  We study the linear stability of an isotropic active fluid in three different
geometries: a film of active fluid on a rigid substrate, a cylindrical thread
of fluid, and a spherical fluid droplet. The active fluid is modeled by the
hydrodynamic theory of an active nematic liquid crystal in the isotropic phase.
In each geometry, we calculate the growth rate of sinusoidal modes of
deformation of the interface. There are two distinct branches of growth rates;
at long wavelength, one corresponds to the deformation of the interface, and
one corresponds to the evolution of the liquid crystalline degrees of freedom.
The passive cases of the film and the spherical droplet are always stable. For
these geometries, a sufficiently large activity leads to instability. Activity
also leads to propagating damped or growing modes. The passive cylindrical
thread is unstable for perturbations with wavelength longer than the
circumference. A sufficiently large activity can make any wavelength unstable,
and again leads to propagating damped or growing modes.
