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 ${\mathbf{p}}$ 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 $|{\mathbf{p}}|$ to change under flow. We show that this effect can give rise to a shear-induced first order phase transition %(instead of the usual second order transition) from isotropic to polar, and significantly change the rheological properties of both active and passive polar fluids.