Nature of thermally excited vortical flow in a microsized nematic volume

The theoretical description of the reorientational dynamics in the case of a hybrid-oriented two-dimensional (2D) liquid crystal (LC) cell, under the influence of a temperature gradient $\nabla T$, caused by a heat flux $\mathbf{\text{q}}$ directed at an angle $\alpha$ across the lower bounding surface with the orientational defect, has been presented. Our calculations, based on the appropriate nonlinear extension of the classical Ericksen-Leslie theory, show that due to interaction between $\nabla T$ and the gradient of the director field $\nabla \widehat{\mathbf{\text{n}}}$ in the LC sample a thermally excited vortical fluid flow is maintained in the bulk of the nematic volume. In order to elucidate the role of both the orientational defect and the heat flux $\mathbf{\text{q}}$ in formation of the vortical flow in the microsized LC volume, we have analyzed the response of the LC material confined in the microsized 2D volume on the effect of the laser beam focused on the bounding surface.

Figure 1

The fragment of initial distribution of the director field ${\widehat{\mathbf{\text{n}}}}_{\mathrm{elast}}^{\mathrm{eq}}(\mathrm{x},\mathrm{z})$ near the orientational defect located at $-\mathrm{L}<\mathrm{x}<\mathrm{L},\mathrm{z}=-1$. Here, $L=\pm 0.5$.

Figure 2

Distribution of the velocity field $\mathbf{\text{v}}=u\widehat{\mathbf{\text{i}}}+w\widehat{\mathbf{\text{k}}}$ in the microscopic nematic volume with the orientational defect located at $-L\le x\le L,z=-1$, when the heat flux ${\mathbf{\text{q}}}^b$ is directed at two values of the angle $\alpha$: (a) ${20}^{\circ }$ and (b) ${40}^{\circ }$, respectively. The heating occurs during time ${\tau }_{\mathrm{in}}=1.6\times {10}^{-4}(\sim 0.29\mathrm{ms})$, whereas the value of the dimensionless heat flux coefficient ${\mathcal{Q}}_0$ is equal to 0.05. Here, 1 mm of the arrow length is equal to $1.8\mu \mathrm{m}/\mathrm{s}$.

Figure 3

Same as in Fig. 2, but the values of the angle $\alpha$ are (c) ${60}^{\circ }$ and (d) ${80}^{\circ }$, respectively.

Figure 4

Same as in Fig. 2, but the value of the angle $\alpha$ is equal to ${90}^{\circ }$.

Figure 5

Same as in Fig. 2, but the values of the angle $\alpha$ are (f) ${100}^{\circ }$ and (h) ${120}^{\circ }$, respectively.

Figure 6

Same as in Fig. 2, but the values of the angle $\alpha$ are (i) ${140}^{\circ }$ and (j) ${160}^{\circ }$, respectively.

Figure 7

Plot of the temperature field distribution $\chi (\mathrm{x},\mathrm{z},\tau ={\tau }_{\mathrm{in}})$ over the nematic volume near the orientational defect located at $-L\le x\le L,z=-1$, when the heat flux ${\mathbf{\text{q}}}^b$ is directed at two values of the angle $\alpha$: (a) ${20}^{\circ }$ and (b) ${160}^{\circ }$, respectively. The heating occurs during time ${\tau }_{\mathrm{in}}=1.6\times {10}^{-4}(\sim 0.29\mathrm{ms})$, whereas the value of the dimensionless heat flux coefficient ${\mathcal{Q}}_0$ is equal to 0.05.