Communications in Mathematical Sciences

Volume 8 (2010)

Number 3

Special Issue: Mathematical Issues of Complex Fluids

Biaxial phases of bent-core liquid crystal polymers in shear flows

Pages: 697 – 720



Jun Li

Sarthok Sircar

Qi Wang


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.


Kinetic theory; biaxiality; V-shaped/bent-core liquid crystal polymers; shear flows; orientational dynamics; steady states; periodic motions; rheology

2010 Mathematics Subject Classification

76M20, 82D30

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