Features of director reorientation in a thin nematic film under the influence of crossed electric and magnetic fields

The theory based on numerical study of the system of hydrodynamic equations, which includes the director motion, shows that under the influence of crossed electric $\mathbf{\text{E}}$ and magnetic $\mathbf{\text{B}}$ fields, the director reorients in such a way that the transient quasiperiodic patterns may arise in microsized nematic volumes if the corresponding distortion mode has the fastest response and thus suppresses all other modes, including uniform ones. It has been shown that there is a threshold value of the amplitude of the thermal fluctuations of the director over the microsized nematic film which provides the nonuniform rotation mode rather than the uniform one, whereas the lower values of the amplitude dominate the uniform mode.

Figure 1

The geometry used for calculations in the HAN film. The $x$ axis is parallel, while the $z$ axis is orthogonal to the electrodes. The magnetic field, $\mathbf{\text{B}}$, electric field, $\mathbf{\text{E}}$, and director, $\widehat{\mathbf{\text{n}}}$, are aligned in the $xz$ plane. The director makes the angle $\theta$ with the $x$ axis, and the electric field makes the angle $\alpha$ with the magnetic field.

Figure 2

Evolution of the angle $\theta (\tau ,x,z=0)$ along the dimensionless length $-10\le x\le 10$ of the HAN film to the stationary distribution ${\theta }^{\mathrm{st}}(x,z=0)$ under the effect of both electric and magnetic fields directed at the angle $\alpha =1.57(\sim 89.{96}^{\circ })$ and $q_x\approx 490.5$, for a number of values ${\theta }_0=0.01$ (a) and 0.001 (b), respectively.

Figure 3

The same as in Fig. 2, but the angle $\alpha =1.565(\sim 89.{67}^{\circ })$ and $q_x\approx 490.5$, for a number of values of ${\theta }_0=0.01$ (a) and 0.002 (b), respectively.

Figure 4

The same as in Fig. 2, but the angle $\alpha =1.56(\sim 89.{38}^{\circ })$ and $q_x\approx 490.5$ for a number of values of ${\theta }_0=0.01$ (a) and 0.002 (b), respectively.

Figure 5

The same as in Fig. 2, but the angle $\alpha =1.55(\sim 88.8^{\circ })$ and $q_x\approx 490.5$ for the value of ${\theta }_0$ to be equal to 0.01.

Figure 6

The same as in Fig. 2, but the angle $\alpha =1.55(\sim 88.8^{\circ })$ and $q_x\approx 490.5$ for a number of values of ${\theta }_0=0.005$ (a) and 0.002 (b), respectively.

Figure 7

The same as in Fig. 2, but the values of the angle $\alpha$ are equal to $1.40(\sim 80.0^{\circ })$ (a) and $1.222(\sim 70.0^{\circ })$(b), respectively. Here $q_x$ is equal to 490.5, while the value of ${\theta }_0$ is equal to be 0.01, respectively.

Figure 8

The same as in Fig. 7, but the values of the angle $\alpha$ is equal to $1.047(\sim 60.0^{\circ })$ (a) and $0.82(\sim 50.0^{\circ })$ (b), respectively.

Figure 9

(a) Stationary distribution of the angle ${\theta }^{\mathrm{st}}(x,z=0)$ along the length $-10\le x\le 10$ of the HAN film, for the number of values of $\alpha$: $1.57(\sim 89.{96}^{\circ })$ (curve 1), $1.40(\sim 80.0^{\circ })$ (curve 2), $1.222(\sim 70.0^{\circ })$ (curve 3), $1.047(\sim 60.0^{\circ })$ (curve 4), and $0.82(\sim 50.0^{\circ })$ (curve 5), respectively. (b) Same as in (a), but the values of $\alpha$ are $1.57(\sim 89.{96}^{\circ })$ (curve 1) and $1.55(\sim 88.8^{\circ })$ (curve 2), respectively.