Variational analysis of electrowetting on dielectric configurations
Abstract/Contents
- Abstract
- This thesis considers a perfectly conducting fluid drop resting on a dielectric in the presence of an applied electric field. We first review background concepts, emphasizing the central role of mean curvature and Young's equation in capillarity. We then review prior work on this problem, which includes the classical Young-Lippmann equation as well as more modern approaches. Our analysis of this problem uses techniques from the calculus of variations to find the minimum energy configuration. In this way, we rigorously show that the fluid height and the electrostatic potential satisfy a pair of coupled differential equations. Our approach allows us to interpret the equation for fluid height geometrically; in particular, we analyze the effects of dielectric breakdown, finite volume, and the divergent field on the mean curvature of the fluid. We compare our analysis to a simplified spherical cap model and then develop the theory of partially conducting drops. Finally we construct an iterative algorithm to successively approximate both the drop shape and electric field, and we develop estimates for important parameters. The algorithm numerically finds that the contact angle saturates with increasing applied voltage, an improvement over the classical Young-Lippmann theory which does not predict saturation. We compare our results with current experiments and find in general qualitative agreement.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2011 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Bhatnagar, Rajat |
|---|---|
| Associated with | Stanford University, Department of Electrical Engineering |
| Primary advisor | Finn, Robert |
| Thesis advisor | Finn, Robert |
| Thesis advisor | Dutton, Robert W |
| Thesis advisor | Solgaard, Olav |
| Advisor | Dutton, Robert W |
| Advisor | Solgaard, Olav |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Rajat Bhatnagar. |
|---|---|
| Note | Submitted to the Department of Electrical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2011. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2011 by Rajat Bhatnagar
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