A collisional model of odd fluids: from Boltzmann equation to chiral hydrodynamics

Breaking of microscopic time-reversal and parity symmetries can change the transport properties of fluids, resulting in transverse response to perturbations. Examples include the emergence of odd viscosity in plasmas under magnetic field and chiral active matters realized in soft matter platforms. We show that a gas of rough and inelastic hard disks under constant torque behaves as such 'odd fluid'. Using Boltzmann kinetic theory and the method of adiabatic elimination, we obtain the macroscopic hydrodynamic equations of the model and explicitly show that many transverse response coefficients emerge. Surprisingly, our results suggest that certain odd transport coefficients can change sign, even when the applied torque remains fixed. While we focus on a particular collision-model in 2D, our approach is applicable to other collision models and higher dimensions.