From Microscopic Theory to Macroscopic Theory: a Systematic Study on Modeling for Liquid Crystals

Jiequn Han, Yi Luo, Wei Wang, Pingwen Zhang, Zhifei Zhang

Research output: Contribution to journalArticle

34 Scopus citations

Abstract

In this paper, we propose a systematic way of liquid crystal modeling to build connections between microscopic theory and macroscopic theory. In the first part, we propose a new Q-tensor model based on Onsager’s molecular theory for liquid crystals. The Oseen–Frank theory can be recovered from the derived Q-tensor theory by making a uniaxial assumption, and the coefficients in the Oseen–Frank model can be examined. In addition, the smectic-A phase can be characterized by the derived macroscopic model. In the second part, we derive a new dynamic Q-tensor model from Doi’s kinetic theory by the Bingham closure, which obeys the energy dissipation law. Moreover, the Ericksen–Leslie system can also be derived from new Q-tensor system by making an expansion near the local equilibrium.

Original languageEnglish (US)
Pages (from-to)741-809
Number of pages69
JournalArchive for Rational Mechanics and Analysis
Volume215
Issue number3
DOIs
StatePublished - Jan 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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