Generalized Navier-Stokes equations for active suspensions

We discuss a minimal generalization of the incompressible Navier-Stokes equations to describe the complex steady-state dynamics of solvent flow in an active suspension. To account phenomenologically for the presence of an active component driving the ambient fluid flow, we postulate a generic nonlocal extension of the stress-tensor, conceptually similar to those recently introduced in granular flows. Stability and spectral properties of the resulting hydrodynamic model are studied both analytically and numerically for the two-dimensional (2D) case with periodic boundary conditions. Future generalizations of this theory could be useful for quantifying the shear properties of active suspensions.