Browsing by Subject "Liquid Crystals"

Now showing 1 - 3 of 3
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    Computational Aspects of Energy Minimization of the Landau-de Gennes Model for Liquid Crystals
    (2017-06) Dassbach, Paula
    From a mathematically rigorous foundation, energy minimizing configurations are numerically computed using the Landau-de Gennes energy expression for a variety of liquid crystal domains in order to compare them with previous experimental and numerical results as well as present new results. The method of manufactured solutions is used to validate numerical computations in two- and three-dimensional domains before computing the minimizers. Many configurations and defect structures seen in experiments were reproduced numerically and studied carefully, with three notable results: First, in the two-dimensional disc domain with normal Dirichlet boundary conditions, the 'split core' defect is shown to be a product of improper mesh refinement. Second, for all concentric cylinder domains with planar radial Dirichlet boundary conditions, biaxial regions were present, which is a marked difference from previous results using the Oseen-Frank model. Third, for a single colloidal particle with normal Dirichlet boundary conditions suspended in a cylinder with everywhere vertical boundary conditions, the core of the Saturn ring defect is shown to be uniaxial with negative scalar order parameter. These three results more accurately describe experimental and theoretical results than those using the vector-based models and motivate the use of the Landau-de Gennes model for future numerical computations.
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    Electrokinetic Phenomena and Singularity-Driven Flows in Nematic Liquid Crystals
    (2017-11) Conklin, Christopher
    Electrokinetic phenomena, including electrophoresis and electroosmosis, provide a significant tool for engineering the transport of fluids and particles at microscopic scales. This thesis describes additional mechanisms for generating electrokinetic flow by using a nematic liquid crystal electrolyte. Under an applied electric field the anisotropic properties of the liquid crystal lead to separation of ionic impurities present in the fluid, which couple with the applied field to produce electrostatic forces that drive fluid and particle motion. This force is quadratic in the electric field, implying that systematic flow occurs even in the presence of an oscillating field. This thesis presents numerical and analytical investigations of this electrokinetic mechanism. We show that the charge density and fluid velocity of a system depends strongly on the topology of the liquid crystal orientation, and we present results for several distinct configurations, including periodic distortions, isolated disclinations, and particle suspensions. We also show that liquid crystal electrokinetic systems can be designed to mimic the behaviors of active nematics – collections of particles which can self-propel along a particular direction.
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    Equilibrium Configurations of Hexagonal Columnar Liquid Crystals with Applications to Materials Science and Biology
    (2018-11) Hiltner, Lindsey
    Using the mathematical theory of liquid crystals, we propose models for equilibrium configurations of the hexagonal columnar phase of lyotropic chromonic liquid crystals (LCLCs). These models are applied in a collection of settings in which the underlying phases are naturally observed, including LCLC toroidal superstructures, liquid crystal confined to a thin capillary, double-stranded DNA packed in bacteriophage viruses, and DNA toroidal clusters that form in the presence of condensing agents. Although the length scale of these superstructures ranges from nanometers to microns, they show the ability to sustain pressures of up to 60 atmospheres. In each setting, we investigate equilibrium configurations and discuss well-posedness of our model. The mathematical work focuses in the analysis of constrained free boundary problems for combined liquid crystal and elastic energies, with a main focus on the very rich structure of defect cores in lyotropic systems. We conclude with potential modifications to the model that could be used to incorporate information such as ionic concentrations present in the medium surrounding this liquid crystal phase.