Lift force due to odd Hall viscosity.

Area of Science:

• Fluid dynamics
• Non-equilibrium thermodynamics

Background:

• Fluid behavior is typically described by even viscosity, obeying time-reversal invariance.
• Certain fluids exhibit broken time-reversal invariance, leading to the presence of odd viscosity.
• Understanding the impact of odd viscosity on fluid flow is crucial for non-equilibrium systems.

Purpose of the Study:

• To investigate the fluid flow of a neutral gas past an infinite cylinder at low Reynolds number.
• To analyze the effects of odd viscosity on fluid dynamics.
• To calculate the lift force generated by odd viscosity.

Main Methods:

• Solving the Oseen approximation of the Navier-Stokes equation.
• Analyzing fluid flow dynamics under low Reynolds number conditions.
• Calculating the lift force induced by the fluid's odd viscosity.

Main Results:

• The Oseen approximation was successfully solved for the specified flow conditions.
• A quantifiable lift force was calculated for the flow past the cylinder.
• The presence of odd viscosity was shown to induce a lift force.

Conclusions:

• Odd viscosity in fluids leads to observable lift forces in low Reynolds number flows.
• The Oseen approximation provides a viable method for studying such phenomena.
• This research contributes to the understanding of non-equilibrium fluid dynamics.