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We theoretically and computationally study the low-Reynolds-numberhydrodynamics of a linear active microswimmer surfing on a compressible thinfluid layer characterized by an odd viscosity. Since the underlyingthree-dimensional fluid is assumed to be very thin compared to any lateral sizeof the fluid layer, the model is effectively two-dimensional. In the limit ofsmall odd viscosity compared to the even viscosities of the fluid layer, weobtain analytical expressions for the self-induced flow field, which includesnon-reciprocal components due to the odd viscosity. On this basis, we fullyanalyze the behavior of a single linear swimmer, finding that it follows acircular path, the radius of which is, to leading order, inversely proportionalto the magnitude of the odd viscosity. In addition, we show that a pair ofswimmers exhibits a wealth of two-body dynamics that depends on the initialrelative orientation angles as well as on the propulsion mechanism adopted byeach swimmer. In particular, the pusher-pusher and pusher-puller-type swimmerpairs exhibit a generic spiral motion, while the puller-puller pair is found toeither co-rotate in the steady state along a circular trajectory or exhibit amore complex chaotic behavior resulting from the interplay between hydrodynamicand steric interactions. Our theoretical predictions may pave the way toward abetter understanding of active transport in active chiral fluids with oddviscosity, and may find potential applications in the quantitativemicrorheological characterization of odd-viscous fluids.

Hydrodynamics of an odd active surfer in a chiral fluid