Characterization of stable kinetic equilibria of rigid, dipolar rod ensembles for coupled dipole-dipole and Maier-Saupe potentials
Wang, H. Y.
Forest, M. G.
MetadataShow full item record
We study equilibria of the Smoluchowski equation for rigid, dipolar rod ensembles where the intermolecular potential couples the dipole-dipole interaction and the Maier-Saupe interaction. We thereby extend previous analytical results for the decoupled case of the dipolar potential only (Fatkullin and Slastikov 2005 Nonlinearity 18 2565-80; Ji et al Phys. Fluids at press; Wang et al 2005 Commun. Math. Sci. 3 605-20) or the Maier-Saupe potential only (Constantin et al 2004 Arch. Ration. Mech. Anal. 174 365-84; Constantin et al 2004 Discrete Contin. Dyn. Syst. 11 101-12; Constantin and Vukadinovic 2005 Nonlinearity 18 441-3; Constantin 2005 Commun. Math. Sci. 3 531-44; Fatkullin and Slastikov 2005 Commun. Math. Sci. 3 21-6; Liu et al 2005 Commun. Math. Sci. 3 201-18; Luo et al 2005 Nonlinearity 18 379-89; Zhou et al 2005 Nonlinearity 18 2815-25; Zhou and Wang Commun. Math. Sci. at press), and prove certain numerical observations for equilibria of coupled potentials (Ji et al Phys. Fluids at press). We first derive stability conditions, on the magnitude of the polarity vector (the first moment of the orientational probability distribution function) and on the direction of the polarity. We then prove that all stable equilibria of rigid, dipolar rod dispersions are either isotropic or prolate uniaxial. In particular, all stable anisotropic equilibrium distributions admit the following remarkable symmetry: the peak axis of orientation is aligned with both the polarity vector (first moment) and the distinguished director of the uniaxial second moment tensor. The stability is essential in establishing the axisymmetry. To demonstrate that the stability is indeed required, we show that there exist unstable non-axisymmetric equilibria.
The article of record as published may be located at http://dx.doi.org/10.1088/0951-7715/20/2/003
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
Showing items related by title, author, creator and subject.
Zhou, Hong; Wang, Hongyun; Wang, Qi (2007);We continue the study on equilibria of the Smoluchowski equation for dilute solutions of rigid extended (dipolar) nematics and dispersions under an imposed electric or magnetic field . We first provide an alternative ...
Steady states and their stability of homogeneous, rigid, extended nematic polymers under imposed magnetic fields Zhou, Hong; Ji, Guanghua; Wang, Qi; Zhang, Pingwen; Wang, Hongyun (2007);We study the steady state phase behavior of homogeneous, rigid, extended (polar) nematic polymers or nematic dispersions under imposed magnetic (or electric ﬁelds), in which the intermolecular dipole-dipole and excluded ...
Study of phase transition in homogeneous, rigid extended nematics and magnetic suspensions using an order-reduction method Zhou, Hong; Ji, Guanghua; Wang, Qi; Zhang, Pingwen (2006);We study the phase transition in rigid extended nematics and magnetic suspensions by solving the Smoluchowski equation for magnetically polarized rigid nematic polymers and suspensions in equilibrium, in which the molecular ...