  Emulsions are omnipresent in the food industry, health care, and chemical
synthesis. In this Letter the dynamics of meta-stable oil-water emulsions in
highly turbulent ($10^{11}\leq\text{Ta}\leq 3\times 10^{13}$) Taylor--Couette
flow, far from equilibrium, is investigated. By varying the oil-in-water void
fraction, catastrophic phase inversion between oil-in-water and water-in-oil
emulsions can be triggered, changing the morphology, including droplet sizes,
and rheological properties of the mixture, dramatically. The manifestation of
these different states is exemplified by combining global torque measurements
and local in-situ laser induced fluorescence (LIF) microscopy imaging. Despite
the turbulent state of the flow and the dynamic equilibrium of the oil-water
mixture, the global torque response of the system is found to be as if the
fluid were Newtonian, and the effective viscosity of the mixture was found to
be several times bigger or smaller than either of its constituents.
