Rayleigh-Benard 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 Delta T and the applied vertical magnetic field H. When possible, these results are compared with theoretical calculations. The experi ments were done with three cylindrical cells of aspect ratios [(radius)/(height)] Gamma = 10.6, 6.2, and 5.0 over the field range 8 less than or similar to h=H/H(F)less than or similar to 80 (H-F = 20.9, 12.6, and 9.3 G are the Freedericksz fields for the three cells). We used the Nusselt number N (effective thermal conductivity) to determine the critical Rayleigh number R-c and the nature of the transition. We analyzed digital images of the how patterns to study the dynamics and to determine the mean wave numbers of the convecting states. For h less than a codimension-two field h(ct)similar or equal to 46 the bifurcation is subcritical and oscillatory, with traveling- and standing-wave transients. Beyond h(ct) the bifurcation is stationary and subcritical until a tricritical field h(t) = 57.2 is reached, beyond which it is supercritical. We analyzed the patterns to obtain the critical wave number k(c) and, for h<h(ct), the Hopf frequency omega(c). 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 R-c, k(c), and Omega(c) are reproduced surprisingly well considering the complexity of the system. However, the value of h(ct) is about 10% higher than the predicted value and the results for k(c) an systematically below the theory by about 2% at small h and by as much as 7% near h(ct). At h(ct), k(c) is continuous within the experimental resolution whereas the theory indicates a 7% discontinuity. The theoretical tricritical field h(t)(th)=51 is somewhat below the experimental one. The fully developed flow above R-c for h<h(ct) has a very slow chaotic time dependence that is unrelated to the Hopf frequency. For h(ct)<h<h(t) the subcritical stationary bifurcation also leads to a chaotic state. The chaotic states persist upon reducing the Rayleigh number below R-c, i.e., the bifurcation is hysteretic. Above the tricritical held h(t), 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 R-c. We discuss the behavior of the system in the high-field limit, and show that at the largest experimental field values R-c and k(c) are within 6% and 1%, respectively, of their values for an infinite field. [S1063-651X(98)00511-X].