Linear Stability for Models of Active Suspensions

Recent work by Saintillan \& Shelley has modeled the dynamics of active suspensions, such as swirling bacterial baths, through a modification of Doi rod theory. However, the sign of the dipolar extra stress can be of the opposite sign of Doi theory, and this leads to large-scale flow instability. We investigate the structure of this system linearized near a state of isotropy and uniformity. We show that concentration fluctuations generally decay, and that while long-wave instability depends upon the particular swimming mechanism, short-wave stability does not. This suggests that the model is well-posed, even in the absence of translational and rotational di ffusion e ffects.