Historically, electrostatic forces and capillary surfaces have been a main focus of scientific inquiry. Recently, with the move towards miniaturization in technology, systems that include the interplay of these two phenomena have become more relevant than ever. This is because at small scales, capillary and electrostatic forces come to dominate familiar macro scale forces and consequently, govern the behavior of many components used in modern technology. In particular, these electro-capillary systems have been applied to areas such self-assembly, “lab-on-a-chip” devices, microelectromechanical systems and mass spectrometry.
In this dissertation, we study two such systems. The first system involves subjecting a planar soap film to a vertically directed electric field. The second is an extension of the first that includes the small effect of gravity (or, similarly, a constant external pressure). Mathematical models for these systems are developed via variational techniques to describe the equilibrium deflection of the soap-film. In contrast to the standard theory, these models include the full effect of capillarity, yielding two prescribed mean curvature problems. These problems are then studied for general and specific domains, using a combination of analytic, asymptotic and numerical techniques. A detailed analysis of the solution set reveals several interesting bifurcation structures. Highlighted areas include a blow-up in the gradient, which occurs at the onset of strictly parametric solutions, and a prediction of the so-called pull-in instability with respect to the aspect ratio of the system, which provides an update to the standard theory. The work here illustrates the effect of including the mean curvature operator in such models and starts to build a general theory of electro-capillary surfaces.
|Advisor:||Pelesko, John A.|
|Commitee:||Cakoni, Fioralba, Edwards, David A., Lindsay, Alan E.|
|School:||University of Delaware|
|Department:||Department of Mathematical Sciences|
|School Location:||United States -- Delaware|
|Source:||DAI-B 75/01(E), Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Mathematics|
|Keywords:||Electric fields, Electro-capillary surfaces, Gravity effects, Palanr films|
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