Abstract

We study the dynamics of active polar fluids in a Taylor–Couette geometry where the fluid is confined between two rotating coaxial cylinders. This system can spontaneously generate flow fields and thereby set the two cylinders into relative rotation either by spontaneous symmetry breaking or via asymmetric boundary conditions on the polarization field at the cylinder surfaces. In the presence of an externally applied torque, the system can act as a rotatory motor and perform mechanical work. The relation between the relative angular velocity of the cylinders and the externally applied torque exhibits rich behaviors such as dynamic instabilities and the coexistence of multiple stable steady states for certain ranges of parameter values and boundary conditions.

Highlights

  • With respect to time-reversal [11,12,13]

  • We study the dynamics of active polar fluids in a Taylor–Couette geometry where the fluid is confined between two rotating coaxial cylinders

  • We study the flow of an active polar fluid in the Taylor–Couette geometry to highlight some of the interesting rheological properties of active fluids in a setup that might be experimentally accessible

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Summary

Hydrodynamic equations for an active polar fluid

We discuss the hydrodynamic equations of an isothermal active polar fluid. Following the logic outlined in [11, 12, 24], we express the conservation laws and introduce the relevant hydrodynamic variables. Based on the conjugate pairs of fluxes and forces in the entropy production, we write the dynamic equations of the system. In the Taylor–Couette geometry discussed here, angular momentum fluxes play an important role and are discussed

Conservation laws
Free energy and hydrostatic stress
Entropy production and constitutive equations
The Taylor–Couette motor
Equation of motion and boundary conditions
Equilibrium steady states
Non-equilibrium steady states
The relation between the rotation rate and applied torque
Variation of the boundary conditions of the polarization field
Conclusions and discussion

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