Fig. 2: Flow-induced double-splay and biaxial-splay configurations.

a The director field neighbouring the stripe pattern appears alternatively blue and yellow when imaged using crossed polarisers and a full-wave-plate optical compensator. The blue colour indicates that the director is almost perpendicular to the slow axis of the optical compensator, \({\vec{\lambda _{{{{{{{{\rm{g}}}}}}}}}}}\), the yellow colour indicates that the director is almost parallel to \({\vec{\lambda_{{{{{{{{\rm{g}}}}}}}}}}}\). b Map of the polar angle θ (colour bar) and the azimuthal angle φ (black rods). The regions adjacent to the stripe pattern are denoted as (i) and (ii); the regions adjacent to the splay wall are denoted as (iii) and (iv). c Probability density function (PDF) of φ (upper panel) and of θ (lower panel) in regions (i)–(iv). Inset: Schematic of the divergent splay deformation in the xz-plane induced by the pressure-driven flow. The black arrows represent the velocity profile, the blue arrows represent the shear rate profile. d Biaxial-splay configuration (upper panel) and double-splay configuration (lower panel). e With increasing rotation angle, β, the director field of the biaxial-splay configuration evolves from a convergent splay deformation in the xy-plane to a divergent splay deformation in the xz-plane (left). For the double-splay configuration, the director field adopts a divergent splay deformation for all β (right). f Evolution of θ at the walls of the microfluidic cell (z = 0 and z = b) for double-splay (blue line) and biaxial-splay (red line) configurations. The arrows indicate the direction in which the director evolves upon a perturbation.