<p>Thin liquid films are often studied by reducing the Navier-Stokes equations</p><p>using Reynolds lubrication theory, which leverages a small aspect ratio</p><p>to yield simplified governing equations. In this dissertation a plate</p><p>coating application, in which polydimethylsiloxane coats a silicon substrate,</p><p>is studied using this approach. Thermal Marangoni stress</p><p>drives fluid motion against the resistance of gravity, with the parameter</p><p>regime being chosen such that these stresses lead to a stable advancing front.</p><p>Additional localized thermal Marangoni stress is used to control the thin film;</p><p>in particular, coating thickness is modulated through the intensity of such</p><p>localized forcing. As thermal effects are central to film dynamics, the dissertation</p><p>focuses specifically on the effect that incorporating temperature dependence</p><p>into viscosity, surface tension, and density has on film dynamics and control.</p><p>Incorporating temperature dependence into viscosity, in particular,</p><p>leads to qualitative changes in film dynamics.</p><p>A mathematical model is developed in which the temperature dependence</p><p>of viscosity and surface tension is carefully taken into account.</p><p>This model is then</p><p>studied through numerical computation of solutions, qualitative analysis,</p><p>and asymptotic analysis. A thorough comparison is made between the</p><p>behavior of solutions to the temperature-independent and</p><p>temperature-dependent models. It is shown that using</p><p>localized thermal Marangoni stress as a control mechanism is feasible</p><p>in both models. Among constant steady-state solutions</p><p>there is a unique such solution in the temperature-dependent model,</p><p>but not in the temperature-independent model, a feature that</p><p>better reflects the known dynamics of the physical system.</p><p>The interaction of boundary conditions with finite domain size is shown</p><p>to generate both periodic and finite-time blow-up solutions, with</p><p>qualitative differences in solution behavior between models.</p><p>This interaction also accounts for the fact that locally perturbed solutions,</p><p>which arise when localized thermal Marangoni forcing is too weak</p><p>to effectively control thin film thickness, exist only for a discrete</p><p>set of boundary heights.</p><p>Modulating the intensity of localized thermal Marangoni forcing is</p><p>an effective means of modulating the thickness of a thin film</p><p>for a plate coating application; however, such control must be initiated before</p><p>the film reaches the full thickness it would reach in the absence of</p><p>such localized forcing. This conclusion holds for both the temperature-independent</p><p>and temperature-dependent mathematical models; furthermore, incorporating</p><p>temperature dependence into viscosity causes qualitative changes in solution</p><p>behavior that better align with known features of the underlying physical system.</p> / Dissertation
| Identifer | oai:union.ndltd.org:DUKE/oai:dukespace.lib.duke.edu:10161/11331 |
| Date | January 2015 |
| Creators | Potter, Harrison David |
| Contributors | Witelski, Thomas P |
| Source Sets | Duke University |
| Detected Language | English |
| Type | Dissertation |
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