Overview
Everyone who has ever shuffled across a carpet on a dry, cold winter day has direct experience with electrostatics. Many have even experienced the interaction between electrostatics and mechanical systems by rubbing a balloon on their hair and "sticking" it to a wall or ceiling. Yet, for most of us, our thinking about electrostatic-elastic systems ends with a short shock or the toy balloon. After all, in our everyday experience, the forces that interact with mechanical systems in a meaningful way are not electrostatic forces. Our automobiles use stored chemical energy, our car door locks use magnetic forces, our elevators are hydraulic, and even our electric trains use time-varying electrodynamic fields. The reason for this is simple; comparatively speaking electrostatic forces are weak. While electrostatic forces may temporarily hold a balloon to the ceiling, it's hard to use electrostatics to do useful work. Electrostatic motors generally remain curiosities. However, this thinking breaks down when we leave the realm of everyday experience and move into the microworld. In the microworld, i.e., where typical length scales are microns (10^-6 meters) electrostatic forces rule the day. Scaling laws render magnetic forces practically useless while electrostatic forces become comparatively strong. Since the late 1960's researchers in micro- and nanoelectromechanical systems (MEMS and NEMS) have been taking advantage of this fact and using electrostatic forces to make small things move. As a consequence, understanding how electrostatic forces make things move has gained in importance. That is, how do coupled electrostatic-elastic systems behave? In the MEC Lab we study this question experimentally by using a modified version of a clever experiment devised by the British fluid dynamicist, G.I. Taylor. Taylor recognized that while in the macroworld it was difficult to make most things move, thin, lightweight, low tension elastic membranes could be deflected when high voltages were applied. Soap films serve wonderfully as these membranes and can be deflected measurably with voltages around 10kV. Taylor used his setup to investigate an instability known to the MEMS community as the pull-in instability. In the MEC Lab, we are extending Taylor's study as well as investigating other aspects of electrostatic-elastic systems. Some of our experiments are outlined below.

 

 

The Pull-In Instability
The pull-in instability can be understood by considering the toy system shown at the left. In this system, a voltage difference, V, is applied between two conducting plates. The bottom plate is held fixed while the top plate is attached to a spring and free to move. If V=0, the system comes to rest with some gap, d, between the plates. If we increase V, d decreases. However, when we get to about d/3, any further increase in V results in the top plate slamming into the bottom plate! That is, the system "pulls-in" when V is turned past a critical voltage. You can imagine that this limits the design of lot's of MEMS and NEMS devices. Understanding this instability and understanding how to control this instability is the focus of much current research.

 

 

More Complex Systems
In the mass-spring system the pull-in phenomena is easy to understand and quantify. In fact, the pull-in distance turns out to be precisely d/3. This value has become a "rule of thumb" for MEMS researchers working with designs far from mass-spring systems! What is the pull-in voltage for the system pictured at the left? How does it vary as the shape of the membrane varies? What do deflections look like? When they pull-in, how long does it take? Where do the plates touch? These are some of the questions we are attempting to answer. Some of our result may be found in the references at the end of this page.

 

 

Our Experimental Setup
  Coming soon!

 

 

Related Links

 

 

References and Suggested Reading
[1] G.I. Taylor, The coalescence of closely spaced drops when they are at different electric potentials, Proc. Roy. Soc. A, 306 (1968), pp. 423-434.
[2] R.C. Ackerberg, On a nonlinear differential equation of electrohydrodynamics, Proc. Roy. Soc. A, 312 (1969), pp. 129-140.
[3] H.C. Nathanson, W.E. Newell, R.A. Wickstrom, and J.R. Davis, The resonant gate transistor, IEEE Trans. on Electron Devices. 14 (1967), pp. 117-133.
[4] J.A. Pelesko and D.H. Bernstein, Modeling MEMS and NEMS, Chapman & Hall/CRC Press, 2002.
[5] J.A. Pelesko and A.A. Triolo, Nonlocal problems in MEMS device control, Proceedings of MSM 2000, San Diego, CA, pp. 509-512, 2000.
 [6] J.A. Pelesko, Multiple solutions in electrostatic MEMS, Proceedings of MSM 2001,  Hilton Head, SC, pp. 290-293. 2001.
[7] J.A. Pelesko, Electrostatic field approximations and implications for MEMS devices, ESA 2001 Proceedings, pp. 126-137.
[8] J.A. Pelesko and A.A. Triolo, Nonlocal problems in MEMS device control, Journal of Engineering Mathematics, v. 41, pp. 345-366, 2001.
[9] J.A. Pelesko, Mathematical modeling of electrostatic MEMS with tailored dielectric properties, SIAM Journal on Applied Mathematics, v. 62, pp. 888-908, 2002.
[10] J.A. Pelesko, D.H. Bernstein, and J. McCuan, Symmetry and symmetry breaking in electrostatic MEMS, Proceedings of MSM 2003, in press.
[11] J.A. Pelesko and X.Y. Chen, Electrostatically deflected circular elastic membranes, Journal of Electrostatics, in press.