Abstract
We study the effects of externally applied shear flow on a model of suspensions of motors and filaments, via the equations of active hydrodynamics (Phys. Rev. Lett., 89 (2002) 058101; 92 (2004) 118101). In the absence of shear, the orientationally ordered phase of both polar and apolar active particles is always unstable at zero wavenumber. An imposed steady shear large enough to overcome the active stresses stabilises both apolar and moving polar phases. Our work is relevant to in vitro studies of active filaments, the reorientation of endothelial cells subject to shear flow and shear-induced motility of attached cells.