Interesting case! I have no experience with this specific system, but I’d like to contribute to your discussion. What you have is a water-in-oil emulsion which is stabilized by deprotonated octanoic acid. So inside the water-droplets there is the COO- group in the interface and the proton solubilized as H3O+. In my opinion the size of the water-droplets depends on how many deprotonated octanoate residues you can fit in the water-oil interface, this will be governed by pH and ‘apparent pKa‘ of the octanoic acid. This apparent pKa differs from the solution pKa as the acid groups are in close proximity and influence each other. Now suppose the remainder of the water-phase is free of ions, in that case there are next to H3O+ no other ions present and the apparent pKa will be substantially higher than the solution value. This means there are relatively few octanoate ions present at the interface to stabilize it and as a consequence the water-droplets are relatively fewer and larger. Now if you add NaNO3 this provides indifferent solution ions that help shield part of the charge of the octanoate ions. The result is that these show less influence on each other and the apparent pKa will go down, allowing more octanoate to be present in the interface and hence more surface can be stabilized leading to smaller water-droplets. If the dosing of ions to the water-phase is continued the size of the water domains may still decrease, until a minimum value is reached. Adding more ions will introduce another effect, I am not sure which but it seems at high ionic strength the water droplets become unstable, possibly because the high ionic strength induces faster coalescence leading to larger droplets. I’ve actually seen a lot of articles describing this droplet growth at high ionic strength but I’ve never seen a convincing explanation for this.