Refinements to the study of electrostatic deflections: Theory and experiment

To study electrostatic actuation, researchers commonly use a setup proposed by G. I. Taylor in [Proc. R. Soc. Lond. Ser. A, 306 (1968), pp. 423-434]. It consists of soap film held at a distance h above a rigid plate so that when a voltage difference is applied between the two components, the top film deflects towards the bottom plate. The most striking feature of this system is when the voltage difference exceeds a critical value V*, the electrostatic forces dominate the surface forces and the soap film gets 'pulled-into' or collapses onto the bottom plate. This so-called 'pull-in' instability is a ubiquitous feature of electrostatic actuation and as a result, has been the subject of many studies. Recently, Siddique et al. [J. Electrostatics, 69 (2011), pp. 1-6] measured the value of V* as a function of the separation distance and found that the standard prediction breaks down as h increases. Here, we continue the work done in [N. D. Brubaker and J. A. Pelesko, European J. Appl. Math., 22 (2011), pp. 455-470] by investigating the cause of this discrepancy. Specifically, we model the effect of gravity on the generalized version of Taylor's model and study whether it provides the proper correction to the predicted value of V*. In doing so, we derive two nonlinear eigenvalue value problems and investigate their solutions sets.