Numerical simulation of rodlike polymers in a uniaxial extensional flow: The distributionhyphen;function version versus the orderhyphen;parameter version of Doirsquo;s theory

摘要

The molecular theory of nematic liquid crystals, proposed by Doi in 1981, exists in two versions: the original kinetic equation written in terms of the orientational distribution function and an averaged approximation of the original kinetic equation written in terms of the order parameter tensor. In this study, the two versions, as well as a third (hybrid) approach by Edwards and Beris (1989), are compared. Due to the complexity of the original kinetic equation, only uniaxial extensional flow in a homogeneous monodomain is considered. The solution of the original kinetic equation without simplifications is obtained for the first timemdash;using a finite difference scheme with an iterative procedure for an integral equation. The solution of the kinetic equation written in terms of the orderhyphen;parameter tensor (a nonlinear algebraic equation) is obtained by Newtonrsquo;s procedure. For the ordered phase, the orderhyphen;parameter version provides acceptable approximation only in the lowhyphen;concentration region, the extent of which decreases with increasing velocity gradient. The hybrid approach of Edwards and Beris (1989) provides no improvement over the orderhyphen;parameter version; in the presence of a strong flow, it actually gives worse results at low concentrations.