Shear-flow enhancement and suppression of fluctuations in smectic liquid crystals

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 ${\mathit{L}}_{\mathrm{\alpha }}$ 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 ${\mathit{L}}_{\mathrm{\alpha }}$ phase in shear flow.