Advertisement

Experiments with Travelling Waves in Electrohydrodynamic Convection

  • Manuel de la Torre Juarez
  • Ingo Rehberg
Part of the NATO ASI Series book series (NSSB, volume 237)

Abstract

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chiffaudel,A., Fauve,S., 1987, Strong Resonance in Forced Oscillatory Convection, Phys.Rev. A35: 4004.CrossRefGoogle Scholar
  2. Gil,L., Lega,J., & Meunier,J.L., 1988, Statistical Properties of the Topological Turbulence, to be published.Google Scholar
  3. Hirakawa,K., Kai,S., 1977 Analogy Between Hydrodynamic Instabilities in Nematic Liquid Crystal and Classical Fluid Mol.Cryst.Liq.Cryst., 40: 261.CrossRefGoogle Scholar
  4. Joets,A., & Ribotta,R., 1988, Localized, Time-Dependent State in the Convection of a Nematic Liquid Crystal, Phys.Rev.Lett., 60: 2164.CrossRefGoogle Scholar
  5. Rasenat,S., Hartung,G., Winkler,B.L., Rehberg,I., 1989, The Shadowgraph Method in Convection Experiments, Experiments in Fluids, in print.Google Scholar
  6. Rehberg,I., Rasenat,S., Fineberg,J., de la Torre Juarez,M., Steinberg,V., 1988 Temporal Modulation of Travelling Waves, Phys.Rev.Lett., 61: 2449.Google Scholar
  7. Rehberg,I., Rasenat,S., Steinberg,V.,1988 Travelling Waves and Defectinitiated Turbulence in Electroconvecting Nematics, to be published.Google Scholar
  8. Riecke,H., Crawford,J.D., Knobloch,E., 1988 Time-Modulated Oscillatory Convection, Phys.Rev.Lett., 61: 1942.MathSciNetCrossRefGoogle Scholar
  9. Walgraef,D., 1988, External Forcing of Spatio-Temporal Patterns, to be publ.Google Scholar
  10. Zimmermann,W., & Thom,W. 1988 Symmetry Breaking Effects in the Electrohydrodynamic Instability in Nematics, to be published.Google Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Manuel de la Torre Juarez
    • 1
  • Ingo Rehberg
    • 1
  1. 1.Physikalisches InstitutUniversität BayreuthBayreuthGermany

Personalised recommendations