Rayleigh-Bénard convection in a homeotropically aligned nematic liquid crystal

We report experimental results for convection near onset in a thin layer of a homeotropically aligned nematic liquid crystal heated from below as a function of the temperature difference DT and the applied vertical magnetic field H . When possible, these results are compared with theoretical calculations. The experiments were done with three cylindrical cells of aspect ratios @~radius!/~height!# G510.6, 6.2, and 5.0 over the field range 8&h[H/HF&80 (HF520.9, 12.6, and 9.3 G are the Fréedericksz fields for the three cells!. We used the Nusselt number N ~effective thermal conductivity! to determine the critical Rayleigh number Rc and the nature of the transition. We analyzed digital images of the flow patterns to study the dynamics and to determine the mean wave numbers of the convecting states. For h less than a codimension-two field hct.46 the bifurcation is subcritical and oscillatory, with travelingand standing-wave transients. Beyond hct the bifurcation is stationary and subcritical until a tricritical field ht557.2 is reached, beyond which it is supercritical. We analyzed the patterns to obtain the critical wave number kc and, for h,hct , the Hopf frequency vc . In the subcritical range we used the early transients towards the finite-amplitude state for this purpose. The bifurcation sequence as a function of h found in the experiment confirms the qualitative aspects of the theoretical predictions. Even quantitatively the measurements of Rc , kc , and Vc are reproduced surprisingly well considering the complexity of the system. However, the value of hct is about 10% higher than the predicted value and the results for kc are systematically below the theory by about 2% at small h and by as much as 7% near hct . At hct , kc is continuous within the experimental resolution whereas the theory indicates a 7% discontinuity. The theoretical tricritical field ht 551 is somewhat below the experimental one. The fully developed flow above Rc for h,hct has a very slow chaotic time dependence that is unrelated to the Hopf frequency. For hct,h,ht the subcritical stationary bifurcation also leads to a chaotic state. The chaotic states persist upon reducing the Rayleigh number below Rc , i.e., the bifurcation is hysteretic. Above the tricritical field ht , we find a bifurcation to a time independent pattern which within our resolution is nonhysteretic. However, in this field range, there is a secondary hysteretic bifurcation that again leads to a chaotic state observable even slightly below Rc . We discuss the behavior of the system in the high-field limit, and show that at the largest experimental field values Rc and kc are within 6% and 1%, respectively, of their values for an infinite field. @S1063-651X~98!00511-X#