Hele-Shaw flow for parity odd three-dimensional fluids

Abstract

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.

11 pages, 4 figures

References in corpus (8)

• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Non-local transport and the Hall viscosity of 2D hydrodynamic electron liquids
• Density-curvature response and gravitational anomaly
• Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
• Hall viscosity, topological states and effective theories
• Stokes flows in three-dimensional fluids with odd and parity-violating viscosities
• Magnetoelasticity theory of incompressible quantum Hall liquids
• Cubic Hall viscosity in three-dimensional topological semimetals

Cited by in corpus (2)

• Observable signatures of Hall viscosity in lowest Landau level superfluids
• Anisotropy of the hydrostatic stress for Hall droplets with in-plane magnetic field