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.

Figure 1

Schematic of our model system. Each molecule with CM at ${\mathbf{r}}^{\alpha }$ (large blue spheres) is composed of many pointlike particles (small black spheres) located at ${\mathbf{r}}^{\alpha \mu }$ with mass $m^{\alpha \mu }$ and momentum ${\mathbf{p}}^{\alpha \mu }$. Each molecule has the same angular momentum ${\mathit{\ell }}^{\alpha }$, which could be a consequence of, e.g., an external field. The angular momentum breaks rotational symmetry.

Figure 2

A polar plot of the two normalized odd excitations as a function of the angle ($\alpha$) between $\mathit{\ell }$ and $\mathbf{k}$. Black lines (reverse triangle for $s_{-}$ and circles for $s_{+}$) are for $k\tilde{\ell }/c=0.7$, blue lines (plus for $s_{-}$ and asterisk for $s_{+}$) are for $k\tilde{\ell }/c=1$, and the red lines (triangles for $s_{-}$ and squares for $s_{+}$) are for $k\tilde{\ell }/c=1.3$. These anisotropic excitations are similar to those found in columnar liquid crystals [52] and nematic elastomers [53].

Figure 3

Illustration of a fluid of torque dipoles that shows inhomogeneous OV. On the right—torque dipole as a model for toque exerted by bacteria (where its head and flagellar are rotating in opposite directions) and for a myosin twisting two actin filaments [19].