Date of Award

2009

Document Type

Open Access Dissertation

Department

Mathematics

First Advisor

Qi Wang

Abstract

In this thesis we derive a hydrodynamical kinetic theory to study the orientational response of a mesoscopic system of nematic liquid crystals in the presence of an external flow field. Various problems have been attempted in this direction. First, we understand the steady-state behavior of uniaxial LCPs under an imposed elongational flow, electric and magnetic field respectively. We show that (1) the Smoluchowski equation can be cast into a generic form, (2) the external field is parallel to one of the eigenvectors of the second moment tensor, and (3) the steady state probability density function is of the Boltzmann type. In the next problem, we study the mono-domain dynamics of rigid rod and platelet suspensions in a linear flow and a steady magnetic field. The flows with a rotational component is mapped to simple shear with rate parameter subject to a transverse magnetic field with strength parameter and the irrotational flows are reduced into a triaxial extensional flow with two extensional rate parameters. For rotational flows, various in-plane and out-of-plane stable steady attractors emerge. For irrotational flows, the biaxial equilibria is characterized generically in terms of an explicit Boltzmann distribution, providing a natural generalization of the analytical results on pure nematic equilibria. Finally, we present the dynamics of a mesoscopic system of biaxial liquid crystal polymers in the presence of a homogenous shear flow. The Smoluchowski equation is derived in the rotating frame and solved using a specially formulated Wigner-Galerkin approximation in selected regions of the material parameter space and a range of accessible shear rates, to investigate the stable mesoscopic states and robust structures.

Rights

© 2009, Sarthok K Sircar

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