The dynamics of a disclination loop (s = ±1/2) in nematic liquid crystals constrained between two coaxial cylinders were investigated based on two-dimensional Landau-de Gennes tensorial formalism by using a finite-difference iterative method. The effect of thickness (d = R₂ - R₁, where R₁ and R₂ represent the internal and external radii of the cylindrical cavity, respectively) on the director distribution of the defect was simulated using different R₁ values. The results show that the order reconstruction occurs at a critical value of dc, which decreases with increasing inner ratio R₁. The loop also shrinks, and the defect center deviates from the middle of the system, which is a non-planar structure. The deviation decreases with decreasing d or increasing R₁, implying that the system tends to be a planar cell. Two models were then established to analyze the combined effect of non-planar geometry and electric field. The common action of these parameters facilitates order reconstruction, whereas their opposite action complicates the process.
Keywords: Landau–de Gennes theory; biaxial transition; cylindrical wall; disclination loop; liquid crystal; order reconstruction.