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Effect of flow on soliton-like director reorientation in a nematic liquid crystal

We study the director reorientation dynamics of the director axis (n(r)) for a homeotropically aligned nematic system under the influence of a constant electric field for different physical situations, especially in the case of free flow, flow with a low velocity limit and under one constant approximation. The director reorientation dynamics of the system is shown to be governed by soliton modes and localized structures in the case of flow with a low velocity limit and under one constant approximation. However, in the free flow case, the reorientation dynamics of the system is shown to be governed by a perturbed soliton. Further investigation reveals that the perturbation is mainly due to the presence of a velocity gradient in the free flow situation. For this, we consider both shear and Poiseuille flows. Further, perturbation analysis of the above system shows that the perturbation does not alter the velocity and amplitude of the soliton of the unperturbed case. However, the perturbation due to flow introduces small fluctuations in the localized region of the soliton.