Hele-Shaw flow for parity odd three-dimensional fluids

A Hele-Shaw cell is a device used to study fluid flow between two parallel plates separated by small gap. The governing equation of within Darcy's law, which also describes through porous medium. In this work, we derive generalization law starting from three-dimensional with parity-broken viscosity tensor no isotropy. We discuss the observable effects parity-odd fluids in various physical setups relevant experiments, such as channel flow, past an obstacle, bubble dynamics, and Saffman-Taylor instability. particular, show that when pushed channel, transverse force exerted on walls, air expands into region fluid, circulation develops far field, both proportional coefficients. stability condition modified, these terms tending stabilize two-fluid interface. Such experiments can principle facilitate measurement coefficients synthetic natural active matter systems.