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