Colloidal systems comprising solid or fluid particles dispersed in nematic monodomains are known to be a convenient means to study topological defects. Recent experiments have shown that twist-bend nematic $\left(N_{\mathrm{TB}}\right)$ droplets in a nematic matrix act as colloidal particles that lead to the formation of elastic dipoles, quadrupoles, and their ordered clusters. In this study, we examine the effect of low-frequency $(f\sim \mathrm{mHz})$ electric fields on such defect configurations. We find that (i) the hyperbolic hedgehogs of elastic dipoles shift toward the negative electrode in static fields and perform oscillatory motion in AC fields, indicating the presence of nonvanishing flexoelectric polarization in the field-free state; (ii) the elastic dipoles, propelled by forces of backflow due to coupled flexoelectric and dielectric distortions, drift uniformly along their axes with the $N_{\mathrm{TB}}$ drops in lead; (iii) the translational velocity $v_d$ increases linearly with both $f$ and the diameter of $N_{\mathrm{TB}}$ drops; and (iv) with increasing applied voltage U, $v_d\left(U\right)$ exhibits a monotonic, slightly nonlinear variation at $f\le 200\mathrm{mHz}$, tending toward linearity at higher frequencies.

• Received 22 February 2021
• Accepted 15 March 2021

DOI:https://doi.org/10.1103/PhysRevE.103.042701