Fig. 7: Effects of finite channel width on the stability of flow-induced patterns.

a–d 2D channel cross sections showing the director field of states \(D\) in a, \(B\) in b, and \({B}^{* }\) in c, d. The side walls force the director to point perpendicularly to the flow, inducing a chiral state near the wall. In \(B\) state, this chirality transitions to the achiral profile away from the walls (b). In the \({B}^{* }\) state, it is continued from the walls across the channel with either a single chirality (c) or with opposite chiralities, meeting at the soliton in the middle (d). e Vertical component \({n}_{z}=\cos \theta\) of the director for different elastic anisotropy values \(\kappa\) sampled along the mid-line (magenta line in d) shows the achiral soliton in the middle of the channel, where left- and right-handed \({B}^{* }\) domains meet. f Critical behaviour of the soliton width \(\xi\) with respect to the elastic anisotropy \(\kappa\). The inset shows the log-log plot of the power-law part of the expression, with the critical exponent \(b\approx 0.42\).