On the simulation of nematic liquid crystalline flows in a 4:1 planar contraction using the Leslie-Ericksen and Beris-Edwards models

Extrusion is an essential element in the production of nematic soft solids, ensuring that the final formulation is sufficiently refined and compacted. The interplay between complex microstructure and processing conditions affects the final product performance and may even lead to material degradation. This paper investigates the flow of nematic liquid crystals in a 4:1 planar contraction as a precursor for material extrusion. We compare two different frameworks for modelling the evolution of the nematic microstructure. The Leslie-Ericksen model represents the liquid crystal microstructure through a lower order (vector) field, where nematic elements are treated as headless rods. We find that the polar nature of the description leads to ambiguity in microstructure orientation on the boundary. As a result, boundary conditions with the same notional interpretation are found to produce significantly varying flow and microstructure distributions. The orientability issue is avoided in the higher-order Beris-Edwards model, where the local orientation and degree of molecular alignment are captured in a single tensor. We find that matching flow and microstructure predictions obtained from both approaches is possible, provided that the boundary orientation is correctly chosen in the Leslie-Ericksen theory. In the lower order framework, a poor choice of boundary condition is found to produce poorer pressure loss predictions in flows through the contraction. The effect is particularly pronounced at low Ericksen numbers, where significant over-prediction of pressure losses can arise.