Direct numerical simulations (DNS) of liquid-liquid dispersions in a three-dimensional periodic domain have been performed by means of the lattice-Boltzmann method. The dispersion was agitated by a random force field such as to produce isotropic turbulence. The turbulence levels and its history were based on a fluid parcel in a turbulently stirred tank traversing the impeller swept region. The DNS provide detailed insight in the coalescence and break-up events brought about by the turbulent flow, the evolution of the drop size distribution in time, and the interaction of the small-scale flow and the droplets as witnessed in terms of the spectral characteristics of the turbulence.