Date of Award

Spring 2012

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)

Department

Mathematical Sciences

First Advisor

Lou Kondic

Second Advisor

Linda Jane Cummings

Third Advisor

Robert M. Miura

Fourth Advisor

Richard O. Moore

Fifth Advisor

P. Palffy-Muhoray

Abstract

The instabilities of Newtonian films and nematic liquid crystal droplets within the framework of the long wave (lubrication) approximation are studied. For Newtonian films, it is found that, under destabilizing gravitational force, a contact line, modeled by a commonly used precursor film model, leads to free surface instabilities without any additional natural or imposed perturbations. In addition, there is a coupling between the surface instabilities and the transverse (fingering) instabilities which leads to complex behavior. All the observed phenomena are characterized by a single parameter D = (3Ca)1/3 cot α where Ca is the capillary number and α is the inclination angle. Variation of D leads to changes in the wavelike properties of the instabilities, allowing us to observe traveling wave behavior, mixed waves, and waves resembling solitary ones. The study is also extended to explore partially wetting fluids by introducing the disjoining pressure in the thin film equation. It is found that there exists an additional regime where the film breaks up into a series of droplets.

For nematic liquid crystal droplets, a model is derived based on the long wave approach available in the literatures. In particular, the surface anchoring energy is chosen such that very thin films admit the isotropic phase while thick ones remain nematic. The model permits fully nonlinear time-dependent simulations. These simulations, for the appropriate choice of parameter values, exhibit most of the phenomena appearing in the series of experiments. Finally, the influence of elastic distortion energy and the effect of anchoring variations at the substrate are explored through simple linear stability analysis, serving as a good indicator of the behavior of more complicated spreading drops.

Included in

Mathematics Commons

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