Molecular simulation of liquid crystal polymer flow : a wavelet-finite element analysis

Abstract

The focus of this thesis was twofold. First, efficient numerical methods were developed for the modeling of the molecular orientation distribution function, f, of rigid rod polymers in flow. These methods were used to investigate the liquid crystal polymer (LCP) system. Second, the distribution function calculations were incorporated into a discontinuous Galerkin finite element framework for the modeling of complex LCP flows. Due to the localized nature of f under flow, the Daubechies D6 wavelets were used as basis functions for the approximation of f, and resulted in an efficient numerical technique to model LCPs. Bifurcation analysis of the Doi LCP model in shear flow showed that steady state solutions are lost due to the formation of a limit point in the plot of structure parameter S vs. concentration parameter N, beyond which time-periodic solutions are the only stable solutions. At low De, the time-periodic solutions onset as tumbling states at a global bifurcation. At high De, they onset as wagging states at a Hopf bifurcation, with a subsequent second transition to tumbling as N is increased. The period of oscillation of all tumbling states follows the experimentally observed scaling with strain. However, the wagging states do not follow this scaling, indicating that tumbling and wagging states belong to different solution. families. Computation of f in pressure-driven channel flow of LCPs using the wavelet­finite element method showed that the range of tumbling periods, combined with the existence of an infinite period tumbling streamline at the centerline, provides a mechanism for texture generation and refinement. The analysis also demonstrated the possibility of predicting biphasic solutions to LCP problems. Simulations of LCP flow in a tapering contraction geometry showed that the Doi model predicts inter­mediate concentrations to be most effective in producing flow-alignment of molecular distributions. At higher concentrations, tumbling is found to be widespread in the tapering section despite the presence of an elongational component in the strain rate. Taken together, these calculations demonstrate the feasibility of performing complex flow calculations with molecular models, which will lead to a better physical under­standing of the effect of molecular configuration in polymer flows.