An active fluid denotes a viscous suspension of particles, cells, or macromolecules able to convert chemical energy into mechanical work by generating stresses on the microscale. By virtue of this internal energy conversion, these systems display unusual macroscopic rheological signatures, including a curious transition to an apparent superfluid-like state where internal activity exactly compensates viscous dissipation. These behaviors are unlike those of classical complex fluids and result from the coupling of particle configurations with both externally applied flows and internally generated fluid disturbances. Focusing on the well-studied example of a suspension of microswimmers, this review summarizes recent experiments, models, and simulations in this area and highlights the critical role played by the rheological response of these active materials in a multitude of phenomena, from the enhanced transport of passive suspended objects to the emergence of spontaneous flows and collective motion.


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