Thin film flows are of central importance to a variety of industrial and scientific processes such as heat and mass transfer, micro- and nanotechnological settings such a lab-on-a-chip devices, and geophysical flows. Understanding their behaviour is thus of central importance. While they have been subjected to a great deal of analysis, there are still regimes in which this behaviour is only partially understood, especially in highly nonlinear free surface flows, and particularly in the presence of other competing physical effects. This dissertation focuses on the behaviour of nonlinear flows in the presence of electric fields. By introducing a potential difference between the surface electrode on which the fluid rests and a second electrode above the fluid, an interfacial stress is induced due to the disparity in electrical properties between the liquid and gas media. It is found via direct numerical computations in both linear and nonlinear regimes that for a broad range of parameters the induced disturbances have wavelengths which are large compared to the thickness of the film layer. This may be exploited in the guise of the lubrication approximation in order to reduce the Navier-Stokes equations to inordinately more tractable forms; these `low-order models' form the core of the study of this thesis. Particular attention is paid to studying these films in a variety of geometries. It turns out that the introduction of curvature to a substrate renders the asymptotic analyses somewhat more delicate than is the case for planar films. The generalised analysis presented herein is applied to several different particular situations, including geometries where the surface is curved in the streamwise or spanwise direction. The resultant models incorporate the effects of capillarity, viscous stress, electrostatically-induced Maxwell stress, and inertia, as well as interfacial charge transport effects. It is demonstrated via comparison to direct numerical computations that this low-order modelling is highly accurate in a wide array of circumstances, where particular attention is given to flows on planes and on the surface of fibres. It is demonstrated that disturbances of particular wavelengths can be either excited or suppressed in a spatiotemporally-specific manner. This gives an enormous degree of control with many practical ramifications. Perhaps most significantly it is demonstrated that this method allows one to overcome the formerly ubquitous assumption that low-order models were confined to use for thin film flows: it is now possible to model `thick' flows. This has only been verified in a small set of geometries, but stands to have significant ramifications as the method could be used to improve any existing model in the literature that is predicated on the thin-film assumption.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:656839 |
| Date | January 2014 |
| Creators | Wray, Alex |
| Contributors | Matar, Omar K.; Papageorgiou, Demetrios T. |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/24957 |
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