  We use a continuum model to examine the effect of activity on a phase
separating mixture of an extensile active nematic and a passive fluid. We
highlight the distinct role of previously considered interfacial active
stresses and bulk active stresses that couple to liquid crystalline degrees of
freedom. Interfacial active stresses can arrest phase separation, as previously
demonstrated. Bulk extensile active stresses can additionally strongly suppress
phase separation by sustained self-stirring of the fluid, substantially
reducing the size of the coexistence region in the temperature/concentration
plane relative to that of the passive system. The phase separated state is a
dynamical emulsion-like steady state of continuously splitting and merging
droplets, as suggested by recent experiments. Using scaling analysis and
simulations, we identify various regimes for the dependence of droplet size on
activity. These results can provide a criterion for identifying the mechanisms
responsible for arresting phase separation in experiments.
