Pattern Formation in Electrohydrodynamic Convection
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le against périodic convective motion. At higher voltages turbulent motion that strongly scatters light also appears in the cell. Because of the strong scattering of light by the turbulent fluid motion, this régime is called the dynamic scattering mode (DSM). The first proposai for a liquid crystal display by
Heilmeier, Zanoni, and Barton in 1968 was based on this "convection" mechanism. 1 However, for displays this mechanism turned out to be less stable and more energy consuming than the one used today. At that time, the possible applications of DSM stimulated a considérable number of expérimental and theoretical investigations about electrohydrodynamic convection. Work duri n g t h i s p e r i o d a n d u p to 1983 is reviewed in the book by L.M. Blinov.2 Electrohydrodynamic convection appears in a System far from thermal equilibrium (open System), with continuous power demand dissipated by the viscous behavior of fluid motion. This property was the starting point for a renaissance of this field. Why? One has only to think of the formation of life on earth to realize the importance pf the formation of organized structures (patterns) in open Systems. Examples of simple natural patterns are animal coat markings, like the stripes on the coat of a zébra. However, to fundamentally understand some features of the usually complex pattern forming processes in différent fields ( i n c l u d i n g biology, chemistry> physics, and also social Systems), one tries to first understand sim-
électrode director électrode Figure 2. In à liquid crystal display, a nematic liquid crystal is sandwiched bettueen two glass plates separated by a distance typically 3 to 10 fini. The plates are covered by transparent électrodes (e.g., tin oxide or indium oxide). Often, appropriate organic materials are deposited on the électrodes that are then buffed or polished to uniformly orient the director, n, parallel to the buffing direction and in the plane of the électrodes. In this figure, n twists 90° between the top and bottom électrodes. Thus, plane-polarized light entering the sample at the bottom and traveling to the top électrode rotâtes 90° as it follows the rotating optical axis of the nematic, i.e., n. When the display is betzveen crossed polarizers, one below and the other above the nematic (not shown in this figure), an incomirig beam of light polarized by the first polarizer below the sample can successfully pass the second polarizer after the nematic. The display appears bright. If the material lias positive dielectric anisotropy (ea> 0), an electric field, E, exerts a torque on n to align it parallel to E. At large fields, thé director is perpendicular to the glass and the tzvisted configuration of n is destroyed nearly everywhere except in tzvo small régions next to the électrodes. In this case, incoming polarized light is not rotafed by the nematic ànd is extinguished by the second polarizer. The display appears black. When the field is turned off, the elastic energy stored in the two small régions near the électrodes restores n t
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