Instability of certain shear flows in nematic liquids

We have studied the simple shear flow, in the laminar regime, of a nematic (uniaxial) liquid film between two glass plates with carefully imposed boundary conditions. In the case considered here, the optical axis at rest is normal both to the flow velocity and to the velocity gradient. Using various methods of optical observation, we find the following facts: (a) When the shear rate s is below a certain threshold $s_c$, the optical axis is unperturbed everywhere. When $s>\mathrm{}{s}_c$, it becomes distorted. $s_c$ is inversely proportional to the sample thickness. (b) When a stabilizing field $H$ is applied, $s_c$ increases. Furthermore, above a certain limiting field $H_L$, the nature of the instability changes: a pattern of rolls appears, the rolls being parallel to the (average) flow lines. These effects are then explained in terms of the Ericksen-Leslie-Parodi equations describing the couplings between orientation and flow in a nematic fluid. This analysis has led in turn to the prediction and observation of other remarkable effects occurring when the shear rate is modulated (at low frequencies) and when two fields $H$ (magnetic) and $E$ (electric) are applied at right angles.