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Viscosity measures the resistance a fluid offers to flow and deformation. It results from internal friction between layers of fluid moving relative to one another. Dynamic viscosity, denoted by the Greek letter mu (μ), quantifies the force needed to move one fluid layer over another. For Newtonian fluids like water and air, the relationship between the shearing stress and the rate of shearing strain is linear, meaning their viscosity remains constant regardless of the applied stress.
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Anisotropic odd viscosity via a time-modulated drive.

Anton Souslov1,2, Andrey Gromov3,4, Vincenzo Vitelli2,5

  • 1Department of Physics, University of Bath, Claverton Down, Bath BA2 7AY, United Kingdom.

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Designing anisotropic odd viscosity in driven fluids creates emergent spatial order and vorticity. This dynamic response, unlike equilibrium states, offers new insights into fluid mechanics and emergent phenomena.

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Area of Science:

  • Non-equilibrium statistical mechanics
  • Fluid dynamics
  • Soft matter physics

Background:

  • Symmetry breaking typically dictates equilibrium phase behavior.
  • Out-of-equilibrium systems can exhibit dynamically emergent spatial order.
  • Previous studies on odd viscosity often assumed conserved angular momentum.

Purpose of the Study:

  • To demonstrate the design of anisotropic viscous coefficients and stresses in far-from-equilibrium fluids.
  • To investigate the emergence of anisotropic structures and mechanical responses.
  • To explore the properties of anisotropic odd viscosity in driven fluids.

Main Methods:

  • Applying a time-modulated drive to fluid constituents.
  • Designing drive-induced rotations that slow down at specific orientations.
  • Analyzing the tensorial, dissipationless component of anisotropic odd viscosity.

Main Results:

  • Anisotropic structures and mechanical responses emerge at long timescales.
  • Anisotropic odd viscosity arises in two-dimensional driven fluids.
  • Classical fluids with internal torques exhibit novel odd viscosity components.
  • Anisotropic odd viscosity acts as a vorticity source, altering bulk flow.
  • Odd viscosity coefficients depend on nonlinear, dissipative responses, not just angular momentum.

Conclusions:

  • Spatial order can be dynamically emergent in non-equilibrium systems.
  • Anisotropic odd viscosity offers a new mechanism for controlling fluid behavior.
  • This work extends the understanding of odd viscosity beyond quantum Hall fluids.
  • The findings have implications for designing active matter and engineered materials.