Flow-driven transition and associated velocity profiles in a nematic liquid-crystal cell

The alignment properties and distribution of flow speed during Poiseuille flow through a microchannel of a nematic liquid crystal in a cell with homeotropic surface alignment has been measured using a combination of conoscopy, fluorescence confocal polarizing microscopy, and time-lapse imaging. Two topologically distinct director profiles, with associated fluid velocity fields, are found to exist with the preferred state dictated by the volumetric flow rate of the liquid crystal. The results show excellent agreement with model data produced using the Ericksen-Leslie nematodynamics theory.

Figure 1

(Color online) $V$ and $H$ states. Modeled director tilt angle versus depth through a channel 3 mm wide and $34\mu \text{m}$ deep for selected volumetric flow rates using viscosity parameters given in Table for (a) $V$-state and (b) $H$-state flows. The schematic diagrams illustrate the director orientation across the liquid crystal cell.

Figure 2

Calculated free energy of 5CB per unit area plotted against mean (in $z$) fluid speed. The $V$ state has the lower free energy at lower speeds (dark dashes), but the $H$ state (dark solid line) has the lower free energy above a critical mean fluid speed ${\mu }_{\text{c}}=55\mu \text{m}{\text{s}}^{-1}$, where the curves cross. Applying an electric field (lighter curves) increases the critical speed.

Figure 3

(Color online) Schematic diagram of the pressure-driven flow cell.

Figure 4

Theoretical and observed steady-state interference figures. Calculated figures are shown on the left and measurements on the right. The polarizer $\left(\mathit{P}\right)$ and analyzer $\left(\mathit{A}\right)$ are crossed and both are inclined at $\pi /4$ with respect to the direction of flow. When there is no flow, the usual Maltese cross figure (a and b) is seen. As the fluid velocity $\mathit{u}$ is increased the cross contracts (c and d) and divides into two dark lobes (e and f). Circular fringes due to thin-film interference are present but dim in these figures. Above a critical flow rate, a different type of figure is seen, in which circular fringes are clearly visible, and a dark horizontal isochrome is present (g and h).

Figure 5

A sequence of interference figures taken in the seconds after a 10 V (peak-to-peak) electric field is applied across the cell. After 5 s, the whole view is still in an $H$ state, then evolves toward a $V$ state nonuniformly. After 12 s, most of the cell is a its homeotropic state.

Figure 6

FCPM data. The low amplitude double peaked curve plots measurements taken below the critical flow rate at $6\mu \text{l}/\text{hr}$ and indicates a $V$ state. Just above the critical flow rate, at $8\mu \text{l}/\text{hr}$, the cell fluoresces strongly near the midplane (dashed curve), implying that the liquid crystal is horizontally aligned there.

Figure 7

(Color online) Measured (symbol) and modeled (solid line) flow velocity profile as a function of depth for a $160\mu \text{m}\times 160\mu \text{m}$ region of a homeotropically aligned liquid crystal cell for selected pressure-driven volumetric flow rates. The legend shows either $V$-state or $H$-state alignment used for the modeling. Each separate data point is for an individual bead.