Anisotropy in the annihilation dynamics of umbilic defects in nematic liquid crystals

Umbilic defects of strength s = +/- 1 were induced in a nematic liquid crystal with negative dielectric anisotropy, confined to Hele-Shaw cells with homeotropic boundary conditions, and their annihilation dynamics followed experimentally. The speeds of individual defects of annihilating defect pairs with strengths of equal magnitude and opposite sign were determined as a function of several externally applied parameters, such as cell gap, electric field amplitude, frequency, and temperature. It was shown that annihilating defects do not approach each other at equal speeds, but that a speed anisotropy is observed, with the positive defect moving faster than the negative one. The defects move more slowly as the strength of the applied electric field or the cell gap is increased. The speed anisotropy is found to be essentially constant for varying external conditions which do not change the material properties of the liquid crystal material, i.e., confinement, electric field amplitude, or frequency. Only for applied conditions that change material properties, such as temperature changing viscosity, does the speed anisotropy vary. The annihilation dynamics was also simulated numerically giving good qualitative agreement with the experiments. Using insight gained from the simulations we interpret the defects' speed in terms of their overlap and the speed asymmetry as arising from backflow effects and anisotropy in the elastic constants.