Analytical predictions for 3D disclination motion in nematic liquid crystals

Predictions of disclination motion in nematic liquid crystals are important for our understanding of coarsening dynamics in passive nematics or mesoscopic turbulence in active nematics, as well as for engineering control over anisotropic transport in all types of nematics. Here we present analytical methods for predicting the motion of three-dimensional line disclinations. We derive an exact kinematic law of disclination motion that depends only on derivatives of the nematic tensor order parameter at the defect core. We show that given a few simple approximations for the order parameter at the core, it leads to analytical predictions of disclination velocity for cases including disclination line recombination, disclination loop annihilation, and defect sorting by director geometry in externally imposed fields and flows. We compare the analytical predictions with three-dimensional numerical computations of the full non-linear equations for nematic dynamics in the tensor order parameter representation.