The Coalescence app tells us we need an energy barrier to keep drops separate. DLVO theory is one way to think about such barriers.
You get to play with the charge on the surfactant and its tail length, which give Debye and Steric barrier forces, which fight against the Hamaker (van der Waals) force that attracts drops. The aim is to get as large a barrier (expressed in units of thermal energy, kT) as possible. The Coalescence app shows that it should be more than 20kT to give adequate stability.
DLVO (Derjaguin and Landau, Verwey and Overbeek) theory is one way for thinking about the barrier against the Coalescence of drops. A detailed model exploring DLVO at the nanoparticle level is elsewhere on the Abbott site. This version is simplified somewhat for the generally larger drops that are typical of emulsions.
The basic idea is that drops are attracted to each other via van der Waals forces. This attraction is calculated via the Hamaker constant, A12 which can be assumed to be 10-20J (10 zeptoJoules) in the absence of other information. The attraction increases with radius, so larger drops are more difficult to keep apart. In the early stages of making emulsions, small drops may find themselves close to large ones, so are more easily annihilated than might be expected from their radius. The graph showing the attraction with distance is shown as VH
Keeping the drops apart are two forces.
- The Debye term (shown as VD) which is repulsion by charges at the surface. For pure oils in water there is a surprisingly large charge created, so it is said, by OH- ions that prefer to be at the surface. The charge distribution is hugely complicated and is measured experimentally as a Zeta potential, which is described in detail on the Zeta Potential page. The rule of thumb is that any Zeta potential less than, say, 30mV (absolute value) is unlikely to give sufficient stability. Ionic surfactants obviously provide significant surface charge - once they've had a chance to reach the interface. The effect of the surface charge is diluted if salt is present in the formulation. The Molar Conc is, in this simplified version, for monovalent salts such as NaCl.
- The Steric term, VS is irrelevant to ionics and likely only to be significant for long EO chains in ethoxlyates. Any chains sticking out will tend to repel other chains. In the simplified version here, there is an impenetrable barrier when the distance between the particles reaches 2δ, where δ is the distance the chain sticks out from the surface. Because ethoxylates are notoriously wound round on themselves the length they stick out is probably something like 0.1nm/EO, so it requires 10 EO to give a barrier at 2x1nm=2nm. Whether 2nm is significant is a matter for debate.
The app allows you to play with the key parameters. The individual curves are shown along with their sum which should rise to a high number of kT at some reasonable distance apart to provide sufficient protection against coalescence. What is "reasonable" in the context of a large, not very solid droplet of emulsion? That's for you to judge.