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Hele-Shaw flow for parity odd three-dimensional fluids

Dylan Reynolds, Gustavo M. Monteiro, and Sriram Ganeshan

  • Department of Physics, City College, City University of New York, New York, New York 10031, USA and CUNY Graduate Center, New York, New York 10031

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Phys. Rev. Fluids 7, 114201 – Published 16 November, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.114201

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.

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Phys. Rev. Fluids 7, 114201– Published 16 November, 2022
  • Received 20 December 2021
  • Accepted 20 September 2022
Article part of CHORUS
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