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We investigate the effects of shear flow on the smectic phase of thermotropic and lyotropic liquid crystals. We show that shear flow transforms a smectic-A thermotropic liquid crystal into an orthorhombic solid by the suppression of undulation fluctuations. In contrast, the lyotropic L_α phase exhibits, in addition, a very striking enhancement of short-wavelength concentration fluctuations---a phenomenon that is analogous to a well-known effect in polymer solutions. We demonstrate this result, using both hydrodynamic theory and a microscopic model based on the Helfrich theory of membranes. The dispersion relation of the concentration fluctuations is in qualitative agreement with recent experiments on the L_α phase in shear flow.
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Bruinsma et al. (1992) studied this question.
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