Emulsion Surface Area
Quick Start
You can control the ultimate drop size of an emulsion via the ratio of surfactant to oil. The more surfactant, the smaller the drops. In the app your radius is an input and you get a calculation (from the surfactant parameters) of whether you have too little or too much surfactant.
As a bonus you get the energy needed to create the drops. It is trivially small, yet you have to put in a lot of energy in the real world. That just shows how inefficient emulsification is; most of the energy just goes in to heating the mix.
Emulsion Surface Area
It is interesting to know just how much surface area is created in an emulsion and how small the amount of energy needed to create it (assuming perfect conversion of energy into surface area). The inputs to the calculation are the volume, V, of oil, the radius, r, of each drop and the interfacial energy γ. The outputs are the surface area in m² (and also in "football fields", using an average of an American and a soccer field), the number of emulsion drops and the energy needed to create that surface area.
In addition, knowing the weight, S, of surfactant used, its area A and its MWt it is possible to work out the % coverage of the emulsion by the surfactant - assuming that all the surfactant is at the interface. If a typical emulsion is 20% oil and 5% surfactant (i.e. 5% of the whole formulation), then the surfactant is 1% of the oil, i.e. 1g for 100g of oil. For small emulsion drops with very high surface areas, coverage is <100%. For larger drops the coverage >100%, i.e. plenty of the surfactant is "wasted" in the bulk phase, presumably as micelles.
The very small amount of energy actually needed to create the surface area is no surprise. An interfacial energy of 1 dyne/cm is the same as 1 mJ/m², so 1000 m² only requires 1 Joule. The fact that in practice we put enormous amounts of energy into creating an emulsion shows how inefficient the process actually is.
