Lift force in chiral, compressible granular matter

Micropolar fluid theory, an extension of classical Newtonian fluid dynamics, incorporates angular velocities and rotational inertias and has long been a foundational framework for describing granular flows. We propose a macroscopic model of granular matter based on micropolar fluid dynamics, which incorporates internal rotations, couple stresses, and broken parity through odd viscosity. Our framework extends traditional micropolar theory to describe chiral granular flows driven far from equilibrium, where energy is continuously injected and dissipated. In particular, we focus on steady states and explicitly neglect energy conservation, reflecting the dissipative nature of granular systems maintained in nonequilibrium by external forcing. Within this setup, we study the lift force experienced by a test bead embedded in a compressible, parity-breaking granular flow. We analyze how odd viscosity and microrotation modify the transverse forces, using both analytical results in the linearized Stokes regime and nonlinear finite-element simulations. Our results demonstrate that micropolar fluids provide a physically consistent and symmetry-informed continuum description of chiral granular matter, capable of capturing lift forces that emerge uniquely from odd transport effects.