fail, and may also provide a method for the spontaneous transport of liquid in microfluidic applications.

References

[12/20] Taroni M., Vella D.: Multiple equilibria in a simple elastocapillary system

[1] Aristoff J.M., Duprat C., Stone H. A.: Elastocapillary imbibition, Inter. J. Nonlinear Mech. 46, 648–656, 2011

[2] Kwon H-M., Kim H-Y., Puell J., Mahadevan L.: Equilibrium of an elastically confined liquid drop, J. Appl. Phys. 103, 093519, 2008