Extended Data Fig. 3: Microscopic origin of anti-symmetric stress.
a. Schematic of orbital angular momentum change during collision. When two frictional active spinners collide, the angular momentum of self-spinning can be interchanged with the angular momentum of orbital motion around their center-of-mass, L = mvrelb, where vrel is the relative moving speed of the particles and b is the impact parameter. The resultant change in the orbital angular momentum ΔL = Lout − Lin gives rise to effective anti-symmetric stress exerted onto the chiral active fluid at the macroscopic level. In the Supplementary Sec. III, we provide a simple kinetic theory to derive the linear relation between anti-symmetric stress τ and the average orbital angular momentum change \(\overline{{{\Delta }}L}\) during collision, \(\tau =\sqrt{\pi {k}_{{{{{\mathrm{B}}}}}}{T}_{{{{{\mathrm{eff}}}}}}/m}\cdot d{n}^{2}\cdot \overline{{{\Delta }}L}\). b. Validation of our kinetic theory. We measure the average orbital angular momentum change \(\overline{{{\Delta }}L}\) by performing scattering simulations and then use it to predict the anti-symmetric stress τ based upon the kinetic theory. The prediction on τ from \(\overline{{{\Delta }}L}\) agrees well with the simulation measurement of a many-body system at the steady state.
