Laser-excited motion of liquid crystals confined in a microsized volume with a free surface

The thermally excited vortical flow in a microsized liquid crystal (LC) volume with a free LC-air interface has been investigated theoretically based on the nonlinear extension of the Ericksen-Leslie theory, with accounting the entropy balance equation. Analysis of the numerical results show that due to interaction between the gradients of the director field $\mathbf{\nabla }\widehat{\mathbf{\text{n}}}$ and temperature field $\mathbf{\nabla }T$, caused by the focused heating, the thermally excited vortical fluid flow is maintained in the vicinity of the heat source. Calculations show that the magnitude and direction of the velocity field $\mathbf{\text{v}}$, as well as the height of the LC-air interface are influenced by the depth of the heat penetration in the LC volume. It has been shown that there is the point in the vicinity of the LC-air interface where the thermally excited vortical flow changes the direction from anticlockwise to clockwise.

Figure 1

(a) The evolution of both the dimensionless height $h\left(x,\tau \right)$ of the LC-air interface and the dimensionless temperature $\chi \left(x,\tau \right)$ (b) on the free LC-air interface $\mathrm{\Gamma }$, during the heating regime with ${\delta }_5=7$ and ${\tau }_{\mathrm{in}}=0.01$, at different times ${\tau }_i=2^i\times {10}^{-5}(i=1,...,10)$, respectively. The numbering of the curves increases from $i=1$ to $i=10$.

Figure 2

Same as described in the caption of Fig. 1, but for evolution of both the horizontal $u\left(x,\tau \right)$ (a) and vertical $w\left(x,\tau \right)$ (b) components of the velocity vector $\mathbf{\text{v}}=u\widehat{\mathbf{i}}+w\widehat{\mathbf{\text{k}}}$ on the LC-air interface during the heating regime. (c) Distribution of the velocity field $\mathbf{\text{v}}=u\widehat{\mathbf{i}}+w\widehat{\mathbf{\text{k}}}$ in the LC sample after heating during $\tau ={\tau }_{\text{in}}$. Here $1\text{mm}$ of the arrow length is equal to $0.4\mu \text{m}/\text{s}.$

Figure 3

The evolution of both the dimensionless height $h\left(x,\tau \right)$ (a) and the dimensionless temperature $\chi \left(x,\tau \right)$ (b) on the free LC-air interface $\mathrm{\Gamma }$, during the cooling regime, at different times ${\tau }_i=2^i\times {10}^{-2}(i=1,...,8)$, respectively.

Figure 4

The evolution of both the dimensionless horizontal $u\left(x,\tau \right)$ (a) and vertical $w\left(x,\tau \right)$ (b) components of the velocity field on the free LC-air interface $\mathrm{\Gamma }$ during the cooling regime, at different times ${\tau }_i=2^i\times {10}^{-2}(i=1,...,8)$, respectively.

Figure 5

Distribution of the dimensionless temperature $\chi \left(x=0,z,\tau \right)$ along the $z$ axis $\left(0.6\le z\le 1.0\right)$, when the laser beam is focused in the center $\left(x=0.0\right)$ of the LC sample, but at different depths: (a) $z_0=0.98$, (b) $z_0=0.94$, (c) $z_0=0.90$, and $z_0=0.80$ (d), respectively.

Figure 6

Distribution of both the horizontal $u\left(x=0,z,\tau \right)$ and vertical $w\left(x=0,z,\tau \right)$ components of the velocity vector $\mathbf{\text{v}}$ along the $z$ axis $\left(0.7\le z\le 1.0\right)$, when the laser beam is focused in the center $\left(x=0.0\right)$ of the LC sample, but at different depths: (a) $z_0=0.98$, (b) $z_0=0.94$, (c) $z_0=0.90$, and $z_0=0.80$ (d), respectively.