Hydrodynamics of pair-annihilating disclination lines in nematic liquid crystals

The pair annihilation of straight line defects with strength +/-1/2 in bulk nematic systems is studied numerically, considering a full coupling of orientational degrees of freedom and hydrodynamics. This work is based on the generalization of the Ericksen-Leslie theory to the tensor order parameter as proposed by Qian and Sheng [T. Qian and P. Sheng, Phys. Rev. E 58, 7475 (1998)]. The approach is particularly suited for the late stages of the annihilation process. It is confirmed that the +1/2 disclination line moves considerably faster than the -1/2 one (e.g., twice as fast) due to the hydrodynamic flow. Symmetries of the important stress tensor terms upon inverting the sign of the winding number and performing a homogeneous in-plane rotation of the Q-tensor eigensystem are discussed. The stress tensor terms that dominantly contribute to the advective flow and to the flow asymmetry are identified.