Hydrodynamics instabilities of cholesterics under a thermal gradient

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Abstract
We present a theoretical study of convective instabilities of cholesteric liquid crystal under a thermal gradient. We consider the case of distortions smooth in comparison with the pitch P but fast in comparison with the sample thickness d. A macroscopic « in layers » description of cholesterics is used. The behavior of cholesterics under thermal gradient is found similar to the one under a. c. electric field (low frequency) or magnetic field, applied parallel to the helical axis. The spatial periodicity of the distortion at the threshold varies as (Pd)1/2, the threshold gradient as (Pd)-2. Convective instabilities are expected by heating the sample from the top in cholesteric with a negative thermal conductivity anisotropy Ka (K∥ , K⟩ being the conductivity parallel and perpendicular to the molecules). On contrary for K a > 0 one expect convective instabilities by heating the sample from the underside

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