Micelle formation is associated with sudden shift in certain properties at CMC such as conductivity, light scattering, absorbance and surface tension. Measurement will depend on instruments available. You can look for change in light scattering intensity. Also, you can look for absorbance changes with iodine. If you google, there are several methods available. What kind of instruments you have access to?
Most widely used molecule for CMC determination by fluorescent technique is pyrene. Intensity vs concentration of emulsion material can be plotted to get the CMC.
In a other way conductometric method can be used. As a break in conductance will be observed at CMC while you plot conductance vs concentration.
DLVO has little to do with the Colloidal Stabilization Effect due to Adsorbed Surfactants. Non-Ionic surfactants will work as well. See my site on Research Gate,
the full text of the paper "OSMOTIC REPULTION FORCE DUE TO ADSORBED SURFACTANTS" is available. The paper is published in COLLOIDS and SURFACES,
Matthiew, unfortunately, precise eguation of state for surfactant solutions was newer worked out. The best approximatin is Posm = RT ( C + A'' C^2 + A" C^3 + ......) whre virial coefficients are to be determined experimentally.
There is very limited data for A' coefficient and none for A". In the case A' is negative, the curve resembles Van der Waals Equetion, straight line can be superimposed over equal areas below and above. The first intersection of the curve with the straight line DETERMINES CMC.
GIBBS adsorption ISOTERM provides CMC data in the case you measure Surface Tention. On the modeling of micels formations and growth, Matt, I refer you to papers of my friend CLAYTON RADKE, UC BERKELY. You can find proper references in my paper on Research Gate site.
Sure, CMC is the bulk effect. Nevertheless, the GIBBS ADSORPTION ISOTERM, wgich is the SURFACE EFFECT, determines CMC as well. I think about unified Theory for about 40 years, but is still not there. Working with the Equation of State leads to ALGEBRA, which is depressing for a person outside HIGH SCHOOL AGE.
your question implies that you want to know the cmc in presence of oil and in the reversed case in oil but in presence of water.
The cmc as the critical concentration above micelles form should of course be influenced by presence of oil in water and by presence of water in oil. Effects of additional oil or water on measurement have to be considered here. For the o/w emulsions spectral shifts of water soluble dyes maybe applicable which should be not effected by presence of oil.