Shear-Induced First-Order Transition in Polar Liquid Crystals

The hydrodynamic theory of polar liquid crystals is widely used to describe biological active fluids as well as passive molecular materials. Depending on the "shear-alignment parameter", in passive or weakly active polar fluids under external shear, the polar order parameter p is either inclined to the flow at a fixed (Leslie) angle, or rotates continuously. Here, we study the role of an additional "shear-elongation parameter" that has been neglected in the recent literature and causes |p| to change under flow. We show that this effect can give rise to a shear-induced first-order phase transition from isotropic to polar, and significantly change the rheological properties of both active and passive polar fluids.