Odd Viscosity in Active Matter: Microscopic Origin and 3D Effects

In common fluids, viscosity is associated with dissipation. However, when time-reversal symmetry is broken a new type of nondissipative "viscosity"emerges. Recent theories and experiments on classical 2D systems with active spinning particles have heightened interest in "odd viscosity,"but a microscopic theory for it in active materials is still absent. Here, we present such first-principles microscopic Hamiltonian theory, valid for both 2D and 3D, showing that odd viscosity is present in any system, even at zero temperature, with globally or locally aligned spinning components. Our work substantially extends the applicability of odd viscosity into 3D fluids, and specifically to internally driven active materials, such as living matter (e.g., actomyosin gels). We find intriguing 3D effects of odd viscosity such as propagation of anisotropic bulk shear waves and breakdown of Bernoulli's principle.