Comparative studies on closure approximations in flows of liquid crystal polymers: I. elongational flows

Abstract

We derive nine approximate models for flows of liquid crystal polymers by applying different closure approximations to the kinetic theory developed by Bhave et al. We then benchmark the approximate models by comparing their uniaxial steady state solutions to the corresponding ones of the kinetic theory in elongational flows. For prolate steady states, we find that all the models give qualitatively acceptable approximations. In particular, when the flow is uniaxially stretching, the models in which the flow-orientation interaction term is approximated by the second Hinch-Leal closure approximation approximate the kinetic theory well in the range of small Peclet numbers; likewise, the models in which the molecule-molecule interaction term is approximated by the Doi closure approximation approximate the kinetic theory well in the range of large Peclet numbers. In the oblate phase, however, all models except for the DD (Doi closure approximation) and DHL2 (Hybrid Doi and HL2 closure approximation) model may produce either fictitious or nonphysical oblate steady states with out-of-range order parameter values. Therefore, we caution the use of the models in this phase. In contrast, the DD and DHL2 model are applicable to all phases for any Peclet numbers and polymer concentration values. In addition, they approximate the kinetic theory well in the oblate phase when the flow is biaxially stretching. In the end, we find that the best overall approximation to the kinetic theory is given by the DHL2 model.