Fig. 5: Vertical director profile variation with flow rate and elastic anisotropy.

Twist angle \(\phi\) and tilt angle \(\theta\), revealed by numerical integration of Eq. (8) (see Methods) for varying elastic anisotropy. \(\kappa\) (left column) and Ericksen number\(\,\text{Er}\,\)(right column). At small elastic anisotropies, director structure is in the achiral \(B\) state, characterised by a sharp transition from \(\phi =9{0}^{\circ }\) to \(\phi =-9{0}^{\circ }\) and large director tilt in the flow direction in the upper and bottom half of the channel. As \(\kappa\) is reduced, \({\theta }_{0}\) in the middle of the channel becomes non-zero and \(\phi\) profile smooths out, indicating a chiral transition from the director tilt in the bottom and in the upper half, characteristic for the \({B}^{* }\) configuration, as already discussed in Fig. 4. Similarly, director is in the \(B\) state for small values of \(\,\text{Er}\,\). The director tilt angle increases with increasing \(\,\text{Er}\,\), until a transition to \({B}^{* }\) state is reached.