Stability of interfaces in active fluids

We study the linear stability of an active nematic fluid at rest in its isotropic phase in the following geometries: (1) a membrane immersed in the fluid, (2) a fluid film of finite height, (3) a spherical droplet of fluid, and (4) a cylindrical thread of fluid. In all four cases, we observe two frequency modes due to the coupling between the dynamics of the interface of the fluid and the dynamics of the nematic molecules. Propagating waves are seen above a value of activity which is independent of surface tension and has the same value in all four cases. For the first three cases, the fluid becomes unstable as the activity is further increased. In cases (1) and (2) the critical activity for instability is the same as for an unconfined active fluid and independent of surface tension. For case (3), the critical activity is larger than that for an unconfined fluid, and increases with increasing surface tension. A cylindrical thread of radius R is always unstable against harmonic perturbations of wavenumber k if kR<1, but the growth rate can be controlled by varying the activity. Perturbations with k>1/R become unstable above a critical activity which changes with k and surface tension.