TY - JOUR
T1 - From Microscopic Theory to Macroscopic Theory
T2 - a Systematic Study on Modeling for Liquid Crystals
AU - Han, Jiequn
AU - Luo, Yi
AU - Wang, Wei
AU - Zhang, Pingwen
AU - Zhang, Zhifei
N1 - Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.
PY - 2014/3
Y1 - 2014/3
N2 - 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.
AB - 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.
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U2 - 10.1007/s00205-014-0792-3
DO - 10.1007/s00205-014-0792-3
M3 - Article
AN - SCOPUS:84921323097
SN - 0003-9527
VL - 215
SP - 741
EP - 809
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 3
ER -