Numerical Simulation of Flow-Induced Flexoelectric Effect in Liquid Crystals

Abstract

As a fundamental research for developing new liquid crystalline devices, numerical simulations on flexoelectric polarization in liquid crystals under shear flow has been performed using the Leslie-Ericksen continuum theory. We have used two types of liquid crystals for computation; one is N-(p-methoxybenzylidene)-p'-butylaniline (MBBA), which is an aligning liquid crystal, and another is 4-n-Octyl-4'-cyanobiphenyl (8CB), which is a tumbling liquid crystal. These liquid crystals are placed between two parallel plates, and one plate is moved to its plane direction in order to impose shear flow on the liquid crystals. For simplification, the director is assumed to lie in the shear plane. As the boundary condition of the director, the director orientation on one plate is anchored strongly, and the director on the other plate is weakly anchored so that the director orientation depends on shear rate. The flexoelectric polarization for the aligning liquid crystal increases monotonically to reach a steady state value, while it shows peaks for the tumbling liquid crystal; the number of peaks depends on the Ericksen number (ratio of viscous to elastic stress), and the peak value is considerably larger than the steady state value for the aligning liquid crystal. Since the flexoelectric polarization is estimated from the difference of the director angle between both plates, it is found that the flexoelectric polarization can be controlled by the anchoring strength as well as the Ericksen number.