We develop a kinetic theory of the biaxial phases for the bent-core or V-shaped liquid crystal polymer solution (VLCPS). The Brownian motion of the biaxial molecules, biaxial molecular excluded interaction, and the rotary convection are modeled explicitly. Using the hydrodynamic theory, we study the flow-driven orientational dynamics and the corresponding rheological response in selected regimes of plane shear flows, strength of intermolecular interaction, and the bent-angle of the molecule. We identify three steady state biaxial phases and three periodic motions at various regimes of the shear rate and strength of the intermolecular potential. Phase transition sequences among the orientational phases and motions are documented with respect to the strength of the intermolecular potential at fixed bent angles. The effect of the molecular configuration (or the bent- angle) of the V-shaped molecule on mesoscopic phases and their transition sequences is investigated as well.
"Biaxial phases of bent-core liquid crystal polymers in shear flows." Commun. Math. Sci. 8 (3) 697 - 720, September 2010.