Liquid relaxation: a new Parodi-like relation for nematic liquid crystals

From a novel hydrodynamic theory of nematic liquid crystals we obtain two independent identities between the six Leslie viscosity coefficients, one of which replicates Parodi’s relation, while the other—which involves five Leslie viscosities in a nonlinear way—is new. We discuss its significance and test its validity against evidence from physical experiments and molecular dynamics simulations.We put forward a hydrodynamic theory of nematic liquid crystals that includes both anisotropic elasticity and dynamic relaxation. Liquid remodeling is encompassed through a continuous update of the shear-stress free configuration. The low-frequency limit of the dynamical theory reproduces the classical Ericksen-Leslie theory, but it predicts two independent identities between the six Leslie viscosity coefficients. One replicates Parodi's relation, while the other - which involves five Leslie viscosities in a nonlinear way - is new. We discuss its significance, and we test its validity against evidence from physical experiments, independent theoretical predictions, and molecular-dynamics simulations