Hydrodynamics of pair-annihilating disclinations in SmC films

The pair annihilation of smectic c-director defects with winding numbers +/-1 in a freestanding SmC film as a representative of the XY model is studied numerically, considering a full coupling of orientational degrees of freedom and hydrodynamics. A reduction of the annihilation time compared to the nonhydrodynamic treatment is observed. It is demonstrated that the +1 disclination moves considerably faster than the -1 one primarily due to hydrodynamic flow, weakly assisted also by elastic anisotropy. The stress tensor terms and material parameters relevant for this effect are identified.