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Odd viscosity in incompressible fluids | | Sriram Ganeshan
; Alexander G. Abanov
; | | Date: |
1 Mar 2017 | | Abstract: | In this letter, we present observable consequences of parity violating odd
viscosity term in incompressible 2+1D hydrodynamics. For boundary conditions
depending on the velocity field (flow) alone we show that: (a) The fluid flow
quantified by the velocity field is independent of odd viscosity, (b) The force
acting on a closed contour is independent of odd viscosity, and (c) The odd
viscosity part of torque on a closed contour is proportional to the rate of
change of area enclosed by the contour with the proportionality constant being
twice the odd viscosity. The last statement allows us to define a measurement
protocol of {it odd viscostance} in analogy to Hall resistance measurements.
We also consider {it no-stress} boundary conditions which explicitly depend on
odd viscosity. A classic hydrodynamics problem with no-stress boundary
conditions is that of a bubble in a planar Stokes flow. We solve this problem
exactly for shear and hyperbolic flows and show that the steady-state shape of
the bubble depends explicitly on the value of odd viscosity. | | Source: | arXiv, 1703.4522 | | Services: | Forum | Review | PDF | Favorites | |
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