Abstract
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 and the applied vertical magnetic field When possible, these results are compared with theoretical calculations. The experiments were done with three cylindrical cells of aspect ratios [(radius)/(height)] 6.2, and 5.0 over the field range 12.6, and 9.3 G are the Fréedericksz fields for the three cells). We used the Nusselt number (effective thermal conductivity) to determine the critical Rayleigh number 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 the bifurcation is subcritical and oscillatory, with traveling- and standing-wave transients. Beyond the bifurcation is stationary and subcritical until a tricritical field is reached, beyond which it is supercritical. We analyzed the patterns to obtain the critical wave number and, for the Hopf frequency 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 and are reproduced surprisingly well considering the complexity of the system. However, the value of is about 10% higher than the predicted value and the results for are systematically below the theory by about 2% at small h and by as much as 7% near At is continuous within the experimental resolution whereas the theory indicates a 7% discontinuity. The theoretical tricritical field is somewhat below the experimental one. The fully developed flow above for has a very slow chaotic time dependence that is unrelated to the Hopf frequency. For the subcritical stationary bifurcation also leads to a chaotic state. The chaotic states persist upon reducing the Rayleigh number below i.e., the bifurcation is hysteretic. Above the tricritical field 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 We discuss the behavior of the system in the high-field limit, and show that at the largest experimental field values and are within 6% and 1%, respectively, of their values for an infinite field.
- Received 22 April 1998
DOI:https://doi.org/10.1103/PhysRevE.58.5885
©1998 American Physical Society