Negative viscosity induced by electrohydrodynamic turbulence in nematic liquid crystals

Negative viscosity, in which flow is amplified rather than dissipated, represents a striking manifestation of nonequilibrium dynamics. In this review, we summarize recent progress in the study of negative viscosity in electrically driven nematic liquid crystals. Experiments have demonstrated that, under sufficiently strong electric fields, these systems undergo a transition to a turbulent state in which the apparent viscosity becomes negative with a remarkably large magnitude. This regime is characterized by spontaneous shear flow under zero applied stress, nonmonotonic flow curves, and self-oscillation. Systematic studies of different materials reveal that the magnitude of negative viscosity depends sensitively on electrical properties such as dielectric permittivity and conductivity. Numerical simulations based on a \bmQ-tensor framework successfully reproduce spontaneous shear flow and nonlinear flow curves, providing insight into the underlying mechanism. In particular, the coupling among director distortions, space-charge generation, and flow, mediated by disclinations, is identified as the key mechanism. These results establish electrically driven nematic liquid crystals as a platform for exploring nonequilibrium rheology.