A theoretical study is presented of nematic liquid crystals confined between two concentric cylindrical surfaces under a radially inhomogeneous electric field, focusing on the interaction among elastic anisotropy, cylindrical geometry, and flexoelectric surfaces. Two alignment regimes are considered: planar under positive dielectric anisotropy, and homeotropic under negative dielectric anisotropy, both with strong anchoring at the inner and outer cylinders. The molecular reorientation behavior is related to measurable electrical quantities by modeling the nematic cell as an equivalent parallel $\mathit{RC}$ circuit and deriving expressions for resistance, capacitance, and time-dependent current under a linearly ramped voltage. Numerical results reveal how the flexoelectric coefficients (magnitude and sign), the elastic anisotropy ratio, and the geometry (inner and outer radii) influence the threshold behavior and post-threshold dynamics of the director field, thereby affecting the electrical response. In particular, it is shown that the electrical response of cylindrical nematic devices can be controlled by adjusting flexoelectric coefficients and the elastic anisotropy in this geometry.

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• Liquid crystals