Shear-induced transitions in passive and active polar liquid crystals: A novel shear-elongation parameter*

Polar order in molecular liquid crystals is relatively rare, hence, it was not thoroughly investigated as other liquid crystalline phases. Recently, it has been discovered that suspensions of magnetic platelets in nematic liquid crystals show polar order at room temperature. Furthermore, polar order is ubiquitous in biology. It is seen in cell migration, swimming bacteria, the cytoskeletal etc. The growing interest in active matter and these recent experimental advances call for further theoretical investigations of polar liquid crystals. In the presence of external shear, polar particles tend to align with the shear flow at the Leslie angle, much like nematics. However, unlike the nematic director, the polar order parameter is not of fixed size. In this talk I will introduce the shear elongation parameter. This often neglected parameter, give rise to new physics such as shear-induced first order transition and significantly changes the rheological properties of the fluid. Active fluids can further exhibit yield stress and negative apparent viscosity.