Date of Award

Spring 5-31-2018

Document Type


Degree Name

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


Mathematical Sciences

First Advisor

Linda Jane Cummings

Second Advisor

Lou Kondic

Third Advisor

Shahriar Afkhami

Fourth Advisor

Catalin C. Turc

Fifth Advisor

Thomas P. Witelski


The dynamics of thin films of nematic liquid crystal (NLC) are studied. Nematic liquid crystals are a type of non-Newtonian fluid with anisotropic viscous effects (due to the shape of the molecules) and elasticity effects (due to interacting electrical dipole moments). Exploiting the small aspect ratio in the geometry of interest, a fourth-order non-linear partial differential equation is used to model the free surface of the thin films. Particular attention is paid to the interplay between the bulk elasticity and the preferred orientation (boundary condition) of NLC molecules at the two interfaces: the substrate and the free surface. This work is a collection of three previously published papers and some recent unpublished work. Two main topics are covered: 1) the flow of thin films of NLC down an inclined substrate under gravity, and 2) the stability of thin NLC films on a horizontal substrate under the influence of surface tension, internal elastic effects, and fluid/solid interactions. Using a combination of analytical and computational techniques allows for a novel understanding of relevant instability mechanisms, and of their influence on transient and fully developed fluid film morphologies. While the analytical results in this thesis focus on NLC films, these results may be extended to a variety of other thin film models. Finally, a numerical code that utilizes a graphics processor unit (GPU) is presented, and the significant performance gains are discussed.

Included in

Mathematics Commons