Experiments with Travelling Waves in Electrohydrodynamic Convection
The experimental setup is the following: A nematic liquid crystal (purified MBBA or Merck-PhaseV) is sandwiched between two transparent electrodes rubbed to produce a prefered direction on the orientation of the molecules. The thickness (13–50μm) was adjusted with polymeric mylar sheets, and the whole cell was sealed. The cell is embedded in an isothermal (±0.1K) box. A shadowgraphic image of the pattern (Rasenat et al. 1989) is observed with a CCD-camera mounted on a polarising microscope and digitized (512×512 pixels, 256 grey scales). Applying an ac-voltage to the cell leads to convection setting in at a critical driving voltage Vc, as shown in Fig.l. Here a direct bifurcation to travelling waves (TW) is observed in the whole conductive regime and even in the dielectric regime, unlike measurements shown elsewhere (Hirakawa & Kai 1977, Joets & Ribotta 1988, Rehberg et al. 1988a,b). The solid line is obtained by linear stability analysis of the Leslie-Erickson equation (Zimmermann & Thom 1988), where MBBA parameters (25°C) are used and the electrical conductivity σ has been adjusted to fit the threshold voltage where the dielectric and the conductive instability meet. This theory predicts a steady bifurcation. A hopf bifurcation from the spatially homogenous state, which would explain the TW observed in the experiment, has not been found for a range of material parameters likely to include the realistic values for MBBA. The agreement of our experiments (Rehberg et al. 1988a) with the theoretical predictions for temporal modulation of a direct hopf bifurcation with O(2) — symmetry (Riecke et al. 1988, Walgraef 1988), however, strongly supports the idea that a hopf bifurcation is responsible for the observed TW.
KeywordsHopf Bifurcation Nematic Liquid Crystal Linear Stability Analysis Travel Wave Oscillatory Convection
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