  We explore the rheology and flow-induced morphological changes of cholesteric
liquid crystal patterns subject to Poiseuille flow within a slab geometry, and
under different anchoring conditions at the wall. Our focus is particularly on
the behaviour of Cholesteric Fingers of the first kind and of Blue Phase II.
Depending on the applied pressure gradient, we observe a number of dynamic
regimes with different rheological properties. Our results provide the first
insight into the flow response of cholesteric phases with fully two- or
three-dimensional director field patterns and normal and planar degenerate
anchoring conditions as commonly realised in experiments. They are also of high
relevance for a fundamental understanding of complex liquid crystals in
confinement and an important step towards future microfluidic applications that
are based on cholesteric liquid crystals.
