33 research outputs found
Lorentz Reciprocal Theorem in Fluids with Odd Viscosity
The Lorentz reciprocal theorem -- that is used to study various transport
phenomena in hydrodynamics -- is violated in chiral active fluids that feature
odd viscosity with broken time-reversal and parity symmetries. Here we show
that the theorem can be generalized to fluids with odd viscosity by choosing an
auxiliary problem with the opposite sign of the odd viscosity. We demonstrate
the application of the theorem to two categories of microswimmers. Swimmers
with prescribed surface velocity are not affected by odd viscosity, while those
with prescribed active forces are. In particular, a torque-dipole can lead to
directed motion.Comment: 10 pages, 3 figure
Hydrodynamics of an odd active surfer in a chiral fluid
We theoretically and computationally study the low-Reynolds-number
hydrodynamics of a linear active microswimmer surfing on a compressible thin
fluid layer characterized by an odd viscosity. Since the underlying
three-dimensional fluid is assumed to be very thin compared to any lateral size
of the fluid layer, the model is effectively two-dimensional. In the limit of
small odd viscosity compared to the even viscosities of the fluid layer, we
obtain analytical expressions for the self-induced flow field, which includes
non-reciprocal components due to the odd viscosity. On this basis, we fully
analyze the behavior of a single linear swimmer, finding that it follows a
circular path, the radius of which is, to leading order, inversely proportional
to the magnitude of the odd viscosity. In addition, we show that a pair of
swimmers exhibits a wealth of two-body dynamics that depends on the initial
relative orientation angles as well as on the propulsion mechanism adopted by
each swimmer. In particular, the pusher-pusher and pusher-puller-type swimmer
pairs exhibit a generic spiral motion, while the puller-puller pair is found to
either co-rotate in the steady state along a circular trajectory or exhibit a
more complex chaotic behavior resulting from the interplay between hydrodynamic
and steric interactions. Our theoretical predictions may pave the way toward a
better understanding of active transport in active chiral fluids with odd
viscosity, and may find potential applications in the quantitative
microrheological characterization of odd-viscous fluids.Comment: 21 pages, 8 figure