Helicoidal instability in cholesteric capillary tubes

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Abstract
Cholesteric samples, with cylindrical concentric layers, and with a non-singular core, show a helical instability with the same helicity as that of the cholesteric, when subjected to a radial dilation. It consists in a helical undulation of the core, the core being a perfect double-twisted zone. This instability develops into textures which we describe. We make an elastic analysis of the problem, which involves frustration and dilation. The correct sign of the helicity of the instability is obtained in any approximation. We calculate the instability threshold for the core region within a square-well approximation and discuss the free surface case where K24 plays an important role. Adding the layers contribution, we obtain a good qualitative agreement with the experiments. An instability of the same nature exists unlocalized in S3, where double-twist is unfrustrated : the helical instability studied here, would therefore be a localized version in R3 of a uniform instability of a double-twisted cholesteric in S3