| We propose a rational approach to approximating the various alignment tensors. It preserves the correct symmetry and leads to consistent results. For the case of uniaxial nematic fluids, the decoupling approximation for a tensor of rank l involves (l-2)/2 scalar functions Sl(S2) in terms of a scalar arguments S2, with Sl(0)=0 and Sl(1)=1. Nothing else can be concluded about the mathematical relationship between moments of the distribution function, and in particular, all consistent decoupling approximations for fourth order moment in terms of second order moments can be characterized by a single S4(S2)=0 function. We will review several decoupling approximations which appeared in the literature (linear, quadratic, natural, Hinch-Leal, Maier-Saupe, Bingham etc.) and discuss their validity. We propose using a convex shaped S4(S2) parameterized by a single scalar to characterize the decoupling approximation. Its value can be motivated by a maximum entropy argument, or determined empirically. This manuscript aims at illustrating some implications from basic symmetry considerations, proposes new and simple closures valid in the uniaxial phase, and also extends the arguments to the polar and biaxial phases and tensors of arbitrary rank.
for LaTeX users @article{MKroger2008-149,
author = {M. Kr\"oger and A. Ammar and F. Chinesta},
title = {Consistent closure schemes for statistical models of anisotropic fluids},
journal = {J. Non-Newtonian Fluid Mech.},
volume = {149},
pages = {40-55},
year = {2008}
}
\bibitem{MKroger2008-149} M. Kr\"oger, A. Ammar, F. Chinesta,
Consistent closure schemes for statistical models of anisotropic fluids,
J. Non-Newtonian Fluid Mech. {\bf 149} (2008) 40-55.MKroger2008-149
M. Kr\"oger, A. Ammar, F. Chinesta
Consistent closure schemes for statistical models of anisotropic fluids
J. Non-Newtonian Fluid Mech.,149,2008,40-55 |
mk@mat.ethz.ch
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