Selection of surfactants for natural and essential oil emulsification is a common activity. However some of the natural oils and oil resin mixtures tend to give rise to sedimentation and instability when stationary for a fairly longer duration.
A good rule of thumb is that a zeta potential of > |30| mV will stabilize an emulsion. That said, I will often formulate to a zeta potential of -70 mV for historical reasons, or make a non-ionic stabilized emulsion with ethoxylated surfactants and a zeta potential of -5 mV. A high zeta potential will typically prevent hard-settle (sedimentation) but it may not stop soft-settle (can be re-dispersed).
Unfortunately there is no relationship between emulsion stability and certain value of zeta potential. The origin of the interface charge depends on the composition of oil, pH and electrolytes present in the water phase.
Zeta potential also does not apply for sterically or electrosterically stabilized dispersions.
as said no universal direct relation. There are several destabilization phenomena. Sedimentation/creaming itself exhibits no direct relation to droplet charge, but to density difference, viscosity, dispersed phase content. Charging of the droplets is one way to minimize destabilization by flocculation and coalescence.