  Phase separation between two fluids in two-dimensions is investigated by
means of Direct Numerical Simulations of coupled Navier-Stokes and
Cahn-Hilliard equations. We study the phase ordering process in the presence of
an external stirring acting on the velocity field. For both active and passive
mixtures we find that, for a sufficiently strong stirring, coarsening is
arrested in a stationary dynamical state characterized by a continuous rupture
and formation of finite domains. Coarsening arrest is shown to be independent
of the chaotic or regular nature of the flow.
