Eur. Phys. J. Special Topics 224, 1349-1358 (2015)
https://doi.org/10.1140/epjst/e2015-02463-2

Regular Article

Generalized Navier-Stokes equations for active suspensions

Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue E17, Cambridge, MA 02139-4307, USA

^a e-mail: jslomka@mit.edu
^b e-mail: dunkel@mit.edu

Received: 26 February 2015
Revised: 18 May 2015
Published online: 24 July 2015

Abstract

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.