Time-Evolution Equations for Particle Dispersions in Nematic Liquid Crystal Media

Abstract

A formal re-definition of the hydrodynamic equations for a compressible uniaxial nematic fluid in the presence of dispersed particles is presented, which is particularly amenable to computational treatment. Starting from the Parodi-Foster formulation of nematodynamics equations, it is shown that a functional formulation of the time evolution equations can be obtained which clearly separate conservative and dissipative terms. A simplified discretization scheme is also proposed, which leads to pseudo-particle representation of the fluid in combination with a standard description of the dispersed particles motion.

Keywords:

• Dispersions
• nematic liquid crystals
• non-linear fluctuation hydrodynamics

Support has been provided by the Ministero dell'Istruzione, Università e Ricerca (MIUR), grant PRIN 2006 (2006033728), and by the Consorzio Interuniversitario per la Scienza e la Tecnologia dei Materiali (INSTM), grant PROMO 2007. Fondazione CARIPARO (MISCHA Project, call 2007) is gratefully acknowledged for financial support.