Lorentz Reciprocal Theorem in Fluids with Odd Viscosity

Abstract

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.

arXiv comment7 pages, 3 figures

References in corpus (35)

• Designing phoretic micro- and nano-swimmers
• What is Nonreciprocity?
• Viscosity of Quantum Hall Fluids
• Dancing Volvox: Hydrodynamic Bound States of Swimming Algae
• Odd viscosity in chiral active fluids
• Measuring Hall Viscosity of Graphene's Electron Fluid
• Odd dynamics of living chiral crystals
• Odd Viscosity and Odd Elasticity
• Topological Origin of Equatorial Waves
• Topological waves in fluids with odd viscosity
• Self-Diffusiophoretic Colloidal Propulsion Near a Solid Boundary
• Odd viscosity in two-dimensional incompressible fluids
• Statistical mechanics of a chiral active fluid
• Odd viscosity in active matter: microscopic origin and 3D effects
• Swimming at Low Reynolds Number in Fluids with Odd (Hall) Viscosity
• A bulk-interface correspondence for equatorial waves
• Stokes flows in three-dimensional fluids with odd and parity-violating viscosities
• Exact phoretic interaction of two chemically-active particles
• Time reversal symmetry breaking and odd viscosity in active fluids: Green-Kubo and NEMD results
• Non-reciprocal response of a two-dimensional fluid with odd viscosity
• Time reversal symmetry breaking in two-dimensional non-equilibrium viscous fluids
• Minimum Dissipation Theorem for Microswimmers
• A reciprocal theorem for the prediction of the normal force induced on a particle translating parallel to an elastic membrane
• Lift force in odd compressible fluids
• A note on the reciprocal theorem for the swimming of simple bodies
• Hydrodynamic lift of a two-dimensional liquid domain with odd viscosity
• Hydrodynamics of two-dimensional compressible fluid with broken parity: variational principle and free surface dynamics in the absence of dissipation
• Minimum Entropy Production by Microswimmers with Internal Dissipation
• Nonequilibrium Transport Induced by Biological Nanomachines
• Hydrodynamics of an odd active surfer in a chiral fluid
• Motor-free Contractility in Active Gels
• Pair dynamics of active force dipoles in an odd-viscous fluid
• Bypassing slip velocity: rotational and translational velocities of autophoretic colloids in terms of surface flux
• Incompressible active phases at an interface. I. Formulation and axisymmetric odd flows
• Generalized Lorentz reciprocal theorem in complex fluids and in non-isothermal systems

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• Chirotactic response of microswimmers in fluids with odd viscosity
• Analytical solution for the hydrodynamic resistance of a disk in a compressible fluid layer with odd viscosity on a rigid substrate
• Slip-induced odd viscous flow past a cylinder
• Odd viscous flow past a sphere at low but nonzero Reynolds numbers
• Symmetry-driven Phononic Metamaterials
• Hydrodynamic flow field and frictional resistance coefficient of a disk rotating steadily in a compressible fluid layer with odd viscosity on a rigid substrate
• Reversal of tracer advection and Hall drift in an interacting chiral fluid
• Dumbbell dimer dynamics in three-dimensional chiral fluids
• Odd elasticity in disordered chiral active materials
• Reciprocity Theorem and Fundamental Transfer Matrix
• Viscotaxis of chiral microswimmer in viscosity gradients
• Kinetic Theory of Chiral Active Disks: Odd Transport and Torque Density
• Linear odd electrophoresis of a sphere in a charged chiral active fluid
• Stokes flow in an electronic fluid with odd viscosity