Extended weakly nonlinear theory of planar nematic convection

Abstract

We study theoretically convection phenomena in a laterally extended planar nematic layer driven by an ac-electric field (electroconvection in the conduction regime) or by a thermal gradient (thermoconvection). We use an order-parameter approach and demonstrate that the sequence of bifurcations found experimentally or in the numerical computations can be recovered, provided a homogeneous twist mode of the director is considered as a new active mode. Thus we elucidate the bifurcation to the new ``abnormal rolls'' [E. Plaut et al., Phys. Rev. Lett. 79, 2367 (1997)]. The coupling between spatial modulations of the twist mode and the mean flow is shown to give an important mechanism for the long-wavelength zig-zag instability. The twist mode is also responsible for the widely observed bimodal instability of rolls. Finally, a Hopf bifurcation in the resulting bimodal structures is found, which consists of director oscillations coupled with a periodic switching between the two roll amplitudes. A systematic investigation of the microscopic mechanisms controlling all these bifurcations is presented. This establishes a close analogy between electroconvection and thermoconvection. Moreover, a ``director--wave-vector frustration'' is found to explain most of the bifurcations.