Swimming at Low Reynolds Number in Fluids with Odd (Hall) Viscosity

Matthew F. Lapa; Taylor L. Hughes

doi:10.1103/physreve.89.043019

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arXiv · 1310.6270

Swimming at Low Reynolds Number in Fluids with Odd (Hall) Viscosity

Matthew F. Lapa·Taylor L. Hughes

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Abstract

We apply the geometric theory of swimming at low Reynolds number to the study of nearly circular swimmers in two-dimensional fluids with non-vanishing Hall, or "odd", viscosity. The Hall viscosity gives an off-diagonal contribution to the fluid stress-tensor, which results in a number of striking effects. In particular, we find that a swimmer whose area is changing will experience a torque proportional to the rate of change of the area, with the constant of proportionality given by the coefficient $η^o$ of odd viscosity. After working out the general theory of swimming in fluids with Hall viscosity for a class of simple swimmers, we give a number of example swimming strokes which clearly demonstrate the differences between swimming in a fluid with conventional viscosity and a fluid which also has a Hall viscosity. A number of more technical results, including a proof of the torque-area relation for swimmers of more general shape, are explained in a set of appendices.

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Matthew F. Lapa, Taylor L. Hughes. 2013-10-23. Swimming at Low Reynolds Number in Fluids with Odd (Hall) Viscosity. https://doi.org/10.1103/physreve.89.043019

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