It depends on the way you made you emulsion: temperature, stirring speed, sonication/ultraturrax, etc. All of these experimental factors will affect the droplet size of the dispersed phase.

Since the emulsion is thermodynamically unstable, the droplets will aggregate and the phase separation mechanism also depends on the size of the particles: can be by Ostwald ripening, coalescence or creaming.

To evaluate how long does it take, its possible to pérform a accelerated stability study (centrifugation in different temperatures) and applying the Arrhenius' equation to determine the shelf life. Besides, there are other techniques on literature: freeze-thawing cycles, humidity absorption, condutivity, turbidity, etc.

BR

In addition to the response given above, which he described nicely in short the fundamentals of emulsion stability, please also note, in the absence of any surfactant, the kinetics of coalescence, or so to speak dispersion stability of two immiscible phases depends on the rheology of the dispersed and dispersion phases as well. A viscous dispersed or dispersion phase can make a dispersion kinetically more stable than those made with less viscous phases. In fact a stable emulsion can also be made simply by controlling and adjusting rheology of the two phases.      

Thanks for your responses!

I was curious how viscosity leads to better stability. How does it exactly prevent coalescence? If the bulk phase is more viscous and the dispersed phase has low viscosity, maybe the rate of their collision is low due to which the merging is delayed. However what happens in the reverse scenario? Which one dominates more the interfacial viscosity difference or the surface tension?

Also is it more dependent upon the viscosity ratio between the two phases or is it just the absolute viscosity numbers that drive the system towards being more stable?

interfacial tension determines how easy emulsion is formed. Obviously interfacial viscosity is proportional to coalescence stability. Having continuous phase with high viscosity is more efficient than high disperse phase viscosity due to damping of droplet movement. Larger droplets coalesce easier than smaller ones. Enhanced concentration due to creaming or sedimentation favours coalescence events but may also lead to phase inversion.

The kinetics of droplet coalescence depends on the spontaneous curvature of the surfactant monolayer at a nucleation hole. The theory was described in detail by Kabalnov and Wennerstrom and was later validated experimentally by Kabalnov and Weers

by the way liquid-liquid dispersions and emulsions are the same.